## Tuesday, September 02, 2008

Fans often complain that stats like OPS and runs created don't take into account the game situation. For example, a walk-off home run is more valuable to a team than a home run when they are up by 12 runs but they both count the same in the statistics. The Win Probability Added (WPA) statistic does consider game situations and gives hitters credit based on the effect their at bats have on their team's probability of winning. These probabilities vary depending on the game score, the runners on base and the number of outs before and after each play. They are based on the results of thousands of games worth of data looking at every possible situation over and over.

More concretely, WPA works as follows. Suppose the Tigers are down by one run with a runner on second and two out in the bottom of the ninth. Using the win expectancy finder, created by the site walkoff balk, they have a .129 (or 12.9%) expectancy of winning. Now suppose, Curtis Granderson singles to tie the game. The probability of winning is now .570. So, Granderson increased the probability of the Tigers winning the game by .570-.129 = .441 with his single.

In another game, the Tigers are up 5-0 with the bases empty and nobody out in the bottom of the eight. Theoretically, this means that they have a probability of .997 of winning the game. In this situation, Gary Sheffield hits a solo homer to make it 6-0. The win probability is now .998 meaning that the home run added only .001 to the win probability. So Sheffield's homer counts a lot less than Granderson's single.

A player can also decrease his team's probability of winning. For example, the Tigers are losing 2-1 in the bottom of the ninth with a runner on first and nobody out. In this case, they have a .320 probability of winning. Then Edgar Renteria hits into a double play which makes probability of winning to .035. So, the double play decreased the probability of winning by .320-.035=.285.

If you add up all the gains and losses for all of a player's at bats, you get his WPA. The good thing about WPA is that is may give a more accurate measure of a player's value to his team during a season. The drawback is that it is not predictive. Thus, if you want to determine how well a player will do in the future, a situation independent statistic such as runs created would be more appropriate.

Table 1 lists the American League WPA leaders as of September 1. The Tigers are listed in Table 2. These data were abstracted from the Fan Graphs web site.

Table 1: American League WPA leaders

Ramirez Bos. 3.94
Quentin, Chi 3.89
Morneau, Min 3.77
Mauer, Min 3.48
Hamilton, Tex 3.43
Sizemore, Cle 3.29
Pena, TB 3.12
Pedroia, Bos 2.79
Cabrera, Det 2.68

Cabrera 2.68
Granderson 2.42
Guillen 1.61
Joyce 1.27
Thames 0.26
Polanco -0.11
Median -0.20
Ordonez -0.32
Inge -0.58
Sheffield -1.21
Renteria -2.26

Tables 3 and 4 below present the Runs Created Per Game leaders for the American League and the Tigers respectively. Looking at Tables 2 and 4 for the Tigers, we can see that Magglio Ordonez has been below average according WPA but above average according to runs created. This indicates that he has not performed as well in high leverage situations as he has in lower impact spots. Since this has not been the case for him in the past, I would say it's just a case of bad luck rather than a lack of ability to perform in the clutch. Conversely, Miguel Cabrera ranks higher on WPA than he does on Runs Created.

Table 3: American League Runs Created Per Game leaders

Rodriguez, NY 8.40
Huff, Bal 8.15
Quentin, Chi 8.06
Sizemore 8.03
Youkilis, Bos 8.02
Drew, Bos 8.00
Markakis, Bal 7.77
Ramirez, Bos 7.71
Granderson, Det 7.58

Table 4: Tigers Runs Created Per Game leaders

Granderson 7.58
Joyce 7.12
Cabrera 6.38
Guillen 6.02
Ordonez 5.94
Polanco 5.40
Thames 5.16
Median 4.80
Inge 4.58
Sheffield 4.04
Renteria 3.76

#### 1 comment:

1. Great stuff. It's nice to see Grandy at the top of Table 4!

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