As I traveled home from college for Christmas break, I started to ponder fantasy baseball. The baseball season in only a few months away, which means it's almost time to start preparing for fantasy baseball. My fantasy baseball history has been mediocre at best, with a few pleasant successes mixed in with a lot of middling results. But this is the year I am going to change that. This year, I am going to develop a system to exploit any market inefficiencies, to properly value players, and to determine the optimal pitcher-player drafting strategy. If it doesn't end up working, then I will return to fighting for that last playoff spot. If it does, then I will be on top of the (fantasy) world.
So what strategy am I going to use to dominate my fantasy baseball league? I got the idea from the seminal paper by Berri, Schmidt, and Brook in which they run regressions to find the value of each basketball play and determine how much each contributes to a player's team winning from the coefficients. (Berri, David J., Schmidt, Martin B., and Brook, Stacey L. The Wages of Wins: Taking Measure of the Many Myths in Modern Sport. Stanford, CA: Stanford Business, 2007, pp. 107. Print.) While the idea was not new to me, and I had seen the paper before, for some reason I started to wonder if this could work when applied to my fantasy baseball team. If I could find just how much a marginal increase in each statistic will add to my total winning percentage, than I can properly valuate players on draft day.
There are a couple of steps in order to determine each player's value. The first is to properly project what his final statistics are going to be in 2012. This is one of the most important steps, as an estimation far from what the player will actually produce will harm my drafting strategy. To properly predict players' statistics, I am going to combine both his statistics from recent previous seasons as well as projections for the upcoming season. I am going to use weighted averages for the player's last three seasons to determine past production as it relates to future production, where a player's season three years ago is valued less than two years ago, and two years ago less than last year. This will be one part of a player's projected production. The other part will be actual future predictions for next year. Thankfully, I do not have to do this myself as much smarter people than I have already (or will soon) do it. The most useful projections for the upcoming season can be found on Fangraphs Projections page. There are a few options to choose from, and although I am not sure what ones I will use, I will probably use those that are available and average them to try and find some sort of middle ground, eliminating any potential outliers. The options on Fangraphs are Marcel projections (from Tom Tango) that also use the weighted averages of players' past productions to determine future projections, ZiPS projections from Baseball Think Factory, fan projections, and RotoChamp projections. Bill James projections are also available on each player's page, and I may also use ESPN or Yahoo! projections in my calculations.
The next step after being comfortable with a player's projections is to properly evaluate what these statistics will mean to a fantasy team. As there are two main types of leagues (rotisserie and head-to-head), as well as many different categories available to use in a fantasy baseball league, I am going to take the simple approach and evaluate the 5x5 categories in a standard roto league. (A brief overview of Rotisserie baseball is available here and another explanation on scoring can be found here.) The 5x5 categories for hitting are batting average, runs, RBI, home runs, and steals. The categories for pitching are wins, saves, strikeouts, ERA, and WHIP. I will need to go back a few years into a league's history (hopefully at least five) to get enough data points, and I will collected total points for each team (if I were to do this for a H2H league I would collect team records), as well as teams' aggregate totals in each of the ten categories.
The next step would be to run a regression, with the independent variables being each of the 5x5 categories and the dependent y variable being total points. The result would be a regression with coefficients on each category determining how much each contributes to the total team winning percentage (in this case, points). I may also include some dummy variables for each team or each year to try and account for differences that may not be present in the categorical variables.
Once I have run the regression and obtained coefficients, I can apply these coefficients to each player's statistics (obviously, hitting coefficients for hitters and pitching coefficients for pitchers only). Multiplying the estimated coefficient by the player's estimated future projection will give me an estimate of how many wins, or team points, each player will be worth. I can then rank by total value, and the differences between my rankings and the rankings of whatever fantasy baseball site I am on will be the market inefficiency which I can exploit. For example, if I believed that Jose Bautista would be the fourth most valuable player in 2012, but the rankings had him as only the ninth most valuable, I should acquire him as he will be worth more to me than to other players because of asymmetrical information. I can also pass on players that are ranked higher that I believe will not produce as much as believed by other players.
There are a few problems that I have already touched on briefly. The first problem is the player projections, as they are highly volatile and you can never be completely sure about a player's production or health in the upcoming season. The next issue is the league differences between my league and the hypothetical 5x5 rotisserie league. This will obviously have to be accounted for, as player rankings will be largely based on what categories the league is using. A strategy for winning in a 5x5 league may not win in a sixteen category lead. I will have to adjust the model accordingly, but once the basic model has been completed I can simply tweak it by adding or subtracting categories. Finally, there may be collinearity in my regression model, as described on pages 10-11 of this paper.
That being said, if I can address the issues and temper their impact on the regression, this model could be very successful. Finding undervalued players in the fantasy baseball "labor" market is somewhat similar to the strategy the Oakland Athletics employed in the early 2000s as detailed in Moneyball. Although I am not looking for a certain type of player that is undervalued (e.g. a high on-base player), I may find certain players undervalued, such as low-win, low ERA pitchers. I am simply looking for outliers, players who are worth more than what it is currently valued at on fantasy baseball sites. If I can find these outliers and acquire them for less than they are worth, there is a high likelihood that the upcoming fantasy baseball season will be successful. I've had enough of the 8th place finishes. I am ready to try something new, just like the A's, and see if it can vault me to the top.
Saturday, December 17, 2011
Sunday, December 4, 2011
Risk Aversion in MLB and its Impact on Winning Percentage
This is a paper I wrote for my Sports Economics class. I attempted to measure risk aversion of owners and GMs in baseball using starting payroll percentage, and then tested whether risk aversion was correlated with winning percentage.
Risk Aversion in MLB
Risk Aversion in MLB
Saturday, August 6, 2011
Differentiating between Luck and Skill Part III
In my last two posts on luck in pitching, I first defined a regression model and then used individual pitchers to determine if different types of pitchers were lucky or unlucky. In this post, I am going to use all of the pitchers in the data set (those pitchers that had enough innings to qualify for the ERA title from 2002-2010), separate them into different types of pitchers, and determine whether those types were lucky or not.
The first step is to determine what a ground ball, fly ball, and strikeout pitcher looks like. To determine this, I found the 90th percentile in the data set for GB%, FB%, and K/9. I then set this number as the lowest possible value a pitcher could have in a certain year to be qualified as a type of pitcher. For example, the 90th percentile for strikeouts per nine innings was 8.63. Only 10% of the time did a pitcher strike out at least this many hitters. So, any time a pitcher struck out more than that in a season, he was qualified as a "strikeout pitcher". I also did this for ground balls (90th percentile = 52.8%) and fly balls (90th percentile = 43.3%), and found that there were 78 qualifying ground ball pitcher seasons, 75 qualifying fly ball pitcher seasons, and 77 qualifying strikeout pitcher seasons. The graph below summarizes the results.
In any season, there has been between 4 and 15 total pitchers that qualify as one of the types. The rest of the pitchers were set as "No Type", and will be ignored for the study. It is interesting to see how the number of groundball, flyball, and strikeout pitchers fluctuate over the past decade. One would think that they would remain relatively constant, as it is mostly the same pitchers pitching year to year.
One reason I can think for the fluctuation is the offensive environment for each year. If there are more runs scored, than there is better hitting, which means worse pitching, which should lead to less pitchers classified as types (this is because I classified based on the 90th percentile of all years, so if there is better pitching, there should be less pitchers that are better than the 90th percentile in that specific year). This is especially true with strikeout pitchers. When we add runs per game on to the graph, we get the following:
We see the the inclusion of R/G slightly explains the fluctuations, as generally the higher the R/G, the lower the amount of pitchers qualified, especially strikeout pitchers. The other fluctuations I believe are due to luck, and determining the answer to that question is not the purpose of this post.
The first group of pitchers I am going to look at are groundball pitchers. The graph below shows both the predicted and actual ERAs by year for ground ball pitchers. Although the points are not paired, which makes the graph less meaningful, we can still use it to figure out some important things.
We can see the range of ERAs for groundball pitchers, as well as any outliers, which would show luck. Most years, the average ERA tends to be slightly below 4.00, but in some years (2003) it is much lower, and in some (2004) it is much higher. Overall, the actual ERA for groundball pitchers was 3.62 and the predicted ERA was 3.63, showing just the slight bit of luck. The model seems to predict fairly well the ERA of a groundball pitcher, but we cannot yet make any significant conclusions about the luck of a groundball pitcher.
Since the mean ERAs don't tell us much about the luck of a groundball pitcher, another measure might. If we look at each individual season (78 in total), we find that there were 34 cases where the actual ERA < predicted ERA, showing that the pitcher was lucky. The other 44 cases showed the pitcher to be unlucky (actual ERA > predicted ERA), meaning that 43.6% of the time, a groundball pitcher will experience a lower ERA than expected. This agrees with the previous conclusion in my last post, showing that Derek Lowe, representing groundball pitchers, was unlucky.
The next group of pitchers I am going to look at are flyball pitchers. The graph below is the same as the one above for flyball pitchers, and although it does look very similar, there are some slight differences.
The average ERA for a flyball pitcher looks to be slightly higher than a groundball pitcher. Also, there seems to be less outliers for flyball pitchers, showing that the regression is probably slightly more accurate for flyball pitchers (probably because FB% was included in the regression but not GB%). The actual ERA for flyball pitchers was 4.08, and the predicted ERA was 4.10, again showing the slightest bit of luck for flyball pitchers.
Again, since the mean actual and predicted ERAs don't tell us much as they are so similar, we turn to individual cases. For fly ball pitchers, 54.7% of the time (41 out of 75) a pitcher had an actual ERA < predicted ERA, showing that he was lucky. This seems to agree with the statement made above from comparing the mean actual and predicted ERAs, and we can conclude that flyball pitchers are most likely lucky, or at least luckier than groundball pitchers.
The final group of pitchers to look at are strikeout pitchers. The graph below again shows ERAs by year for strikeout pitchers. The most interesting thing to note is how there is often an actual ERA outlier, showing that strikeout pitchers more often have their predicted ERA further from their actual ERA.
The mean actual ERA for strikeout pitchers was 3.32, while the predicted ERA was 3.28, showing that strikeout pitchers were actually slightly unlucky. There is slightly bigger gap in the predicted ERA, showing what I mentioned above about actual ERA outliers. For strikeout pitchers, 42.9% of the time (33 out of 77) the pitcher had an actual ERA < predicted ERA, showing that the pitcher was lucky. So just like groundball pitchers, strikeout pitchers tended to be more unlucky than lucky.
Now that we have looked at all of the different types of pitchers, we can see which pitchers tend to be lucky and which tend to be unlucky. The luckiest pitchers by far seem to be flyball pitchers. More often than not, their actual ERAs were lower than their predicted ERAs. Groundball and strikeout pitchers were more unlucky, as they tended to have higher actual ERAs.
