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Primate Studies — Where BTF's Members Investigate the Grand Old Game Monday, August 19, 2002Win Values: A New Method to Evaluate Starting Pitchers  Part 5 Part
1: Introduction Empirical Data for AL 2000In 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>
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 19, 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(RARS, Z), for AL 2000>
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 1run behind varies depending upon what inning the game is in.? After 1 inning, the probability a team can expect to overcome a 1run 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 1run deficit can be expected to be overcome .344 after five innings, a 2run deficit .234, a 3run deficit .164, etc. Table 6: ?Could Have Been? Run Scored Probabilities, Smear(m;RS,Z), for AL 2000>
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, 1run .267, 2runs .155, 3runs .105, etc.? The bolded elements correspond to the ?could have? runs scored being equal to the actual runs scored. Table 7:? Pct Park Adders, PAddPct(RS), for AL 2000
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 37 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.

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