Improving a Team - Pitching or Hitting?

After the close of the baseball season in early November, teams look to build for next year through trades, free agency, and the draft (which is more for 3-5 years into the future). But how do you build a better team, and more specifically, what will allow you to have a better team? The old question of pitching vs. hitting is always addressed differently by different teams. Last year, the Giants used spectacular pitching with timely hitting to win the World Series, but just the year before the Yankees used a powerful lineup to bulldoze their way to a World Series win. So which is preferable - scoring more runs, or preventing more runs?

In order to answer that question, I looked at every team's statistics in the last 11 years (2000-2010), and gave each team a value for "Playoffs". A 1 meant that the team made the playoffs, a 0 meant the team did not make the playoffs. To estimate hitting, I used the statistic "runs per game", and to estimate pitching I used the statistic "runs against per game" (this really represents overall defense, including both fielding and pitching - to truly isolate pitching a more appropriate statistic would be something like ERA). I then ran a simple linear regression model, with RpG and RApG estimating the binary "Playoffs" statistic. The table below shows the results:

Coefficients:
                  Estimate       Std. Error      t value      Pr(>|t|)   
Intercept    0.28029       0.24027         1.167        0.244   
RpG           0.41595       0.03884         10.709      <2e-16 ***
RApG        -0.41884      0.03694        -11.339      <2e-16 ***
***: significant at the 0.001 level

So the regression line is: Playoffs = 0.28029 + 0.41595*RpG - 0.41884*RApG. The intercept means that disregarding runs for and against, a team will have a 28% chance of making the playoffs. We know that this is close to being correct, as there are 30 teams competing for 8 playoffs spots, so the probability of any team making the playoffs, given that all teams are equal, is 0.2667. The coefficient of runs per game shows that a one-run per game increase in RpG is associated with a 41.6% higher probability of a team making the playoffs. Runs against per game is very similar except it is inverse, as a one-run per game increase in RApG is associated with a 41.9% lower probability of a team making the playoffs. As an example, if a team scores 4.50 runs per game and allows 4.50 runs per game, the probability of the team making the playoffs is 0.2673. If they increase their runs per game to 5.50 (an increase of exactly 1), the probability of the team making the playoffs will increase by 0.416 to 0.6832. If they then increase their runs against per game to 5.50 (again an increase of 1), their probability of making the playoffs will decrease to 0.2644 (a decrease of 0.419).

What this all means is that scoring runs and preventing runs have a very similar impact on a team's success (success defined by a team making the playoffs). Runs against is very slightly more important, but the difference is most likely negligible. Obviously this was a quick study, and only based on a small sample, but we can see that teams should be more concerned with overall talent of acquisitions rather than worry about acquiring only players that will help their hitting or pitching.

Predicting Playoff Series

Now that the first round of the playoffs is over, we are left with only 4 teams: the Yankees, the Rangers, the Phillies, and the Giants. In the American League Championship Series, the Rangers are hosting the Yankees, while in the NLCS the Phillies are hosting the Giants. The Phillies and Yankees are the prohibitive favorites to win their respective series' and advance to the World Series for a rematch of last year. But what are the chances of each of the four teams winning their series?

To calculate the odds of each team advancing, I used three different statistics. The first was the team's regular season record in 162 games, which I converted to a probability between 0 and 1 (each team is actually between 55% and 60%. The second is their Pythagorean Win-Loss record, which uses runs scored and run against to predict what each team's record should have been. I again converted the Pythagorean Win-Loss record to a probability. Finally, I used the team's overall record, combining the regular season record and playoff record through the Division Series', and converted it to a probability. These three estimates will all be used to predict the probability of each team advancing, as three estimates should produce a more accurate result than one. The summary for each team is found below:
 
Texas Rangers
Regular Season record: 90 wins - 72 losses (win probability = 0.55555)
Pythagorean W-L = 91-71 (0.56173)
Overall record: 93-74 (0.55689) - Won their first round series 3-2.

New York Yankees
Regular Season record: 95-67 (0.58642)
Pythagorean W-L = 97-65 (0.59877)
Overall Record: 98-67 (0.59394) - Won their first round series 3-0.

Philadelphia Phillies
Regular Season record: 97-65 (0.59877)
Pythagorean W-L = 95-67 (0.58642)
Overall Record: 100-65 (0.60606) - Won their first round series 3-0.

San Francisco Giants
Regular Season record: 92-70 (0.56790)
Pythagorean W-L = 94-68 (0.58025)
Overall Record: 95-71 (0.57229) - Won their first round series 3-1.

The next part gets a little tricky, as I used a statistical software package to compare the win probability means. I generated 1000 random data points for each win probability, and each data set had a normal distribution of mean = win probability and standard deviation = 1. These data sets are very close to the standard normal distribution of mean = 0 and standard deviation = 1 (if you want to know more about the standard normal distribution, you can see Wikipedia). What this means is that 68% of the data points will be between win probability - 1 and win probability + 1, and since we are creating two different data sets, there should be some difference between the sets if they have different means. The standard deviations represent the differences in performances, as a team will play a different game every night, and not always perform the same. I used 1000 data points so that I could sufficiently determine whether or not there was a difference between the teams, as the more data points, the more precise the estimate. I then subtracted the two data points for the teams that were playing against each other, and figured out a difference. The difference was "home team" - "away team", so if the difference was >= 0, it meant the home team was "better" than the away team, or in my analysis, that the home team won the series. If the difference of "home team" - "away team" < 0, then it meant that the away team would win the series. Finally, I totaled the differences to determine how many times out of 1000 each team would win the series. I did this for each set of win probabilities (regular season, Pythagorean, and total) to find three estimates to the probability of each team winning a series, found below.