This is by no means significant proof that different types of pitchers tend to have different luck, but it does show that based on the regression I ran, flyball pitchers are slightly luckier than any others. However, they did also have by far the highest ERA, showing that while it may be good to be lucky, it is much better to be skilled.
The first step is to determine what a ground ball, fly ball, and strikeout pitcher looks like. To determine this, I found the 90th percentile in the data set for GB%, FB%, and K/9. I then set this number as the lowest possible value a pitcher could have in a certain year to be qualified as a type of pitcher. For example, the 90th percentile for strikeouts per nine innings was 8.63. Only 10% of the time did a pitcher strike out at least this many hitters. So, any time a pitcher struck out more than that in a season, he was qualified as a "strikeout pitcher". I also did this for ground balls (90th percentile = 52.8%) and fly balls (90th percentile = 43.3%), and found that there were 78 qualifying ground ball pitcher seasons, 75 qualifying fly ball pitcher seasons, and 77 qualifying strikeout pitcher seasons. The graph below summarizes the results.
In any season, there has been between 4 and 15 total pitchers that qualify as one of the types. The rest of the pitchers were set as "No Type", and will be ignored for the study. It is interesting to see how the number of groundball, flyball, and strikeout pitchers fluctuate over the past decade. One would think that they would remain relatively constant, as it is mostly the same pitchers pitching year to year.
One reason I can think for the fluctuation is the offensive environment for each year. If there are more runs scored, than there is better hitting, which means worse pitching, which should lead to less pitchers classified as types (this is because I classified based on the 90th percentile of all years, so if there is better pitching, there should be less pitchers that are better than the 90th percentile in that specific year). This is especially true with strikeout pitchers. When we add runs per game on to the graph, we get the following:
We see the the inclusion of R/G slightly explains the fluctuations, as generally the higher the R/G, the lower the amount of pitchers qualified, especially strikeout pitchers. The other fluctuations I believe are due to luck, and determining the answer to that question is not the purpose of this post.
The first group of pitchers I am going to look at are groundball pitchers. The graph below shows both the predicted and actual ERAs by year for ground ball pitchers. Although the points are not paired, which makes the graph less meaningful, we can still use it to figure out some important things.
We can see the range of ERAs for groundball pitchers, as well as any outliers, which would show luck. Most years, the average ERA tends to be slightly below 4.00, but in some years (2003) it is much lower, and in some (2004) it is much higher. Overall, the actual ERA for groundball pitchers was 3.62 and the predicted ERA was 3.63, showing just the slight bit of luck. The model seems to predict fairly well the ERA of a groundball pitcher, but we cannot yet make any significant conclusions about the luck of a groundball pitcher.
Since the mean ERAs don't tell us much about the luck of a groundball pitcher, another measure might. If we look at each individual season (78 in total), we find that there were 34 cases where the actual ERA < predicted ERA, showing that the pitcher was lucky. The other 44 cases showed the pitcher to be unlucky (actual ERA > predicted ERA), meaning that 43.6% of the time, a groundball pitcher will experience a lower ERA than expected. This agrees with the previous conclusion in my last post, showing that Derek Lowe, representing groundball pitchers, was unlucky.
The next group of pitchers I am going to look at are flyball pitchers. The graph below is the same as the one above for flyball pitchers, and although it does look very similar, there are some slight differences.
The average ERA for a flyball pitcher looks to be slightly higher than a groundball pitcher. Also, there seems to be less outliers for flyball pitchers, showing that the regression is probably slightly more accurate for flyball pitchers (probably because FB% was included in the regression but not GB%). The actual ERA for flyball pitchers was 4.08, and the predicted ERA was 4.10, again showing the slightest bit of luck for flyball pitchers.
Again, since the mean actual and predicted ERAs don't tell us much as they are so similar, we turn to individual cases. For fly ball pitchers, 54.7% of the time (41 out of 75) a pitcher had an actual ERA < predicted ERA, showing that he was lucky. This seems to agree with the statement made above from comparing the mean actual and predicted ERAs, and we can conclude that flyball pitchers are most likely lucky, or at least luckier than groundball pitchers.
The final group of pitchers to look at are strikeout pitchers. The graph below again shows ERAs by year for strikeout pitchers. The most interesting thing to note is how there is often an actual ERA outlier, showing that strikeout pitchers more often have their predicted ERA further from their actual ERA.
The mean actual ERA for strikeout pitchers was 3.32, while the predicted ERA was 3.28, showing that strikeout pitchers were actually slightly unlucky. There is slightly bigger gap in the predicted ERA, showing what I mentioned above about actual ERA outliers. For strikeout pitchers, 42.9% of the time (33 out of 77) the pitcher had an actual ERA < predicted ERA, showing that the pitcher was lucky. So just like groundball pitchers, strikeout pitchers tended to be more unlucky than lucky.
Now that we have looked at all of the different types of pitchers, we can see which pitchers tend to be lucky and which tend to be unlucky. The luckiest pitchers by far seem to be flyball pitchers. More often than not, their actual ERAs were lower than their predicted ERAs. Groundball and strikeout pitchers were more unlucky, as they tended to have higher actual ERAs.
This is by no means significant proof that different types of pitchers tend to have different luck, but it does show that based on the regression I ran, flyball pitchers are slightly luckier than any others. However, they did also have by far the highest ERA, showing that while it may be good to be lucky, it is much better to be skilled.
Saturday, July 23, 2011
Differentiating between Pitching Luck and Skill Part II
In my first post on differentiating luck and skill for pitchers, I defined a regression model for determining a pitcher's skill. In this post, I want to look at different individuals pitchers as examples of certain types of pitchers to see if some are luckier than others, or if some are more skilled than they seem.
To review: a pitcher's career ERA is the defined baseline, or average skill of the pitcher. His predicted ERA is taken from the regression model and used to define his skill for that particular year as the difference from career ERA. His actual ERA is observed yearly, and any difference from predicted ERA is due to luck. One thing that is noticeable is that the predicted values are much closer to the actual values for these graphs as opposed to the hitter's AVGs. This is because the R-squared of the pitching regression is .807, while in the hitting regression it was only .344, so much more of the variability is explained by the independent variables.
The first pitcher I want to look at is Roy Halladay. Halladay has been remarkably consistent over the past few years, so it will be interesting to see if the model follows his ERA or jumps around each year. As we can see in the graph below, there has been an interesting split to Halladay's career. Until 2008, his actual ERA was always higher than his predicted ERA, showing that he was unlucky. However, from 2008 through today, his actual ERA has been lower than his predicted ERA, showing that he has been lucky.
There are a couple of possible reasons behind the change in "luck" for Halladay. Since 2008, he has had a much lower WHIP than before, has induced more fly balls, thrown many more first pitch strikes, and has had a much higher swinging strike percentage. The lower WHIP played a huge role in him decreasing his ERA almost a full run (3.71-2.78) from 2007 to 2008, and also would result in the model predicting a much lower ERA.
The other factors are much more interesting, and can explain the difference in luck much better. A higher FB% should result in more home runs and a higher ERA, but Halladay offset this by having a much lower HR/FB ratio. He was allowing many more fly balls but only slightly more home runs. And since fly balls result in lower AVG and OBP, Halladay was basically mitigating the bad result of more fly balls (home runs), and simply using them to his advantage.
The other two differences, throwing more first pitch strikes and a higher swinging strike percentage, go hand-in-hand in explaining the luck factor. Because he increased both variables, the model predicted that his ERA would increase, at least from these variables. In fact, he had a much lower ERA, and this is probably due in large part to the more strikes he threw and the swings and misses he generated. Getting ahead of more hitters probably led to a lower WHIP, which would decrease his ERA. This really goes back to the previous post and the controversial regression model. I believe that in Halladay's case, more strikes led to a lower ERA and not a higher ERA as the regression model predicted. This would perfectly explain his luck.
Now that I have discussed some factors of luck and skill, I want to look at different types of pitchers, using examples of pitchers to try and acknowledge type. I am going to do this by looking at GB%, FB%, and K%, but I am also going to look at the experience of each pitcher. I want pitchers who have pitched in MLB for a decent amount of time so their regressions are more stable.
The first type of pitcher I want to look at is a ground ball pitcher. I am going to use Derek Lowe as an example, as in 2010 he had the third highest ground ball rate in MLB at 58.8%. He has had a long career, and his reputation as a ground ball pitcher has only grown with time as he has relied more and more on his sinker as his career has progressed.
Lowe's ERA has fluctuated a lot since 2002. In five seasons he has had a predicted ERA below his career ERA of 3.87, and in five seasons he has had a predicted ERA above his career ERA. In nine of ten seasons his actual ERA has been higher than his predicted ERA, showing that he has been unlucky. Only in 2005 has he shown to have any kind of luck, when his predicted ERA was 3.96 and his actual ERA was 3.61. A much lower WHIP (1.61 in 2004, 1.25 in 2005) led to a lower predicted ERA, but he also had career highs in first pitch strike %, HR/9, and HR/FB in 2005. All of these were predicted to increase his ERA, but Lowe actually managed to post an ERA almost two runs lower while allowing more home runs. So these factors led to his predicted ERA only decreasing a small amount compared to his actual ERA decrease.
2005 seems like an outlier, and that's why the model shows that he was much luckier in 2005 than any other year. The important take away is that Lowe seems to be overall an unlucky pitcher, at least by the regression's standpoint. This is an interesting point, because the regression says that the higher the FB%, the higher the ERA, so a pitcher with a low FB% should have a lower ERA. But this is not the case. I am very curious now as to what the result of a fly ball pitcher will be.
I am going to look at Ted Lilly as an example of a fly ball pitcher. He posted by far the highest FB% of any pitcher in 2010 at 52.6%. He has always been a fly ball pitcher, but has become more so as his career has progressed.
Lilly has an interesting chart: he seems to fluctuate between being lucky and unlucky from 2003-2007, and since then he has performed exactly as predicted. Between 2008 and 2010, the model predicted his ERA to be within 3 points of his actual ERA every season (including dead on in 2009), and this year it is only off by about 16 points so far. Lilly may not be the best example of a fly ball pitcher as his FB% has fluctuated over the years. A follow up study on all fly ball pitchers, and not just Lilly, will be required to determine if they are lucky or not, because Lilly seems to have performed just as predicted (although that may be the case for all fly ball pitchers).
The final type of pitcher I want to look at is strikeout pitchers. I am going to use Justin Verlander as an example, even though he only finished 11th in baseball in K/9 in 2010 with 8.79 K/9. All of the pitchers above him were younger and had less experience, which may show how pitchers change over time. Young pitchers may be able to get by with mostly a fastball, but once they age and their fastball loses some speed they have to rely on other pitches and craftiness to get hitters out.
