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## Monday, August 19, 2002

#### Win Values:  A New Method to Evaluate Starting Pitchers - Part 5

Empirical Data for AL 2000

## Empirical Data for AL 2000

In this section I will present examples of the empirical data corresponding   to all the variables entering the Win Values formulas presented above.? For   convenience the AL 2000 will serve as the representative season.? The following   tables will present the empirical distributions using the entire AL 2000 season   as the database.? In the Win Values framework, these distributions are derived   separately for each league and for each season under study.

### Table 4:? Win Probs with Average Pitching, AWin(RS,Z), for AL 2000

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 At the conclusion of the Zth inning Run Scored (RS) 1 2 3 4 5 6 7 8 9 0 .436 .383 .346 .288 .235 .189 .126 .051 .000 1 .580 .496 .403 .347 .332 .277 .197 .146 .068 2 .597 .574 .535 .463 .371 .318 .296 .260 .204 3 .742 .715 .622 .599 .531 .444 .390 .321 .281 4 .800 .786 .725 .680 .633 .583 .516 .440 .431 5 .875 .840 .810 .788 .692 .646 .641 .615 .551 6 .950 .870 .839 .820 .810 .772 .702 .651 .610 7 .970 .913 .878 .857 .840 .820 .800 .759 .728 8 1.000 1.000 .958 .900 .891 .874 .850 .845 .840 9 1.000 1.000 .975 .965 .955 .945 .923 .880 .860 10 1.000 1.000 1.000 .975 .960 .950 .940 .932 .887 11 1.000 1.000 1.000 1.000 .975 .960 .950 .940 .900 12 1.000 1.000 1.000 1.000 .980 .965 .960 .950 .940 13+ 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Table 4 reports the empirical win probabilities using the entire AL 2000   season.? The first row of the table presents the probabilities a team will   go on to win the game when it has scored exactly 0 runs at the conclusion   of each inning 1-9, given average pitching.? Of course, based solely upon   runs scored information, before the game starts each team has a .500 expected   win prob.? If a team is scoreless after 1 inning, its win prob falls to .436,   after 2 innings to .383, and so on until it has .000 chance of winning with   0 runs after 9 innings.

Maybe the better way to look at the table is by column, that is by what   inning the game is in.? After 5 innings, a team that has yet to score has   a .235 win prob with average pitching, a team with 1 run has a .332 win prob,   a team with 2 runs has a .371 win prob, and so on all the way up to a 1.000   win prob if the team has scored 13 or more runs.

As described above, these win probabilities are based upon every game in   the entire AL 2000 season.? Accordingly, I treat these probabilities as being   reflective of the win probabilities a team would have with ?average? pitching.

### Table 5:? Win Probs using Pitcher?s   Performance, DWin(RA-RS, Z), for AL 2000

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 At the conclusion of the Zth inning Deficit (RA-RS) 1 2 3 4 5 6 7 8 9 0 .500 .500 .500 .500 .500 .500 .500 .500 .500 1 .410 .390 .380 .365 .344 .274 .226 .179 .000 2 .358 .299 .275 .264 .234 .200 .114 .062 .000 3 .215 .205 .195 .176 .164 .089 .059 .023 .000 4 .146 .130 .115 .107 .075 .051 .030 .015 .000 5 .105 .085 .077 .068 .060 .045 .025 .010 .000 6 .050 .040 .035 .030 .027 .025 .014 .005 .000 7 .025 .020 .015 .010 .005 .000 .000 .000 .000 8+ .000 .000 .000 .000 .000 .000 .000 .000 .000

Table 5 reports the expected win probabilities using the performance of   the starting pitcher under study.? That is, we use both the team?s offensive   run support (RS) and also the runs allowed (RA) the starting pitcher has given   up.? As above, the win probabilities vary by what inning the game is in.

By extensive analysis I have found that the win probabilities are based   largely on the deficit (or lead) the team faces, and that the specific RA,   RS information is not needed.? This allows a more robust estimation of these   probabilities since there are not enough games in any season that have the   exact same score at the conclusion of any specific inning.? But there are   lots of games that have the same deficit.