ALCS
Using regular season record: Rangers win series 474 times = 47.4%, Yankees win series 52.6%
Using Pythagorean regular season record: Rangers win series 495 times = 49.5%, Yankees win 50.5%
Using regular season and playoff record: Rangers win series 483 times = 48.3%, Yankees win 51.7%

NLCS
Using regular season record: Phillies win series 527 times = 52.7%, Giants win series 47.3%
Using Pythagorean regular season record: Phillies win series 506 times = 50.6%, Giants win series 49.4%
Using regular season and playoff record: Phillies win series 529 times = 52.9%, Giants win series 47.1%

So in the ALCS, the Yankees win the series between 50.5% and 52.6% (and on average 51.6%) of the time according to this estimate. In the NLCS, the Phillies win the series between 50.6% and 52.9% (and on average 52.07%) of the time. These estimates are slightly lower than some other estimates (like here), but this is probably because as the number of data points increases, the probability of each time tends towards 50%. It is a delicate balance between having enough data points to provide an accurate estimate, but not having too many so that the probability is very close to 50% just because of the large n.

So my picks are that both series should be pretty close, but just like popular opinion, the Phillies and Yankees should prevail and meet in the World Series for a second straight year.

National League Playoff Race

The race for the final two playoffs spots in the National League has come down to the final day. Currently, the Giants lead the Padres by one game in the NL West, while the Padres and Braves are tied for the wild card. Tomorrow, the Padres and Giants face off for the NL West title, and possibly a wild card berth, while the Phillies and Braves square off with the Braves trying to get the last wild card spot. It will be an exciting day, with a possible three-team playoff (the first one in history) on Monday and Tuesday. In this post I want to determine the probability of each of the three teams (Giants, Padres, and Braves) making the playoffs and facing the Phillies and Reds.

There are four possible scenarios for tomorrow's games:

Scenario 1: Giants and Braves win, Padres lose
Scenario 2: Padres win, Giants and Braves lose
Scenario 3: Giants win, Padres and Braves lose
Scenario 4: Padres and Braves win, Giants lose

For the purpose of this exercise, I am going to assuming the probability of any team winning any game is .5 (a reasonable assumption, but probably not entirely accurate). So the probability of each scenario above happening is 0.25. In the first scenario, the Giants and Braves will make the playoffs, and San Diego will go home. This means that the probability of the Giants and Braves making the playoffs is 1.0, and the probability of the Padres making the playoffs is 0.0. The second scenario is similar, with the Padres and Giants both making the playoffs (prob. = 1.0) and the Braves going home (prob. of playoffs = 0.0).

The third scenario is where things start to get a little trickier. In this scenario, San Francisco wins, so they have a 1.0 probability of making the playoffs, while the Padres and Braves will face off in a one-game playoff on Monday. So the Padres and Braves will both have a probability of 0.5 of making the playoffs (in each case, 2 out of the 3 teams make the playoffs, so each scenario's probability should add up to 2.0).

The final scenario is the most difficult, as there is now a three-team playoff. The first playoff would be Monday, when the Giants and Padres play (winner goes to the playoffs), and then Tuesday the loser would play the Braves for the final spot. The easiest way to think about this is that in scenario 4, there are "four" possible scenarios given the two outcomes of each of the two playoff games. The four scenarios would work like this: a) Giants win, then Padres win, b) Giants win, then Braves win, c) Padres win, then Giants win, and finally d) Padres win, then Braves win. So in this final scenario, the probability of San Francisco and San Diego making the playoffs is 0.75 (they make the playoffs in 3 of the four cases), and the probability of Atlanta making the playoffs is 0.5 (they make the playoffs in 2 of the four cases).

The final step is to figure out the probability of each team making the playoffs. To do this, we multiply the probability of the team making the playoffs in each scenario with the probability of the scenario.

Probability(Giants making playoffs) = 1*.25 + 1*.25 + 1*.25 + .75*.25 = .9375 = 15/16
Probability(Padres making playoffs) = 1*.25 + .5*.25 + .75*.25 = .5625 = 9/16
Probability(Braves making playoffs) = 1*.25 + .5*.25 + .5*.25 = .50 = 8/16

So overall, there are 16 possible scenarios for the playoffs that will determine the two playoff teams in the next three days. In 15 of them, the Giants make the playoffs (the only way they will not make the playoffs is if they lose tomorrow and the Braves win tomorrow, then they lose consecutive one-game playoffs to the Padres and Braves, and the probability of this happening is 0.5⁴, or 1/16. In 9 scenarios, the Padres will make the playoffs, and in 8 scenarios the Braves will make the playoffs. We can see that the total probability of the teams making the playoffs is 32/16 = 2, so we can see that the probabilities are correct in that two of the teams will make the playoffs.

What does this mean? Basically, the race is a two-team race for the final spot, with one team all but clinched. The Giants are all but assured of a playoff birth, while the Padres and Braves are left fighting for the last spot (almost always the wild card, but potentially the Padres could win the NL West and the Braves could win the wild card, although the probability is only 1/16). The Padres do have a slight edge because they can potentially win the division, while the Phillies have already locked up the NL East, leaving the Braves with only the wild card possibility.

So keep yours eyes on the games tomorrow, the Braves and Phillies play at 1:30 and the Padres and Giants play at 4, so even by 4 pm tomorrow we will have a much clearer picture of the possible playoff spots. It will be an interesting day, and possibly an interesting 2 or 3 days, all to probably get beaten by the Phillies and Reds in the first round.