Verlander's actual ERA and predicted ERA seem to mirror each other in the graph, except that his actual ERA is always slightly higher (except for 2006) than his predicted ERA, showing that he is unlucky. The worst year for luck (2008), Verlander had a predicted ERA of 4.15 but an actual ERA of 4.84. Much of the difference in skill for 2008 seems to be due to a career high WHIP, but the difference in luck is less clear. One reason, which I haven't talked about yet, may be Verlander's left on base % (LOB%). This variable measures the number of runners a pitcher leaves stranded out of the total amount of runners on base (so 1 - LOB% would be the percentage of runners who score). In 2008, Verlander had a LOB% of only 65.4%, which is by far the lowest percentage in his career (his next lowest percentage is 72.0%). Although his increase in WHIP showed that he was allowing more runners, thus more runs (which was predicted by the model), he was also allowing more of those baserunners to score, which would not be predicted by the model. Thus the model would show him to be unlucky.
It will be interesting to see if this conclusion holds up for all strikeout pitchers. They have higher swinging strike % and should have higher first pitch strike %, but also probably have lower strike zone swing % and strike zone contact %. These factors oppose one another, and it will be interesting to see whether they cancel out, or if one effect dominates another and the pitchers are shown to be either lucky or unlucky.
In this post, I used individual pitchers to represent different types of pitchers. This was not an especially effective method, but it was good to explain some of the reasons behind the difference in luck and skill for certain pitchers. In my next post, I am going to actually separate pitchers into different types based on GB%, FB%, and K% to see if there is any differences by type. This will allow the differences to be much more clear instead of simply seeing differences due to individual pitcher types. This post concluded that ground ball and strikeout pitchers are shown to be unlucky, while no conclusion can be made for fly ball pitchers. It remains to be seen if those conclusions will hold up in the next post.
To review: a pitcher's career ERA is the defined baseline, or average skill of the pitcher. His predicted ERA is taken from the regression model and used to define his skill for that particular year as the difference from career ERA. His actual ERA is observed yearly, and any difference from predicted ERA is due to luck. One thing that is noticeable is that the predicted values are much closer to the actual values for these graphs as opposed to the hitter's AVGs. This is because the R-squared of the pitching regression is .807, while in the hitting regression it was only .344, so much more of the variability is explained by the independent variables.
The first pitcher I want to look at is Roy Halladay. Halladay has been remarkably consistent over the past few years, so it will be interesting to see if the model follows his ERA or jumps around each year. As we can see in the graph below, there has been an interesting split to Halladay's career. Until 2008, his actual ERA was always higher than his predicted ERA, showing that he was unlucky. However, from 2008 through today, his actual ERA has been lower than his predicted ERA, showing that he has been lucky.
There are a couple of possible reasons behind the change in "luck" for Halladay. Since 2008, he has had a much lower WHIP than before, has induced more fly balls, thrown many more first pitch strikes, and has had a much higher swinging strike percentage. The lower WHIP played a huge role in him decreasing his ERA almost a full run (3.71-2.78) from 2007 to 2008, and also would result in the model predicting a much lower ERA.
The other factors are much more interesting, and can explain the difference in luck much better. A higher FB% should result in more home runs and a higher ERA, but Halladay offset this by having a much lower HR/FB ratio. He was allowing many more fly balls but only slightly more home runs. And since fly balls result in lower AVG and OBP, Halladay was basically mitigating the bad result of more fly balls (home runs), and simply using them to his advantage.
The other two differences, throwing more first pitch strikes and a higher swinging strike percentage, go hand-in-hand in explaining the luck factor. Because he increased both variables, the model predicted that his ERA would increase, at least from these variables. In fact, he had a much lower ERA, and this is probably due in large part to the more strikes he threw and the swings and misses he generated. Getting ahead of more hitters probably led to a lower WHIP, which would decrease his ERA. This really goes back to the previous post and the controversial regression model. I believe that in Halladay's case, more strikes led to a lower ERA and not a higher ERA as the regression model predicted. This would perfectly explain his luck.
Now that I have discussed some factors of luck and skill, I want to look at different types of pitchers, using examples of pitchers to try and acknowledge type. I am going to do this by looking at GB%, FB%, and K%, but I am also going to look at the experience of each pitcher. I want pitchers who have pitched in MLB for a decent amount of time so their regressions are more stable.
The first type of pitcher I want to look at is a ground ball pitcher. I am going to use Derek Lowe as an example, as in 2010 he had the third highest ground ball rate in MLB at 58.8%. He has had a long career, and his reputation as a ground ball pitcher has only grown with time as he has relied more and more on his sinker as his career has progressed.
Lowe's ERA has fluctuated a lot since 2002. In five seasons he has had a predicted ERA below his career ERA of 3.87, and in five seasons he has had a predicted ERA above his career ERA. In nine of ten seasons his actual ERA has been higher than his predicted ERA, showing that he has been unlucky. Only in 2005 has he shown to have any kind of luck, when his predicted ERA was 3.96 and his actual ERA was 3.61. A much lower WHIP (1.61 in 2004, 1.25 in 2005) led to a lower predicted ERA, but he also had career highs in first pitch strike %, HR/9, and HR/FB in 2005. All of these were predicted to increase his ERA, but Lowe actually managed to post an ERA almost two runs lower while allowing more home runs. So these factors led to his predicted ERA only decreasing a small amount compared to his actual ERA decrease.
2005 seems like an outlier, and that's why the model shows that he was much luckier in 2005 than any other year. The important take away is that Lowe seems to be overall an unlucky pitcher, at least by the regression's standpoint. This is an interesting point, because the regression says that the higher the FB%, the higher the ERA, so a pitcher with a low FB% should have a lower ERA. But this is not the case. I am very curious now as to what the result of a fly ball pitcher will be.
I am going to look at Ted Lilly as an example of a fly ball pitcher. He posted by far the highest FB% of any pitcher in 2010 at 52.6%. He has always been a fly ball pitcher, but has become more so as his career has progressed.
Lilly has an interesting chart: he seems to fluctuate between being lucky and unlucky from 2003-2007, and since then he has performed exactly as predicted. Between 2008 and 2010, the model predicted his ERA to be within 3 points of his actual ERA every season (including dead on in 2009), and this year it is only off by about 16 points so far. Lilly may not be the best example of a fly ball pitcher as his FB% has fluctuated over the years. A follow up study on all fly ball pitchers, and not just Lilly, will be required to determine if they are lucky or not, because Lilly seems to have performed just as predicted (although that may be the case for all fly ball pitchers).
The final type of pitcher I want to look at is strikeout pitchers. I am going to use Justin Verlander as an example, even though he only finished 11th in baseball in K/9 in 2010 with 8.79 K/9. All of the pitchers above him were younger and had less experience, which may show how pitchers change over time. Young pitchers may be able to get by with mostly a fastball, but once they age and their fastball loses some speed they have to rely on other pitches and craftiness to get hitters out.
Verlander's actual ERA and predicted ERA seem to mirror each other in the graph, except that his actual ERA is always slightly higher (except for 2006) than his predicted ERA, showing that he is unlucky. The worst year for luck (2008), Verlander had a predicted ERA of 4.15 but an actual ERA of 4.84. Much of the difference in skill for 2008 seems to be due to a career high WHIP, but the difference in luck is less clear. One reason, which I haven't talked about yet, may be Verlander's left on base % (LOB%). This variable measures the number of runners a pitcher leaves stranded out of the total amount of runners on base (so 1 - LOB% would be the percentage of runners who score). In 2008, Verlander had a LOB% of only 65.4%, which is by far the lowest percentage in his career (his next lowest percentage is 72.0%). Although his increase in WHIP showed that he was allowing more runners, thus more runs (which was predicted by the model), he was also allowing more of those baserunners to score, which would not be predicted by the model. Thus the model would show him to be unlucky.
It will be interesting to see if this conclusion holds up for all strikeout pitchers. They have higher swinging strike % and should have higher first pitch strike %, but also probably have lower strike zone swing % and strike zone contact %. These factors oppose one another, and it will be interesting to see whether they cancel out, or if one effect dominates another and the pitchers are shown to be either lucky or unlucky.
In this post, I used individual pitchers to represent different types of pitchers. This was not an especially effective method, but it was good to explain some of the reasons behind the difference in luck and skill for certain pitchers. In my next post, I am going to actually separate pitchers into different types based on GB%, FB%, and K% to see if there is any differences by type. This will allow the differences to be much more clear instead of simply seeing differences due to individual pitcher types. This post concluded that ground ball and strikeout pitchers are shown to be unlucky, while no conclusion can be made for fly ball pitchers. It remains to be seen if those conclusions will hold up in the next post.
Thursday, July 14, 2011
Differentiating between Pitching Luck and Skill Part I
A few weeks ago, I did a couple of posts on differentiating between luck and skill for hitters. I want to now look at it from the other side: how to differentiate between luck and skill for pitchers. This time, instead of using batting average like I did for hitters, I am going to use ERA. Batting averages against pitchers have shown to be wildly inconsistent, and as such, a better dependent variable would be to look at the runs that a pitcher gives up, because it is much more consistent and definitive over time. I don't want to simply look at counting variables such as strikeouts, walks, and home runs, but look at batted ball statistics and detailed pitching statistics.
Just like last time, I want to introduce a bunch of variables and figure out which of them are important using Mallow's Cp and p-values. I tried running a stepwise regression on all of the variables together, but there were too many variables, so I ran two separate regressions and combined the results.
The first stepwise regression I ran is with counting and batted ball stats. The regression predicting ERA includes K/9, BB/9, HR/9, WHIP, GB/FB, LD%, GB%, FB%, and HR/FB. When we run the stepwise regression, we find that the best regression predicting ERA is ERA = K/9 + BB/9 + HR/9 + WHIP + GB/FB + FB%.
The second stepwise regression involves the "plate discipline" variables. These variables deal with things such as how often a batter swings and makes contact or the percentage of pitches in the strike zone. I collected 9 of these variables from Fangraphs, divided into three categories. Swinging includes O-Swing %, the percentage of pitches a batter swings at outside of the strike zone, Z-Swing %, the percentage of pitches a batter swings at inside of the strike zone, and Swing %, which is the total percentage of pitches swung at. Contact includes O-Contact %, the percentage of pitches a batter makes contact with when swinging at pitches outside the strike zone, Z-Contact %, the percentage of pitches a batter makes contact with when swinging at pitches inside the strike zone, and Contact %, which is the total percentage of contact made when swinging at all pitches. Finally, accuracy includes Zone %, the percentage of pitches inside of the strike zone, F-Strike %, which is the first strike percentage, and SwStr %, which is the percentage of strikes that were swung at and missed.
When I ran a stepwise regression with all of these variables, the best regression output is ERA = Z-Swing % + Swing % + Z-Contact % + First Strike % + SwStr %.
Now that I have run two separate stepwise regressions, I can combine the results and run one more stepwise regression to make sure the model is the best it can be. When I do that, I find that Swing % no longer becomes needed. Another change I need to make concerns confounding variables. Since the variable WHIP includes walks in it's calculations, I can't have both WHIP and BB/9 in the regression. Since WHIP includes hits, which could be important in predicting ERA, I must remove BB/9 from the regression.