The first row of the table indicates that the expected win probability of   a team in a game that is tied at the conclusion of any inning is .500.? The   second row indicates how the win probability of a team that is 1-run behind   varies depending upon what inning the game is in.? After 1 inning, the probability   a team can expect to overcome a 1-run deficit (going on to win the game) is   .410; after 2 innings .390, etc.

The columns of the table indicate how the win probability changes with the   deficit[1] to be overcome at the conclusion of a specific   inning.? For example, the 5th column indicates that a 1-run deficit can be   expected to be overcome .344 after five innings, a 2-run deficit .234, a 3-run   deficit .164, etc.

### Table 6: ?Could Have Been? Run Scored   Probabilities, Smear(m;RS,Z), for AL 2000

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 Actual Runs Scored (RS); at Z=9 Could Have Scored (m) 0 1 2 3 4 5 6 7 8 0 .338 .130 .059 .033 .015 .010 .008 .005 .002 1 .267 .306 .148 .099 .052 .047 .022 .015 .012 2 .155 .192 .279 .166 .110 .074 .049 .030 .023 3 .105 .153 .198 .264 .179 .116 .082 .062 .045 4 .060 .090 .130 .176 .234 .154 .133 .100 .071 5 .038 .062 .079 .104 .141 .231 .175 .124 .081 6 .020 .029 .053 .068 .114 .162 .209 .157 .136 7 .014 .015 .023 .041 .067 .089 .122 .202 .157 8 .003 .011 .014 .022 .036 .045 .081 .119 .184 9 .000 .006 .007 .010 .023 .031 .045 .069 .089 10 .000 .003 .004 .007 .014 .020 .036 .052 .073 11 .000 .002 .003 .004 .005 .007 .018 .034 .069 12 .000 .001 .002 .003 .004 .005 .008 .014 .022 13 .000 .000 .001 .002 .003 .004 .005 .006 .017 14 .000 .000 .000 .001 .002 .003 .004 .005 .009 15 .000 .000 .000 .000 .001 .002 .002 .003 .005 16 .000 .000 .000 .000 .000 .000 .001 .002 .003 17 .000 .000 .000 .000 .000 .000 .000 .001 .002 18 .000 .000 .000 .000 .000 .000 .000 .000 .000 SUM 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Table 6 reports the ?could have been? smearing probabilities for a team?s   possible run support, given that it actually scored a specific number of runs   in the game.? The table is a partial reporting of these smearing probabilities   for the final scores (after 9 innings); there is a different smearing probability   array for each inning.

This table should be viewed by column only.? Each column represents the   probability distribution that the team could have scored any number of runs   (indicated by the row labels), given that it actually scored the number of   runs indicated by the column header.? For example, the first column (with   column header 0) indicates that a team that actually scored 0 runs in a game   ?could have? scored 0 runs with probability .338, 1-run .267, 2-runs .155,   3-runs .105, etc.? The bolded elements correspond to the ?could have? runs   scored being equal to the actual runs scored.

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 Run Scored (RS) Pct Park Adder 0 .000 1 .002 2 .004 3 .007 4 .010 5 .009 6 .008 7 .006 8 .004 9 .002 10+ .000

Table 7 shows how the effect of a home park on a team?s win probability   varies by how many runs it scores in a game.? As described above, the entries   were estimated empirically as the per percentage point park effect.? For example,   the Oakland Coliseum had a 97 park factor, indicating that runs scored were   generally 6% less prevalent than in a neutral park.? Thus, for games played   in Oakland the numbers in the table above would be multiplied by 6.? As the table   reflects, parks have a negligible effect on winning when a team is shutout   or scores 10 or more runs.? The park has the most effect when a team scores   around 3-7 runs.

[1]?   The win prob of a team with a lead of X runs is, of course, simply equal to   1 minus the win prob of a team facing a deficit of X runs.

Rob Wood Posted: August 19, 2002 at 06:00 AM | 0 comment(s) Login to Bookmark
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