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.
Showing posts with label winning. Show all posts
Showing posts with label winning. Show all posts
Sunday, October 3, 2010
Sunday, August 29, 2010
The Cost of Winning: Staying Successful and Profitable in Baseball
The key to running a successful major league baseball team is essentially maximizing the performance on the field (e.g. the more wins the more success the franchise has) while also maximizing the profit of the organization. There are really two ways to achieve financial success: either spend the minimum on players and staff, and gain money even though the team is terrible (see the Pittsburgh Pirates), or spend a ton of money, become a very successful team, and reap the benefits on the balance sheet (see the New York Yankees; even though that story is six years old, the balance sheet still shows the huge difference between the two franchises' finances).
The best case scenario, however, is to draft well, develop your young players, and have them blossom into stars while you still only have to pay them near the MLB minimum salary. The Tampa Bay Rays are a good recent example of this, as they drafted and developed young stars such as Carl Crawford, Evan Longoria, James Shields (not quite a star but still performed very well in the 2008 playoffs), and Matt Garza. They won the AL East in 2008, and made it to the World Series before losing to the Phillies, while still turning a profit (a lot of that due to the current revenue sharing agreement in the MLB). However, the one problem with this is that eventually, your young stars will need to be paid a lot of money. The Rays will run into this problem this summer, when Carl Crawford and Carlos Pena, both free agents, will be due hefty raises that the Rays probably won't be able to afford. So how do teams sustain both success on the field and on the balance sheet for multiple years?
The real key to success is to find players that cost only a small amount (relative to their peers) while putting up good numbers on the field. A good way to measure the performance of a player over a season or career is by Wins Above Replacement (WAR), which measures how much better the player is compared to a AAA-level replacement player. It is very convenient to use just this one stat to compare how good each player is to another. You can view the 2009 MLB WAR leaders here. The highest WAR per season is usually under 10 (Albert Pujols led with 9.6 in 2008 and 9.2 in 2009). This means that Pujols is "worth" approximately 9-10 wins for the Cardinals, because if they did not have him playing first (and only had a AAA replacement), they would lose 9-10 more games per year.
While WAR measures the performance of the player, teams also need to keep in mind how cost-effective the player is. For example, is it worth spending around $30 million on Alex Rodriguez, who is only worth about 4-5 extra wins per year, when you can spend that money on three or four above average players who will each be worth 2-3 (or more) wins per year? If you are the Yankees, the answer is yes, but for most teams, A-Rod is not a viable option (and that's just in terms of money, we haven't even got into the chemistry and happiness of the team when he's around!). So teams need to also view the salary of the player, and when combined with WAR, a very useful statistic for measuring success is $/WAR. This statistic measures how much money it costs for an extra win per player. For example, last year Pujols earned $13,870,949 in salary while being worth an extra 9.6 wins. So the Cardinals paid $1,444,890.52 per extra win that Albert Pujols was worth. The key to being successful is to have players with a low $/WAR, which means that it costs a low amount of money (again, relative to their peers) for each extra win that the player is worth.
With the $/WAR statistic in hand, in the next few days I am going to explore the conclusions that can be drawn from analyzing the past couple of years with $/WAR, and post the results. What the study should show is that the successful teams will either have a high WAR regardless of cost (e.g. the Yankees and Red Sox, who spend a lot of money to make money), or a low $/WAR, which most teams need to have in order to be successful on the field while making a profit. I am also going to explore how to predict a player's $/WAR, which, if successful, will be the key to running a successful team. If you can predict a player's cost-effectiveness, then you will be able to obtain successful players at lower costs, thus exploiting the market for baseball players and making your franchise successful on the field and on the balance sheet.
The best case scenario, however, is to draft well, develop your young players, and have them blossom into stars while you still only have to pay them near the MLB minimum salary. The Tampa Bay Rays are a good recent example of this, as they drafted and developed young stars such as Carl Crawford, Evan Longoria, James Shields (not quite a star but still performed very well in the 2008 playoffs), and Matt Garza. They won the AL East in 2008, and made it to the World Series before losing to the Phillies, while still turning a profit (a lot of that due to the current revenue sharing agreement in the MLB). However, the one problem with this is that eventually, your young stars will need to be paid a lot of money. The Rays will run into this problem this summer, when Carl Crawford and Carlos Pena, both free agents, will be due hefty raises that the Rays probably won't be able to afford. So how do teams sustain both success on the field and on the balance sheet for multiple years?
The real key to success is to find players that cost only a small amount (relative to their peers) while putting up good numbers on the field. A good way to measure the performance of a player over a season or career is by Wins Above Replacement (WAR), which measures how much better the player is compared to a AAA-level replacement player. It is very convenient to use just this one stat to compare how good each player is to another. You can view the 2009 MLB WAR leaders here. The highest WAR per season is usually under 10 (Albert Pujols led with 9.6 in 2008 and 9.2 in 2009). This means that Pujols is "worth" approximately 9-10 wins for the Cardinals, because if they did not have him playing first (and only had a AAA replacement), they would lose 9-10 more games per year.
While WAR measures the performance of the player, teams also need to keep in mind how cost-effective the player is. For example, is it worth spending around $30 million on Alex Rodriguez, who is only worth about 4-5 extra wins per year, when you can spend that money on three or four above average players who will each be worth 2-3 (or more) wins per year? If you are the Yankees, the answer is yes, but for most teams, A-Rod is not a viable option (and that's just in terms of money, we haven't even got into the chemistry and happiness of the team when he's around!). So teams need to also view the salary of the player, and when combined with WAR, a very useful statistic for measuring success is $/WAR. This statistic measures how much money it costs for an extra win per player. For example, last year Pujols earned $13,870,949 in salary while being worth an extra 9.6 wins. So the Cardinals paid $1,444,890.52 per extra win that Albert Pujols was worth. The key to being successful is to have players with a low $/WAR, which means that it costs a low amount of money (again, relative to their peers) for each extra win that the player is worth.
With the $/WAR statistic in hand, in the next few days I am going to explore the conclusions that can be drawn from analyzing the past couple of years with $/WAR, and post the results. What the study should show is that the successful teams will either have a high WAR regardless of cost (e.g. the Yankees and Red Sox, who spend a lot of money to make money), or a low $/WAR, which most teams need to have in order to be successful on the field while making a profit. I am also going to explore how to predict a player's $/WAR, which, if successful, will be the key to running a successful team. If you can predict a player's cost-effectiveness, then you will be able to obtain successful players at lower costs, thus exploiting the market for baseball players and making your franchise successful on the field and on the balance sheet.
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