The regression now looks like this: ERA = K/9 + HR/9 + WHIP + GB/FB + FB% + Z-Swing % + Z-Contact % + First Strike % + SwStr %. When I run a linear regression on this model, I find that the p-value for GB/FB rate is an astronomically high 0.864, so it is clearly not as important as I first thought. K/9 also has a very high p-value of 0.594, so that can also be taken out. We are left with seven variables that should, with relatively high confidence, predict a pitcher's ERA. The final regression model is as follows: ERA = WHIP + HR/9 + FB% + Z-Swing % + Z-Contact % + First Strike % + SwStr %. The output table from R is below.
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -6.89402 0.92749 -7.433 2.83e-13 ***
WHIP 3.82090 0.12118 31.532 < 2e-16 ***
HRper9 0.95049 0.05343 17.791 < 2e-16 ***
Fbperc 0.49971 0.24764 2.018 0.043950 *
Zswingperc 0.95022 0.42860 2.217 0.026914 *
Zcontactperc 3.55909 0.80202 4.438 1.04e-05 ***
Fstrikeperc 1.32946 0.39701 3.349 0.000851 ***
Swstrperc 2.44227 1.26266 1.934 0.053452 .
R-Squared = 0.8071
The R-squared value for the regression is actually quite good, showing that over 80% of the variation in ERA can be explained by the seven independent pitching variables.
An increase of one in WHIP is associated with an increase of 3.821 runs in ERA. Again, this one makes a lot of logical sense. Giving up one more baserunner per earning should really hurt your ERA. Since ERA is based on 9 innings, we can see that the one extra baserunner per inning would increase the runs allowed per inning by 0.425 runs. This number makes a lot of sense both intuitively and through statistics. Looking at the expected runs matrix from The Book, we can see the effect of one extra baserunner per inning. If you subtract the expected runs for a certain base/out situation by the base/out situation with one less runner, and sum all of the possibilities, we can get a good estimate of the effect of extra baserunners. For example, the expected runs for no out and no runners is 0.555, and the expected runs for no outs and a runner on first is 0.953. The difference between those is 0.398. If we calculate all of the differences, we find that the expected increase in runs per inning is 0.4129 with one more baserunner per inning. Now this is not rigorous math, but a simple way of showing that the coefficient for ERA makes a lot of sense.
An increase of one HR/9 is associated with an increase of 0.9505 runs in ERA. Clearly, giving up more home runs is the fastest way to increase your ERA. However, this value does seem somewhat low. In January, I found that the true value of a home run hit in 2010 was worth 1.406 runs. So giving up a home run should right away be worth about 1.41 runs, which means your ERA should increase by about 1.41. Unearned runs are playing a part in decreasing that value, but shouldn't decrease it by close to half a run.
A one-percentage point increase in a pitcher’s fly ball percentage is associated with an increase of 0.5 runs in ERA. As I found in my post on hitting luck vs. skill, a higher fly ball percentage leads to a lower batting average for hitters, which seems to contradict this result. However, fly balls are associated with a much higher slugging percentage than ground balls, and the chance of a fly ball becoming a home run is a great risk to ERA. As an example, Javier Vazquez had a great season in 2009, with a 2.87 ERA and a FB% of only 34.8%. When he moved to the Yankees in 2010, his fly ball rate jumped to 47% and his ERA blew up to 5.32. So far in 2011, he has a 48.1% FB% and an ERA of 5.23, pretty much in line with his 2010 stats. Although FB% is clearly not the only reason why his ERA jumped, it certainly contributed, especially because his HR/FB rate jumped from 10.1% in 2009 to 14.0% last year.
A one-percentage point increase in a pitcher's swing percentage in the strike zone is associated with an increase of 0.95 runs in ERA. If pitchers are inducing more swings and misses, then this should be a good thing, but it is possible that hitters could simply be hacking more often because the pitches look much better to hit. Pitchers that are truly successful will be able to get outs by pitching to corners and making the batter only swing at a good "pitcher's pitch". A pitcher constantly painting corners will make the batter take more pitches as he looks for better pitches to hit, before being forced to swing with two strikes.
A one-percentage point increase in a pitcher's contact percentage in the strike zone is associated with an increase of 3.559 runs in ERA. Obviously, if hitters are hitting a higher percentage of pitches, then they are most likely seeing the ball better and hitting it more squarely. This would definitely lead to a higher ERA. Although the coefficient may seem very high, contact percentages are pretty consistent, so a big jump is rare and would lead to a much higher ERA.
A one-percentage point increase in a pitcher's first strike percentage is associated with an increase of 1.33 runs in ERA. This is really the first debatable result in the regression. One would think that throwing more first pitch strikes would lead to a lower ERA, but that is not the case. One plausible explanation can be found in this table. That shows the hitting splits for all of MLB in 2010 on different counts. The slash stats for hitters on the first pitch of an at-bat is a robust .334/.340/.534. That is well above league average, so if a hitter hits a first pitch they are going to have more success overall. Throwing more first pitch strikes leads to more hittable pitches and thus a higher ERA. However, throwing less first pitch strikes leads to pitchers getting behind in the count, and when that happens hitters hit .302/.473/.498. Although BA and SLG are lower, the OBP is much higher (mostly due to walks), and it is the statistic that is most important in creating runs. This coefficient needs to be looked at more in-depth, but right now the regression believes that more first pitch strikes leads to a higher ERA, so we are going to take that as a given.
A one-percentage point increase in a pitcher's swinging strike percentage is associated with an increase of 2.442 runs in ERA. This is an almost identical explanation to the coefficient for swing percentage in the strike zone. The more strikes a batter swings at means there are less strikes that they are simply taking. Strikes that aren't swung at have no negative consequences (other than maybe stolen bases) because the ball has no chance of being put in play, so pitchers should want the swinging strike percentage to be lower, because it will lead to a lower ERA. However, having a lower swinging strike percentage does not necessary lead to a lower ERA. A pitcher must have great control in order to take advantage of a hitter.
In my next post, I will explore different pitchers' luck and skill, just like I did for hitters. Now that the model has been defined, it will again show a pitcher's predicted ERA, and the fluctuations from career ERA to predicted ERA will show the improvements the pitcher has made that season and will be defined as skill. The difference between predicted ERA and actual ERA will show the pitcher's luck. It will be interesting to look at certain examples of pitchers who are lucky or not, and whether they fit a certain stereotype. Maybe ground ball pitchers have, on the whole, a lower ERA than their counterpart fly ball pitchers. I will show examples of certain pitchers, and we will be able to figure out whether they are truly a good pitcher, or have simply gotten lucky.
Just like last time, I want to introduce a bunch of variables and figure out which of them are important using Mallow's Cp and p-values. I tried running a stepwise regression on all of the variables together, but there were too many variables, so I ran two separate regressions and combined the results.
The first stepwise regression I ran is with counting and batted ball stats. The regression predicting ERA includes K/9, BB/9, HR/9, WHIP, GB/FB, LD%, GB%, FB%, and HR/FB. When we run the stepwise regression, we find that the best regression predicting ERA is ERA = K/9 + BB/9 + HR/9 + WHIP + GB/FB + FB%.
The second stepwise regression involves the "plate discipline" variables. These variables deal with things such as how often a batter swings and makes contact or the percentage of pitches in the strike zone. I collected 9 of these variables from Fangraphs, divided into three categories. Swinging includes O-Swing %, the percentage of pitches a batter swings at outside of the strike zone, Z-Swing %, the percentage of pitches a batter swings at inside of the strike zone, and Swing %, which is the total percentage of pitches swung at. Contact includes O-Contact %, the percentage of pitches a batter makes contact with when swinging at pitches outside the strike zone, Z-Contact %, the percentage of pitches a batter makes contact with when swinging at pitches inside the strike zone, and Contact %, which is the total percentage of contact made when swinging at all pitches. Finally, accuracy includes Zone %, the percentage of pitches inside of the strike zone, F-Strike %, which is the first strike percentage, and SwStr %, which is the percentage of strikes that were swung at and missed.
When I ran a stepwise regression with all of these variables, the best regression output is ERA = Z-Swing % + Swing % + Z-Contact % + First Strike % + SwStr %.
Now that I have run two separate stepwise regressions, I can combine the results and run one more stepwise regression to make sure the model is the best it can be. When I do that, I find that Swing % no longer becomes needed. Another change I need to make concerns confounding variables. Since the variable WHIP includes walks in it's calculations, I can't have both WHIP and BB/9 in the regression. Since WHIP includes hits, which could be important in predicting ERA, I must remove BB/9 from the regression.
The regression now looks like this: ERA = K/9 + HR/9 + WHIP + GB/FB + FB% + Z-Swing % + Z-Contact % + First Strike % + SwStr %. When I run a linear regression on this model, I find that the p-value for GB/FB rate is an astronomically high 0.864, so it is clearly not as important as I first thought. K/9 also has a very high p-value of 0.594, so that can also be taken out. We are left with seven variables that should, with relatively high confidence, predict a pitcher's ERA. The final regression model is as follows: ERA = WHIP + HR/9 + FB% + Z-Swing % + Z-Contact % + First Strike % + SwStr %. The output table from R is below.
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -6.89402 0.92749 -7.433 2.83e-13 ***
WHIP 3.82090 0.12118 31.532 < 2e-16 ***
HRper9 0.95049 0.05343 17.791 < 2e-16 ***
Fbperc 0.49971 0.24764 2.018 0.043950 *
Zswingperc 0.95022 0.42860 2.217 0.026914 *
Zcontactperc 3.55909 0.80202 4.438 1.04e-05 ***
Fstrikeperc 1.32946 0.39701 3.349 0.000851 ***
Swstrperc 2.44227 1.26266 1.934 0.053452 .
R-Squared = 0.8071
The R-squared value for the regression is actually quite good, showing that over 80% of the variation in ERA can be explained by the seven independent pitching variables.
An increase of one in WHIP is associated with an increase of 3.821 runs in ERA. Again, this one makes a lot of logical sense. Giving up one more baserunner per earning should really hurt your ERA. Since ERA is based on 9 innings, we can see that the one extra baserunner per inning would increase the runs allowed per inning by 0.425 runs. This number makes a lot of sense both intuitively and through statistics. Looking at the expected runs matrix from The Book, we can see the effect of one extra baserunner per inning. If you subtract the expected runs for a certain base/out situation by the base/out situation with one less runner, and sum all of the possibilities, we can get a good estimate of the effect of extra baserunners. For example, the expected runs for no out and no runners is 0.555, and the expected runs for no outs and a runner on first is 0.953. The difference between those is 0.398. If we calculate all of the differences, we find that the expected increase in runs per inning is 0.4129 with one more baserunner per inning. Now this is not rigorous math, but a simple way of showing that the coefficient for ERA makes a lot of sense.
An increase of one HR/9 is associated with an increase of 0.9505 runs in ERA. Clearly, giving up more home runs is the fastest way to increase your ERA. However, this value does seem somewhat low. In January, I found that the true value of a home run hit in 2010 was worth 1.406 runs. So giving up a home run should right away be worth about 1.41 runs, which means your ERA should increase by about 1.41. Unearned runs are playing a part in decreasing that value, but shouldn't decrease it by close to half a run.
