Part   1: Introduction
  Part   2: Conceptual Framework
  Part 3: High-Level Results
  Part   4: Formulas
  Part   5: Empirical Data for AL 2000
  Part 6: Example: David Wells in AL 2000
  Part   7: Yearly Results for 1978-2001
  Part   8: Top Stars
  Part   9: Concluding Remarks

David Wells in AL 2000

In this section I will provide the details of the Win Value calculation for   a specific pitcher.? Doing so will allow the reader to gain a greater appreciation   of the method.? David Wells in 2000 is the example I will use.?

Wells went 20-8 for the Toronto Blue Jays and led the league in wins, despite   a 4.11 ERA.? WAA, based largely upon Wells? fairly high ERA, is 2.1.? Win   Values is able to evaluate Wells? season on a game-by-game basis, so is better   able to give a more accurate evaluation of Wells? contributions to the Blue   Jays that season.? Wells accumulated a 3.33 Win Value since he did a good   job of ?managing? the runs support he received each game.

Table 8: David Wells? 2000 Game-by-Game   Win Values

*?? Z is the last inning David Wells appeared in;   so that partial innings, including facing one or more batters without recording   an out, count as a full inning.?

** The score is at   the conclusion of both halves of the Zth inning; my method evaluates performances   by the whole inning, not half-innings.

Let me describe Wells? first game to make sure the reader understands the   method and what is being reported in the table.? The first row indicates that   Wells started at home against Kansas City on April 3.? Wells lasted into the 7th inning,   and the score at the conclusion of the 7th inning was 4-2 in favor of Toronto.?

By using the empirical probabilities of winning when leading by a certain   number of runs at the conclusion of the 7th inning, together with the ?could   have been? run scored smearing probabilities, I estimate that Toronto had   a .776 chance of winning that game based upon the score at the conclusion   of the 7th inning.

The next column of the table asks what was the probability that Toronto would win a game given   that it had scored 4 runs at the conclusion of the 7th inning, with league   average pitching.? By using the empirical probabilities of winning when scoring   a certain number of runs at the conclusion of the 7th inning, together with   the ?could have been? run scored smearing probabilities, I estimate that Toronto   had a .502 chance of winning such a game with league average pitching.

The Park Adder is reported in the next column.? In 2000, Toronto?s home park was a   slight hitters park.? The Park Adder of .013 is based upon the park factor,   the number of innings Wells pitched, and the number of runs Toronto scored in those innings.?   As described above, the Park Adder is an estimate of the additional win probability   differential of Wells? contribution given that the game that day was in a   slight hitters park.

The final column gives the Win Value for each game.? It is the estimate   of the additional win probability that Wells contributed that day over what   a league average pitcher would have been expected to contribute.? Algebraically,   the .286 Win Value for the April 3 game is .776 (the win prob of the game   with Wells? performance if it were in a park-neutral setting) minus .502 (the   win prob of the game with league average pitching if it were in a park-neutral   setting), plus .013 (the additional win prob differential due to the effect   of the home park).? Wells? Win Value for the season is simply the sum of the   Win Values for each of his starts.

The game that Win Values deems to have been Wells? largest contribution   (.621) during the season was the April 8 game at Texas.? Wells pitched a complete game shutout   and the Blue Jays beat the Rangers 4-0.? The game that Win Values deems to   have been Wells? worst contribution (-.446) was his last start of the season   on October 1 at Cleveland.? Wells was knocked out in the third inning, at the conclusion of which   the score was 7-2 in favor of the Indians.?

It may be interesting to note that Wells also received a significant   negative Win Value (-.415) for a game in which he was the winning   pitcher.? On June 17, at Fenway Park the Blue Jays and Red Sox engaged in a classic slugfest.? Ramon Martinez started   for Boston but was knocked out in the 4th inning.? David Wells lasted a little longer,   but was knocked out in the 7th inning with Toronto leading 11-10, which turned out to be the   final score.? The Win Value approach penalizes Wells for almost squandering   what should have been a sure-win (11 runs of run support).?