A one-percentage point increase in a pitcher’s fly ball percentage is associated with an increase of 0.5 runs in ERA. As I found in my post on hitting luck vs. skill, a higher fly ball percentage leads to a lower batting average for hitters, which seems to contradict this result. However, fly balls are associated with a much higher slugging percentage than ground balls, and the chance of a fly ball becoming a home run is a great risk to ERA. As an example, Javier Vazquez had a great season in 2009, with a 2.87 ERA and a FB% of only 34.8%. When he moved to the Yankees in 2010, his fly ball rate jumped to 47% and his ERA blew up to 5.32. So far in 2011, he has a 48.1% FB% and an ERA of 5.23, pretty much in line with his 2010 stats. Although FB% is clearly not the only reason why his ERA jumped, it certainly contributed, especially because his HR/FB rate jumped from 10.1% in 2009 to 14.0% last year.
A one-percentage point increase in a pitcher's swing percentage in the strike zone is associated with an increase of 0.95 runs in ERA. If pitchers are inducing more swings and misses, then this should be a good thing, but it is possible that hitters could simply be hacking more often because the pitches look much better to hit. Pitchers that are truly successful will be able to get outs by pitching to corners and making the batter only swing at a good "pitcher's pitch". A pitcher constantly painting corners will make the batter take more pitches as he looks for better pitches to hit, before being forced to swing with two strikes.
A one-percentage point increase in a pitcher's contact percentage in the strike zone is associated with an increase of 3.559 runs in ERA. Obviously, if hitters are hitting a higher percentage of pitches, then they are most likely seeing the ball better and hitting it more squarely. This would definitely lead to a higher ERA. Although the coefficient may seem very high, contact percentages are pretty consistent, so a big jump is rare and would lead to a much higher ERA.
A one-percentage point increase in a pitcher's first strike percentage is associated with an increase of 1.33 runs in ERA. This is really the first debatable result in the regression. One would think that throwing more first pitch strikes would lead to a lower ERA, but that is not the case. One plausible explanation can be found in this table. That shows the hitting splits for all of MLB in 2010 on different counts. The slash stats for hitters on the first pitch of an at-bat is a robust .334/.340/.534. That is well above league average, so if a hitter hits a first pitch they are going to have more success overall. Throwing more first pitch strikes leads to more hittable pitches and thus a higher ERA. However, throwing less first pitch strikes leads to pitchers getting behind in the count, and when that happens hitters hit .302/.473/.498. Although BA and SLG are lower, the OBP is much higher (mostly due to walks), and it is the statistic that is most important in creating runs. This coefficient needs to be looked at more in-depth, but right now the regression believes that more first pitch strikes leads to a higher ERA, so we are going to take that as a given.
A one-percentage point increase in a pitcher's swinging strike percentage is associated with an increase of 2.442 runs in ERA. This is an almost identical explanation to the coefficient for swing percentage in the strike zone. The more strikes a batter swings at means there are less strikes that they are simply taking. Strikes that aren't swung at have no negative consequences (other than maybe stolen bases) because the ball has no chance of being put in play, so pitchers should want the swinging strike percentage to be lower, because it will lead to a lower ERA. However, having a lower swinging strike percentage does not necessary lead to a lower ERA. A pitcher must have great control in order to take advantage of a hitter.
In my next post, I will explore different pitchers' luck and skill, just like I did for hitters. Now that the model has been defined, it will again show a pitcher's predicted ERA, and the fluctuations from career ERA to predicted ERA will show the improvements the pitcher has made that season and will be defined as skill. The difference between predicted ERA and actual ERA will show the pitcher's luck. It will be interesting to look at certain examples of pitchers who are lucky or not, and whether they fit a certain stereotype. Maybe ground ball pitchers have, on the whole, a lower ERA than their counterpart fly ball pitchers. I will show examples of certain pitchers, and we will be able to figure out whether they are truly a good pitcher, or have simply gotten lucky.
Tuesday, June 14, 2011
Ichiro Without Speed
After finishing my posts on luck vs. skill, I decided to look at a couple more individual players who would have very interesting regression lines. The first one that came to mind was Ichiro. He came to MLB from Japan in 2001, and since then he has had 10 straight 200 hit seasons and never hit lower than .303. However, this year he is hitting .256, and only on pace for about 177 hits. There has been a lot of talk about what is wrong with him, including this article on Fangraphs which shows his BABIP on different types of hits.
Clearly Ichiro is an outlier in the regression model. We know that even before looking at his luck and skill, because his unique hitting approach allows him to get hits on balls that almost every other major leaguer would be out on. Since 2002 (the first year advanced batted ball data was available, unfortunately we cannot capture his rookie season), Ichiro has 407 infield hits, by far the most in MLB, and has the highest infield hit % (IFH/GB) in baseball. As such, although his batted ball data may not look all that impressive, he still manages to get a ton of hits.
However, although we expect him to be an outlier, his batting average graph is still very surprising.
Ichiro's career .328 batting average is much higher than any of his predicted averages, and until this year his actual averages were also always quite higher. The most incredible season, 2004, he had a predicted batting average of .263, which would mean his "skill" cost him 65 points relative to his career average, yet his luck accounted for 109 points, leaving him with an incredible batting average of .372. It's impossible for a hitter to hit .370 over an entire season by just getting lucky, yet that's exactly what this graph is showing. So obviously there is something going on.
The difficulty in predicted Ichiro's average relative to league average is easy to pinpoint. His speed gets him hits, and until this year that speed made up for any sort of batted ball statistics that he had in any year. An interesting way to look at it is that if Ichiro had league-average speed, his batted ball statistics show him to be about a career .260-.270 hitter. In actuality he is a .328 career hitter, so that speed has increased his batting average by about 60 points. So what is happening this year? Has he lost a step, or maybe just gotten slightly unlucky?
There are a couple of ways we can determine if he has lost a step. He has stolen 16 bases so far this year and only been caught 4 times, which are not far off from his 162 game averages of 39 steals and 9 CS. So at first glance, he does not seem to be any slower. But if we look further into the statistics, we can see an interesting trend. His infield hit % is down over 5% this year compared to last year and 2.5% off his career rate. This has already cost him about 17 hits this year, which would bump his average up about 22 points to .278, still not .300 but much closer.
Does this decrease in IFH% due to luck or skill? Unfortunately, we can't exactly quantify the differences, but we do see that over his career, his IFH% has fluctuated between 9.5% in 2005 to 16% in 2009. That is a huge difference, and one major reason why he had his worst batting average of his career (.303) in 2005 and his second best (.352) in 2009. So maybe ground balls are just not quite finding the holes that they normally do. This is plausible, but we are getting into a large enough sample size (300 PAs) that the IFH% should start regressing towards the mean. If it doesn't, then he has definitely lost a step.
One other contributing factor is that Ichiro has yet to hit a home run this year. He has never been a big power guy, but he has hit at least 6 homers in every season, and is currently looking like he might not hit more than 3 or 4. With his FB% at 20.8%, the lowest total since 2004, he looks like he is becoming even more of a pure singles hitter. This could be resulting in outfielders playing even more shallow, taking hits away that used to drop in front of them as they are not afraid of balls going over their heads.
So why is Ichiro having such a poor season? We can see that although he may be getting unlucky, it is also due to age slowly creeping up to him. It is affecting both his power and also probably slightly affecting his speed. Ichiro may bounce back the rest of the season and end up hitting .300, but it is much more likely that he will end the year hitting .280-.290. Unfortunately, the regression model does not help much in predicting his batting averages by season, but it is very interesting to look at what type of player he would be with just league-average speed.
Clearly Ichiro is an outlier in the regression model. We know that even before looking at his luck and skill, because his unique hitting approach allows him to get hits on balls that almost every other major leaguer would be out on. Since 2002 (the first year advanced batted ball data was available, unfortunately we cannot capture his rookie season), Ichiro has 407 infield hits, by far the most in MLB, and has the highest infield hit % (IFH/GB) in baseball. As such, although his batted ball data may not look all that impressive, he still manages to get a ton of hits.
However, although we expect him to be an outlier, his batting average graph is still very surprising.
 |
| Ichiro AVG, 2002-2011 |
The difficulty in predicted Ichiro's average relative to league average is easy to pinpoint. His speed gets him hits, and until this year that speed made up for any sort of batted ball statistics that he had in any year. An interesting way to look at it is that if Ichiro had league-average speed, his batted ball statistics show him to be about a career .260-.270 hitter. In actuality he is a .328 career hitter, so that speed has increased his batting average by about 60 points. So what is happening this year? Has he lost a step, or maybe just gotten slightly unlucky?
There are a couple of ways we can determine if he has lost a step. He has stolen 16 bases so far this year and only been caught 4 times, which are not far off from his 162 game averages of 39 steals and 9 CS. So at first glance, he does not seem to be any slower. But if we look further into the statistics, we can see an interesting trend. His infield hit % is down over 5% this year compared to last year and 2.5% off his career rate. This has already cost him about 17 hits this year, which would bump his average up about 22 points to .278, still not .300 but much closer.
Does this decrease in IFH% due to luck or skill? Unfortunately, we can't exactly quantify the differences, but we do see that over his career, his IFH% has fluctuated between 9.5% in 2005 to 16% in 2009. That is a huge difference, and one major reason why he had his worst batting average of his career (.303) in 2005 and his second best (.352) in 2009. So maybe ground balls are just not quite finding the holes that they normally do. This is plausible, but we are getting into a large enough sample size (300 PAs) that the IFH% should start regressing towards the mean. If it doesn't, then he has definitely lost a step.
One other contributing factor is that Ichiro has yet to hit a home run this year. He has never been a big power guy, but he has hit at least 6 homers in every season, and is currently looking like he might not hit more than 3 or 4. With his FB% at 20.8%, the lowest total since 2004, he looks like he is becoming even more of a pure singles hitter. This could be resulting in outfielders playing even more shallow, taking hits away that used to drop in front of them as they are not afraid of balls going over their heads.
So why is Ichiro having such a poor season? We can see that although he may be getting unlucky, it is also due to age slowly creeping up to him. It is affecting both his power and also probably slightly affecting his speed. Ichiro may bounce back the rest of the season and end up hitting .300, but it is much more likely that he will end the year hitting .280-.290. Unfortunately, the regression model does not help much in predicting his batting averages by season, but it is very interesting to look at what type of player he would be with just league-average speed.
Saturday, June 4, 2011
Differentiating between Luck and Skill Part II
The last post explained how we used batted ball statistics to determine a batter's skill in his batting average. In this post, I want to show how much of a batter's difference from his career mean is due to luck and how much is due to skill.
The first thing to do is to figure out a hitter's career batting average. This is, with a large enough sample size, his "average skill". So a hitter with ten seasons in the majors with a career .300 batting average is a ".300 hitter". If he is batting over .300, then he is having a better season, and there is some amount of skill and luck as to why he is batting better. If he is batting under .300, then maybe he is getting unlucky, or maybe he is losing some skill as he ages.
Once we get a hitter's career average, as well as his actual batting average for every season and his predicted average for every season from the regression equation we have already run, we can graph all three. The career average is the baseline and the difference between the career average and the predicted average is the batter's difference due to skill. The difference between the hitter's predicted average and his actual average is the difference due to luck. Anyone familiar with statistics will realize the procedure: the difference between a variable's mean and it's predicted value is the "Sums of Squares Explained", and the difference between the predicted value and observed value is the "Sums of Squares Residuals". The batter's skill is explained, and his luck is a residual, or error, which is unexplained.
The first example I want to use is a player very familiar to the Blue Jays: Vernon Wells. He spent his entire career in Toronto until being traded to the Angels this past offseason. He had a couple of good seasons, as well as some bad seasons, so he should be a good example, showing variance in both actual and predicted AVGs. He is a career .277 hitter, so the blue line in the graph below is his "average skill" as a hitter. The red line shows his observed averages over each season from 2002-2011 (excluding 2008 when he missed a lot of time due to injuries), and the green line is the regression's predicted values for his average.
There are a lot of interesting things to see on the graph. Although Wells is a career .277 hitter, he has had only two full seasons hitting above that (as well as hitting .300 in 2008 in limited action). In 2003, his second full season, he hit .317 even though his predicted average was only .282. This means that of the extra 40 points of batting average above his career mean (.317-.277), 5 of those were due to skill, and 35 due to luck, or randomness. The regression saw him not as a .317 hitter, but more of a .282 hitter, and was correct as the next season he batted only .272. It is interesting to note that in both of his first full season, his batted ball statistics suggested that he was a .282 hitter, but he hit 42 points higher in his second season. That seems to show the luck he had in his second year. This also happened in 2005-06, when the regression predicted he was a .271 hitter, but he hit .269 in 2005 and then .303 in 2006. Unfortunately Wells was seen as a much better hitter than he actually was, and was rewarded with a huge contract that the Jays had to unload for players with lesser than Wells' ability.
Another thing to notice on the graph is how far Vernon has fallen off this year. He is currently hitting only .183 (through Thursday's games), but the regression is expecting him to be hitting .247. This means that although he has lost about 30 points of skill, from .277 to .247, he has also been very unlucky, hitting 64 points lower than expected. This is still a small sample size, so we will need to see how he performs the rest of the season to truly judge whether or not he has simply lost it or if he was unlucky.
Now that we have seen a good example, we can move on to what this entire exercise was all about: figuring out how much of Jose Bautista's increase in average so far this year is due to luck and how much is due to skill. Bautista is a career .252 hitter, so any average above that means that he has either been getting lucky or has become more skilled. Last year, the regression predicted that he would hit .261, and he actually hit .260, showing that all of his increase in batting AVG was skill, and he was actually slightly unlucky (by 1 point, more due to randomness than anything else).
And that leads us to this year. Bautista is currently hitting .363 (through Thursday's games), an amazing 111 points above his career average. The regression predicted that he would be hitting .326 at this point, so 74 points are due to skill and only 37 are due to luck. This means that 2/3 of his increase in batting average is entirely due to skill. Obviously it is still a somewhat small sample size, and we need to see how he finishes the year, but we can say with certainty that this increase in batting average is not due to some fluke. All of the keys to increasing batting average that I mentioned in the last post are evident in Bautista this year. He has increased his GB/FB rate, increased his line drive % by 5%, decreased his FB% by 8%, increased his HR/FB rate by 8%, and decreased his strikeout percentage by 3%. These have all lead to a predicted increase in average, and thus we can see that the increase is mostly due to skill.
This post was a mission to answer the question "can we differentiate between luck and skill in a batter's AVG?", and ended up answering an emphatic yes. We showed that much of a hitter's variation in batting average can be attributed to skill, especially in the case of Jose Bautista. As I said in this post on Bautista, "Bautista probably won't end the year hitting .350, but we can reasonably expect him to finish the year hitting .320 or so." That was my gut feeling, and it is nice to know that the numbers back up that statement. He may well end up hitting over .350 this year, but it is more reasonable to expect him to hit somewhere around .330. He has fundamentally changed his approach in the last two years, and last year reaped the benefits by hitting 54 home runs. This year, he is still hitting home runs, but has now also become a high average hitter, due almost all to skill.
The first thing to do is to figure out a hitter's career batting average. This is, with a large enough sample size, his "average skill". So a hitter with ten seasons in the majors with a career .300 batting average is a ".300 hitter". If he is batting over .300, then he is having a better season, and there is some amount of skill and luck as to why he is batting better. If he is batting under .300, then maybe he is getting unlucky, or maybe he is losing some skill as he ages.
Once we get a hitter's career average, as well as his actual batting average for every season and his predicted average for every season from the regression equation we have already run, we can graph all three. The career average is the baseline and the difference between the career average and the predicted average is the batter's difference due to skill. The difference between the hitter's predicted average and his actual average is the difference due to luck. Anyone familiar with statistics will realize the procedure: the difference between a variable's mean and it's predicted value is the "Sums of Squares Explained", and the difference between the predicted value and observed value is the "Sums of Squares Residuals". The batter's skill is explained, and his luck is a residual, or error, which is unexplained.
The first example I want to use is a player very familiar to the Blue Jays: Vernon Wells. He spent his entire career in Toronto until being traded to the Angels this past offseason. He had a couple of good seasons, as well as some bad seasons, so he should be a good example, showing variance in both actual and predicted AVGs. He is a career .277 hitter, so the blue line in the graph below is his "average skill" as a hitter. The red line shows his observed averages over each season from 2002-2011 (excluding 2008 when he missed a lot of time due to injuries), and the green line is the regression's predicted values for his average.
 |
| Vernon Wells AVG from 2002-2011 |
Another thing to notice on the graph is how far Vernon has fallen off this year. He is currently hitting only .183 (through Thursday's games), but the regression is expecting him to be hitting .247. This means that although he has lost about 30 points of skill, from .277 to .247, he has also been very unlucky, hitting 64 points lower than expected. This is still a small sample size, so we will need to see how he performs the rest of the season to truly judge whether or not he has simply lost it or if he was unlucky.
Now that we have seen a good example, we can move on to what this entire exercise was all about: figuring out how much of Jose Bautista's increase in average so far this year is due to luck and how much is due to skill. Bautista is a career .252 hitter, so any average above that means that he has either been getting lucky or has become more skilled. Last year, the regression predicted that he would hit .261, and he actually hit .260, showing that all of his increase in batting AVG was skill, and he was actually slightly unlucky (by 1 point, more due to randomness than anything else).
 |
| Jose Bautista AVG from 2010-2011 |
And that leads us to this year. Bautista is currently hitting .363 (through Thursday's games), an amazing 111 points above his career average. The regression predicted that he would be hitting .326 at this point, so 74 points are due to skill and only 37 are due to luck. This means that 2/3 of his increase in batting average is entirely due to skill. Obviously it is still a somewhat small sample size, and we need to see how he finishes the year, but we can say with certainty that this increase in batting average is not due to some fluke. All of the keys to increasing batting average that I mentioned in the last post are evident in Bautista this year. He has increased his GB/FB rate, increased his line drive % by 5%, decreased his FB% by 8%, increased his HR/FB rate by 8%, and decreased his strikeout percentage by 3%. These have all lead to a predicted increase in average, and thus we can see that the increase is mostly due to skill.
This post was a mission to answer the question "can we differentiate between luck and skill in a batter's AVG?", and ended up answering an emphatic yes. We showed that much of a hitter's variation in batting average can be attributed to skill, especially in the case of Jose Bautista. As I said in this post on Bautista, "Bautista probably won't end the year hitting .350, but we can reasonably expect him to finish the year hitting .320 or so." That was my gut feeling, and it is nice to know that the numbers back up that statement. He may well end up hitting over .350 this year, but it is more reasonable to expect him to hit somewhere around .330. He has fundamentally changed his approach in the last two years, and last year reaped the benefits by hitting 54 home runs. This year, he is still hitting home runs, but has now also become a high average hitter, due almost all to skill.
Friday, June 3, 2011
Differentiating between Luck and Skill Part I
In my last post on Jose Bautista, I noted that "the difference in batting average from his career to this season is due to both luck and skill, and unfortunately we can't exactly differentiate the two." After finishing the post, I realized that there was a way to differentiate between luck and skill, although it would take some time to figure out.
To accomplish this task, I decided to get hitting statistics and run regressions showing what statistics will predict AVG and BABIP. These stats aren't hits, home runs, or RBIs, rather I looked at stats such as line drive, ground ball, and fly ball percentages, and home run per fly ball ratios. These stats should more accurately show whether a player is getting lucky, or has made an adjustment and is now reaping the benefits.
The batted ball statistics that I am using are only available back until 2002, so my data set is all hitters that qualified for the batting title from 2002 through 2010. I decided not to include 2011, as most hitters have only played around 50 games, and the smaller sample size may skew results, albeit slightly. There are a total of 1397 players in the data set, each with at least 500 plate appearances per season.
The first thing to do is get the best regression model. Batting average could be modeled very well through statistics such as BABIP, sac flies, and home runs, but the goal of this analysis is to model average using batted ball statistics. As such, the regression equation will not explain as much of the data (lower R2 value), but should better explain how much of the batting average is due to luck and how much due to skill. To figure out the best regression model, I included all of the variables I thought would be useful (GB/FB ratio, LD%, GB%, FB%, HR/FB ratio, and SO), and ran a best subsets analysis. I did not include home runs, because HR/FB ratio represents how often a player will hit a home run, and including home runs would just be introducing a confounding variable. The model also recognized this by recommending the regression model AVG = GB/FB + LD% + FB% + HR/FB + SO, omitting GB%. This was measured using Mallow's Cp, and also makes sense intuitively, as if we have all GB/FB, GB%, and FB%, we have three variables, where one can be solved for without taking up a degree of freedom.
Now that I had the proper regression equation, I could run a simple linear regression to determine the coefficients for each of the independent variables.
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
Intercept 0.2579 1.899e-02 13.581 <2e-16 ***
GB/FB 5.233e-03 4.113e-03 1.272 0.2036
LD% 0.2365 2.492e-02 9.491 <2e-16 ***
FB% -0.05494 2.899e-02 -1.895 0.0583 .
HR/FB 0.2129 1.151e-02 18.492 <2e-16 ***
SO -3.791e-04 2.166e-05 -17.503 <2e-16 ***
In my next post, I am going to show how we can use this model to determine whether batters get lucky or whether their increases in batting average are due to skill. We can graphically show how a batter's increase (or decrease) from his career average can be broken down into both luck and skill partitions. We will be able to see whether Jose Bautista's average this year is due to luck or skill, which will help us determine whether his average is sustainable or not.
To accomplish this task, I decided to get hitting statistics and run regressions showing what statistics will predict AVG and BABIP. These stats aren't hits, home runs, or RBIs, rather I looked at stats such as line drive, ground ball, and fly ball percentages, and home run per fly ball ratios. These stats should more accurately show whether a player is getting lucky, or has made an adjustment and is now reaping the benefits.
The batted ball statistics that I am using are only available back until 2002, so my data set is all hitters that qualified for the batting title from 2002 through 2010. I decided not to include 2011, as most hitters have only played around 50 games, and the smaller sample size may skew results, albeit slightly. There are a total of 1397 players in the data set, each with at least 500 plate appearances per season.
The first thing to do is get the best regression model. Batting average could be modeled very well through statistics such as BABIP, sac flies, and home runs, but the goal of this analysis is to model average using batted ball statistics. As such, the regression equation will not explain as much of the data (lower R2 value), but should better explain how much of the batting average is due to luck and how much due to skill. To figure out the best regression model, I included all of the variables I thought would be useful (GB/FB ratio, LD%, GB%, FB%, HR/FB ratio, and SO), and ran a best subsets analysis. I did not include home runs, because HR/FB ratio represents how often a player will hit a home run, and including home runs would just be introducing a confounding variable. The model also recognized this by recommending the regression model AVG = GB/FB + LD% + FB% + HR/FB + SO, omitting GB%. This was measured using Mallow's Cp, and also makes sense intuitively, as if we have all GB/FB, GB%, and FB%, we have three variables, where one can be solved for without taking up a degree of freedom.
Now that I had the proper regression equation, I could run a simple linear regression to determine the coefficients for each of the independent variables.
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
Intercept 0.2579 1.899e-02 13.581 <2e-16 ***
GB/FB 5.233e-03 4.113e-03 1.272 0.2036
LD% 0.2365 2.492e-02 9.491 <2e-16 ***
FB% -0.05494 2.899e-02 -1.895 0.0583 .
HR/FB 0.2129 1.151e-02 18.492 <2e-16 ***
SO -3.791e-04 2.166e-05 -17.503 <2e-16 ***
Although the R2 value of the regression is only 0.3437, the goal of the regression is not to explain most of the variance in batting averages, it is to use advanced batted ball statistics to try and best model batting averages. The main statistics that we are interested in are the coefficients on each of the independent variables. I want to quickly interpret these coefficients, as well as provide some reasoning as to why these values make intuitive sense.
An increase of 1 in the ratio of ground balls to fly balls is associated with an increase of 5.23 points in a player’s batting average (e.g. from .250 to .25523). Ground balls have a higher probability of becoming hits than fly balls, so hitting more ground balls should lead to more hits. However, this will not affect batting average all that much, as 90% of the GB/FB rates are between 0.75 and 1.75. A player that tried to increase this ratio without fundamentally changing his swing would only see a small increase, and thus only a small increase in batting average.
An increase of 1 in the ratio of ground balls to fly balls is associated with an increase of 5.23 points in a player’s batting average (e.g. from .250 to .25523). Ground balls have a higher probability of becoming hits than fly balls, so hitting more ground balls should lead to more hits. However, this will not affect batting average all that much, as 90% of the GB/FB rates are between 0.75 and 1.75. A player that tried to increase this ratio without fundamentally changing his swing would only see a small increase, and thus only a small increase in batting average.
A one-percentage point increase in a player’s line drive percentage is associated with an increase of 2.36 points in a player’s batting average. Line drives are the batted balls that most often fall for hits, so hitting more line drives will result in a higher batting average. An increase in LD% is due to almost all skill, as it means that a player is squaring the ball up better. It's not possible to simply be lucky and have a significantly higher line drive percentage for an extended period of time.
A one-percentage point increase in a player’s fly ball percentage is associated with a decrease of 0.55 points in a player’s batting average. Fly balls fall for hits the least, so hitting more fly balls will have a negative impact on batting average. The magnitude of this coefficient is about four times less than line drive %, which can be explained by two things: fly balls happen about twice as much as line drives, so the change in hitting one more line drive is worth more than one fly ball. This means that line drives have about twice the effect on batting average that fly balls do.
An increase of 1 in the ratio of home runs to fly balls is associated with an increase of 2.13 points in a player’s batting average. The more fly balls that leave the yard, the less that get caught, so the higher the batting average.
Finally, an increase of 10 strikeouts is associated with a decrease of 3.79 points in a player’s batting average. Obviously, if the batter does not put the ball in play, he cannot get a hit, so the more often a player strikes out, the lower his average will be. The following table summarizes the interpretation of the coefficients.
Finally, an increase of 10 strikeouts is associated with a decrease of 3.79 points in a player’s batting average. Obviously, if the batter does not put the ball in play, he cannot get a hit, so the more often a player strikes out, the lower his average will be. The following table summarizes the interpretation of the coefficients.
An increase of 1 in the following: | Leads to a change in AVG of the following: |
GB/FB rate | + 5.23 points |
LD% | + 2.37 points |
FB% | - 0.55 points |
HR/FB rate | + 2.13 points |
Strikeouts | - 0.38 points |
Overall, the key to being a good hitter is to hit lots of line drives, hit more ground balls than fly balls, but those fly balls that you hit should have a higher than league average chance of becoming home runs, and avoiding striking out. All of these traits are due mostly to skill, as batters must make conscious adjustments to make more contact as well as better contact.
In my next post, I am going to show how we can use this model to determine whether batters get lucky or whether their increases in batting average are due to skill. We can graphically show how a batter's increase (or decrease) from his career average can be broken down into both luck and skill partitions. We will be able to see whether Jose Bautista's average this year is due to luck or skill, which will help us determine whether his average is sustainable or not.
Sunday, May 29, 2011
Jose Bautista's Hot Start
I haven't written a post in awhile, but I am now home for the summer and will hopefully be writing a few posts a week. I wanted to write one today on Jose Bautista. I wrote about him at the end of last season here, and I wanted to do a study on why he is even better than last year.
The major difference between this year's version of Bautista and last year's is his much better batting average. He is still managing to hit a ton of home runs, but after hitting only .260 last season, he is now hitting .353 (all statistics through Saturday's games), good enough for second in the AL. One of the biggest reasons behind this increase in batting average is that his BABIP (batting average on balls in play) has increased from .233 to .321 this year. His career rate of .273 suggests that he was somewhat unlucky last year, and has gotten lucky this year. This may be misleading, as his changed swing naturally leads to more fly balls, usually meaning a lower BABIP. It seems as though last year he was simply trying to hit the ball out of the park, while this year he has become more of a line drive hitter while still hitting home runs. This can be seen in his line drive %, which was only 14.4% last year and is up to 17.1% this year. Line drive % shows how "lucky" a hitter is getting, as line drives are usually end up falling for hits, while ground balls and fly balls are more frequently outs. The increase in LD% shows that Bautista hasn't actually been any luckier this season, he is simply hitting the ball much harder in a higher percentage of at-bats and is being rewarded with a higher BABIP and subsequently batting average.
We can demonstrate what could have happened in previous seasons had Bautista hit as many line drives, leading to a higher BABIP. BABIP is calculated as: (hits - home runs) divided by (at-bats minus strikeouts and home runs plus sac flies). Last year, Bautista had 569 at-bats, 148 hits of which 54 were home runs, 116 strikeouts, and 4 sac flies. If we set his hits total as unknown, we can solve for the amount of hits he would have had with different BABIP. He had a total of 94 non-HR hits last year, and if he had even had his career BABIP of .273, he would have produced 110 non-HR hits. This would have left him with a batting average of (164/569) = .288. If he had this year's .321 BABIP, he would have had an batting average of .322, much closer to this year's .353. The difference in batting average from his career to this season is due to both luck and skill, and unfortunately we can't exactly differentiate the two, but we do know that Bautista has become a better hitter, and is hitting for a higher average at least due to some skill.
So where is the other 30 point difference coming from? The BABIP formula shows us that it comes from the number of home runs and strikeouts a hitter accumulates (also sac flies, but they are minimal and can be ignored). As discussed in the last post, a large determinant of the number of home runs a hitter has is his HR/FB ratio, which is mainly due to luck. Obviously, hitters like Bautista who make a conscious effort to hit fly balls very hard will have higher HR/FB rates, and thus more home runs. The league average is usually around 10.6% (actually, the HR/FB rate is now below 9% for 2011), and last year Bautista ended the year with a 21.7% rate, more than double league average. This year, Bautista has a 31.3% HR/FB rate, which is insane. This means that roughly for every three fly balls he hits, one ends up over the wall for a home run. This is by far the highest rate in the majors this year, with Lance Berkman having the second highest rate at 23.4%, which is 34% lower than Bautista's rate. Even with Bautista's violent swing, this rate is bound to regress at least somewhat towards the mean. This shows that Bautista has gotten somewhat lucky this year, but it is impossible to determine what his final HR/FB rate will be, so we cannot determine exactly how lucky.
The last determinant of BABIP is from strikeouts. Bautista has dramatically increased in this area, decreasing his strikeout rate from 20.4% last year to 17.3% this year. This may not sound like much, but over a full season of 500 or so at-bats, that's 16 more balls put in play, and with a BABIP of .321, five more hits. That's about 10 extra points on his batting average over a full season, simply due to striking out less. What makes this even more impressive is that while he is striking out less, mainly due to the fact that he decreased his swinging strike percentage from 7.7% to 6.7%, he still has the ability to hit the ball extremely hard, actually harder this year. In almost every case, a hitter will sacrifice power in order to make more contact, yet Bautista has managed to become better at both. This is certainly not luck, and we can attribute this part of his increased batting average all to skill.
What does this all mean? I have presented a lot of different statistics, and what I hoped to accomplish was to show that while Bautista has gotten a little lucky in his huge increase in AVG this year, it has mainly been from skill. Although at first you may want to credit luck from his increased BABIP, he hasn't simply had more balls "find holes" this year, he has been hitting more line drives, which show that he has become a better hitter. Yes, his home run total has been somewhat inflated by his incredible HR/FB rate, so maybe we shouldn't expect him to hit 40+ home runs the rest of the season and instead expect him to finish with 50 or so home runs. If his HR/FB rate regresses even all the way to last year (which I don't expect it will), he should still end up with 48 home runs. Finally, he has managed to swing and miss less pitches, which decreases strikeouts and allows him to hit more balls in play. This is due to a systematic adjustment, and is not lucky at all. Although we know Bautista won't end the year hitting .350, with all of these factors we just discussed, we can reasonably expect him to finish the year hitting .320 or so. Many people expected Bautista to slump this year and not be able to hit as well as last year, but he has managed to play even better, and should end up with better numbers this season than last, which is hard to believe.
The major difference between this year's version of Bautista and last year's is his much better batting average. He is still managing to hit a ton of home runs, but after hitting only .260 last season, he is now hitting .353 (all statistics through Saturday's games), good enough for second in the AL. One of the biggest reasons behind this increase in batting average is that his BABIP (batting average on balls in play) has increased from .233 to .321 this year. His career rate of .273 suggests that he was somewhat unlucky last year, and has gotten lucky this year. This may be misleading, as his changed swing naturally leads to more fly balls, usually meaning a lower BABIP. It seems as though last year he was simply trying to hit the ball out of the park, while this year he has become more of a line drive hitter while still hitting home runs. This can be seen in his line drive %, which was only 14.4% last year and is up to 17.1% this year. Line drive % shows how "lucky" a hitter is getting, as line drives are usually end up falling for hits, while ground balls and fly balls are more frequently outs. The increase in LD% shows that Bautista hasn't actually been any luckier this season, he is simply hitting the ball much harder in a higher percentage of at-bats and is being rewarded with a higher BABIP and subsequently batting average.
We can demonstrate what could have happened in previous seasons had Bautista hit as many line drives, leading to a higher BABIP. BABIP is calculated as: (hits - home runs) divided by (at-bats minus strikeouts and home runs plus sac flies). Last year, Bautista had 569 at-bats, 148 hits of which 54 were home runs, 116 strikeouts, and 4 sac flies. If we set his hits total as unknown, we can solve for the amount of hits he would have had with different BABIP. He had a total of 94 non-HR hits last year, and if he had even had his career BABIP of .273, he would have produced 110 non-HR hits. This would have left him with a batting average of (164/569) = .288. If he had this year's .321 BABIP, he would have had an batting average of .322, much closer to this year's .353. The difference in batting average from his career to this season is due to both luck and skill, and unfortunately we can't exactly differentiate the two, but we do know that Bautista has become a better hitter, and is hitting for a higher average at least due to some skill.
So where is the other 30 point difference coming from? The BABIP formula shows us that it comes from the number of home runs and strikeouts a hitter accumulates (also sac flies, but they are minimal and can be ignored). As discussed in the last post, a large determinant of the number of home runs a hitter has is his HR/FB ratio, which is mainly due to luck. Obviously, hitters like Bautista who make a conscious effort to hit fly balls very hard will have higher HR/FB rates, and thus more home runs. The league average is usually around 10.6% (actually, the HR/FB rate is now below 9% for 2011), and last year Bautista ended the year with a 21.7% rate, more than double league average. This year, Bautista has a 31.3% HR/FB rate, which is insane. This means that roughly for every three fly balls he hits, one ends up over the wall for a home run. This is by far the highest rate in the majors this year, with Lance Berkman having the second highest rate at 23.4%, which is 34% lower than Bautista's rate. Even with Bautista's violent swing, this rate is bound to regress at least somewhat towards the mean. This shows that Bautista has gotten somewhat lucky this year, but it is impossible to determine what his final HR/FB rate will be, so we cannot determine exactly how lucky.
The last determinant of BABIP is from strikeouts. Bautista has dramatically increased in this area, decreasing his strikeout rate from 20.4% last year to 17.3% this year. This may not sound like much, but over a full season of 500 or so at-bats, that's 16 more balls put in play, and with a BABIP of .321, five more hits. That's about 10 extra points on his batting average over a full season, simply due to striking out less. What makes this even more impressive is that while he is striking out less, mainly due to the fact that he decreased his swinging strike percentage from 7.7% to 6.7%, he still has the ability to hit the ball extremely hard, actually harder this year. In almost every case, a hitter will sacrifice power in order to make more contact, yet Bautista has managed to become better at both. This is certainly not luck, and we can attribute this part of his increased batting average all to skill.
What does this all mean? I have presented a lot of different statistics, and what I hoped to accomplish was to show that while Bautista has gotten a little lucky in his huge increase in AVG this year, it has mainly been from skill. Although at first you may want to credit luck from his increased BABIP, he hasn't simply had more balls "find holes" this year, he has been hitting more line drives, which show that he has become a better hitter. Yes, his home run total has been somewhat inflated by his incredible HR/FB rate, so maybe we shouldn't expect him to hit 40+ home runs the rest of the season and instead expect him to finish with 50 or so home runs. If his HR/FB rate regresses even all the way to last year (which I don't expect it will), he should still end up with 48 home runs. Finally, he has managed to swing and miss less pitches, which decreases strikeouts and allows him to hit more balls in play. This is due to a systematic adjustment, and is not lucky at all. Although we know Bautista won't end the year hitting .350, with all of these factors we just discussed, we can reasonably expect him to finish the year hitting .320 or so. Many people expected Bautista to slump this year and not be able to hit as well as last year, but he has managed to play even better, and should end up with better numbers this season than last, which is hard to believe.
Wednesday, March 2, 2011
Blue Jays Batting Order
Now that the offseason has winded down and spring training games have begun, it is time to look forward to the 2011 season. An important question for this year (and any year) is what will the batting order look like? This breaks down how exactly a lineup should be constructed to optimize players' talents. Basically, the old-school thoughts on building a lineup (speed at #1, bunter #2, power hitters #3-5, worst hitters #6-9) are mostly incorrect, according to sabermetric research. The article does a nice job of explaining who should hit where and why. It does note that a specific permutation of players in a batting order does not make a huge difference, only about a maximum of one win per season. However, it is a fun exercise to construct a projected lineup.
This post was inspired by this post, which detailed the optimized lineup for the Indians. I want to do the same thing with the Blue Jays. The data I am using is the Cairo projections (found here), which project a player's upcoming season based on weighted average of a player's past few seasons. The statistic that is used to figure out the optimal lineup is wOBA, or weighted on-base average. Two good explanations of the statistic can be found here and here. In short, wOBA combines on-base percentage and slugging percentage into one statistic, scaled to OBP, so it is easy to understand. Why not simply use on-base plus slugging? For one, OPS weighs OBP and SLG equally, while in reality OBP is more important. wOBA is calculated using the actual run values of each event, so it will better predict how much more valuable something is worth rather than simply OPS.
Although it sounds confusing, and the math behind it is, the end result is one simple number which tells you how valuable a player is to his team while hitting. If this sounds similar to Wins Above Replacement, it's because wOBA is used to calculate the hitting aspect of WAR.
Now, onto the data. Here are the splits for all of the Blue Jays involved in the Cairo projections.
I am going to use lineups against both LH and RH pitchers, as the projections include platoon splits. The optimal lineup, according to sabermetrics, is #1, #4, #2, #5, #3, #6, #7, #8, #9 in terms of avoiding outs. So the highest wOBA will be first, then 4th, all the way to 9th.
Lineup vs. LHP
Lineup vs. RHP
We can see some interesting things in the two lineups. Seven players appear in both lineups, although maybe not who you would think: Bautista, Encarnacion, Ruiz, Arencibia, Rivera, Escobar, and Figueroa. Rajai Davis and Aaron Hill are only hitting against lefties, and Lind and Snider are only hitting against righties.
The projections are obviously not perfect, if Luis Figueroa is starting every day for the Jays, but they do provide some insight into where certain hitters should hit. With a league average wOBA of .321 last year in the majors, the Jays' lineups should be much better than average again this year, even with the loss of Vernon Wells and John Buck.
This post was inspired by this post, which detailed the optimized lineup for the Indians. I want to do the same thing with the Blue Jays. The data I am using is the Cairo projections (found here), which project a player's upcoming season based on weighted average of a player's past few seasons. The statistic that is used to figure out the optimal lineup is wOBA, or weighted on-base average. Two good explanations of the statistic can be found here and here. In short, wOBA combines on-base percentage and slugging percentage into one statistic, scaled to OBP, so it is easy to understand. Why not simply use on-base plus slugging? For one, OPS weighs OBP and SLG equally, while in reality OBP is more important. wOBA is calculated using the actual run values of each event, so it will better predict how much more valuable something is worth rather than simply OPS.
Although it sounds confusing, and the math behind it is, the end result is one simple number which tells you how valuable a player is to his team while hitting. If this sounds similar to Wins Above Replacement, it's because wOBA is used to calculate the hitting aspect of WAR.
Now, onto the data. Here are the splits for all of the Blue Jays involved in the Cairo projections.
| Player | Projected wOBA | Vs L | Vs R |
| Jose Bautista | .373 | .367 | .375 |
| Travis Snider | .339 | .314 | .344 |
| J.P. Arencibia | .335 | .350 | .327 |
| Adam Lind | .331 | .293 | .345 |
| Edwin Encarnacion | .331 | .349 | .325 |
| Juan Rivera | .329 | .343 | .323 |
| Luis Figueroa | .329 | .327 | .330 |
| Randy Ruiz | .328 | .339 | .322 |
| Yunel Escobar | .326 | .335 | .322 |
| Rajai Davis | .325 | .339 | .318 |
| Aaron Hill | .321 | .336 | .316 |
| Jason Lane | .312 | .323 | .306 |
| Chris Aguila | .309 | .317 | .304 |
| Mike McCoy | .307 | .320 | .298 |
| John McDonald | .288 | .302 | .281 |
| Callix Crabbe | .285 | .288 | .283 |
| Jose Molina | .283 | .297 | .276 |
I am going to use lineups against both LH and RH pitchers, as the projections include platoon splits. The optimal lineup, according to sabermetrics, is #1, #4, #2, #5, #3, #6, #7, #8, #9 in terms of avoiding outs. So the highest wOBA will be first, then 4th, all the way to 9th.
Lineup vs. LHP
# | Name | Position | wOBA |
1 | Jose Bautista | RF | .367 |
2 | Edwin Encarnacion | 3B | .349 |
3 | Randy Ruiz | 1B | .339 |
4 | J.P. Arencibia | C | .350 |
5 | Juan Rivera | LF | .343 |
6 | Rajai Davis | CF | .339 |
7 | Aaron Hill | 2B | .336 |
8 | Yunel Escobar | SS | .335 |
9 | Luis Figueroa | DH | .327 |
Lineup vs. RHP
# | Name | Position | wOBA |
1 | Jose Bautista | CF | .375 |
2 | Travis Snider | LF | .344 |
3 | J.P. Arencibia | C | .327 |
4 | Adam Lind | 1B | .345 |
5 | Luis Figueroa | 2B | .330 |
6 | Edwin Encarnacion | 3B | .325 |
7 | Juan Rivera | RF | .323 |
8 | Randy Ruiz | DH | .322 |
9 | Yunel Escobar | SS | .322 |
We can see some interesting things in the two lineups. Seven players appear in both lineups, although maybe not who you would think: Bautista, Encarnacion, Ruiz, Arencibia, Rivera, Escobar, and Figueroa. Rajai Davis and Aaron Hill are only hitting against lefties, and Lind and Snider are only hitting against righties.
The projections are obviously not perfect, if Luis Figueroa is starting every day for the Jays, but they do provide some insight into where certain hitters should hit. With a league average wOBA of .321 last year in the majors, the Jays' lineups should be much better than average again this year, even with the loss of Vernon Wells and John Buck.
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