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October 25, 2007

Projecting the World Series

Changing Pitchers Changes Outcomes

by Clay Davenport

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Since I've gotten a lot of e-mail about the postseason odds and their nod to the Rockies as a favorite-more questions than I can readily answer, certainly-I thought I'd take a look not only at that, but a number of other projections as well.

Of the various formulations we have, many of which Nate touched on here, the one I think is most likely to be useful is the Elo post-season odds report. At the close of the season, Boston had a commanding 1564-1539 advantage over the Rockies. The postseason has not substantially changed that gap-Boston's Elo has increased to 1579, up 15 points, while Colorado is up 17 to 1556. Colorado's superior post-season record, 7-0 to Boston's 7-3, is offset by Boston's beating better teams. Playing out the World Series through Elo standards would make Boston a 58-42 (percentage) favorite.

That still doesn't address the specific matchups these pitchers would have on the opposing lineup. The earlier reports used the fact that Boston was 25-23 against left-handed starters this year, compared to 71-43 against right-handers, to build in an advantage against righties and a disadvantage against southpaws. The Rockies were even more lopsided in their splits-20-24 left, 70-49 right. The thinking behind the playoffs odds reports was that the Rockies were not going to be treated as a .552 club; they were going to be treated as a .503 club against lefties and a .570 club against righties, in each case averaging the club's overall record with their specific handedness record. The Red Sox likewise went from being a generic .593 to being either .557 or .608. Things were adjusted even more with specific pitchers; a Morales/Matsuzaka matchup, in particular, was tilting very strongly in the Rockies' favor, and was the key reason why they were showing as favorites.

Of course, the news from this morning once rosters were set that the Red Sox do have a good chance of starting a lefty, in the person of Jon Lester, as a replacement for the injured Tim Wakefield, and that the Rockies would not use lefty Franklin Morales, choosing to go with Aaron Cook instead, undid all of that logic. Going with rotations of Beckett, Schilling, Matsuzaka, and Lester for Boston, and using Francis, Jimenez, Fogg, and Cook for the Rockies, the odds turn to show a 59-41 Boston advantage.

I'd like to get even more specific in reviewing the teams. Let us assume, for working purposes, that the demonstrated left/right splits each player had this year was genuine, as was their Equivalent Average during the season. I'm going to use their EqAs from the player cards, adjusted for all-time; for the pitchers I'll take their all-time NRA as gospel, and convert it into an equivalent EqA. If the player spent significant time in the minors (as Ellsbury, Jimenez, and Spilborghs did) I also include his DT-EqAs from the minors. Although we're starting to cut the data into dangerously small samples, we can establish an expected EqA for each pitcher/batter matchup, based on how each of them did in split fashion. Let me work one out in detail: David Ortiz versus Jeff Francis, for example.

David Ortiz, overall, had a .355 EqA this year, which resolves into a .381 against right-handed pitchers and .289 against lefties, an unusually large split. Francis' numbers, converted into EqA terms, works out to a total EqA of .236, with .243 against righties and .210 against lefties. To put those together into a batter-pitcher confrontation, I converted them into win percentages, where an average player is .260. Turning EqAs into, essentially, offensive win percentages (OWP) is a very simple matter; you pretty much use the Pythagorean formula, with an exponent of 5 instead of (2 for the normal pythagorean, times 2.5, because runs are EqA eqato the 2.5 power).

So, to skip English for a second, Ortiz comes out like this: .289^5/(.289^5+.260^5) = .629 OWP against left-handed pitchers. Francis boils down to: .260^5/(.260^5+.210^5)=.744 win percentage against left-handed hitters. Use the Log5 of a .744 team against a .629 team, and you get a .632/.368 split. Ortiz in this case is the .368, and you can run the pythagorean math backwards to figure out that his EqA against Francis should be .233. Ouch.

Anyway, I've done the above math for all the starters and expected players, so let's see where that takes us. From this point on I don't know the results ahead of time; I'm calculating and writing in real time.


Game One, in Boston
Colorado vs Beckett        Boston vs Francis
Taveras      .210          Pedroia      .285
Matsui       .233          Youkilis     .272
Holliday     .271          Ortiz        .233
Helton       .292          Ramirez      .336
Atkins       .241          Lowell       .276
Hawpe        .280          Drew         .188
Tulowitzki   .223          Varitek      .266
Spilborghs   .213          Ellsbury     .200
Torrealba    .198          Lugo         .226
Average      .243                       .259

Colorado doesn't have any options to raise their average; Sullivan's expected EqA would be .209, less than Spilborghs, but then he also doesn't overtake Spilborghs in any of the potential matchups. If Crisp were starting, his expected .255 would be a marked improvement over either Drew or Ellsbury. As is, this plots out to a 57.9 percent chance of a Boston win. Note that the average needs to be calculated with each value raised to the 2.5 power, not that it makes that big a difference between calculating with a straight average.


Game Two, in Boston
Colorado vs Schilling       Boston vs Jimenez
Taveras      .225           Pedroia     .264
Matsui       .246           Youkilis    .279
Holliday     .290           Ortiz       .412
Helton       .309           Ramirez     .261
Atkins       .258           Lowell      .282
Hawpe        .296           Drew        .323
Tulowitzki   .239           Varitek     .302
Spilborghs   .228           Ellsbury    .304
Torrealba    .211           Lugo        .221
Average      .260                       .301

Crisp (.279) should be on the bench in this game. This is a .675 win percentage for the Sox, ruthlessly exploiting Jimenez' .240/.281 right/left split with four lefties (including the switch-hitting Varitek). At this point, there's a 39.1 percent chance of Boston being up 2-0 in the series, 13.7 percent that they're down 2-0, and 47.2 percent chance of a 1-1 tie.


Game Three, in Colorado
Colorado vs Matsuzaka       Boston vs Fogg
Taveras      .235           Pedroia     .284
Matsui       .254           Youkilis    .300
Holliday     .304           Ortiz       .378
Helton       .318           Ramirez     .281
Atkins       .270           Lowell      .304
Hawpe        .305           Varitek     .277
Tulowitzki   .250           Ellsbury    .279
Torrealba    .222           Lugo        .237
Average      .273                       .296

None of Boston's pitchers have much of a split; Beckett's .214 vs RHBs and .226 vs LHBs is the largest at 12 points. However, none of them can match Fogg's zero split, .258 and .258. I chose to utilize the Youkilis in right field gambit, but for this particular matchup Youkilis, Lowell, and Drew (.297) are essentially the same on offense. This rates as a .600 Boston win, so our total odds stand at Boston possibly being up 3-0 23.4 percent of the time, up 2-1 44.0 percent of the time, Colorado up 2-1 27.1 percent, and Rockies up 3-0 in only 5.5 percent of the simulations.

If this had been the Morales matchup that I had anticipated, Boston's score was going to be .265, giving the Rockies one favorite for a game. Instead, we get this:


Game Four, in Colorado
Colorado vs Lester         Boston vs Cook
Taveras       .292         Pedroia      .281
Tulowitzki    .292         Youkilis     .296
Holliday      .300         Ortiz        .341
Helton        .240         Ramirez      .278
Atkins        .258         Lowell       .300
Spilborghs    .311         Varitek      .250
Matsui        .233         Ellsbury     .252
Torrealba     .236         Lugo         .234
Average       .273                      .282

The splits here dramatically favor putting Spilborghs over Hawpe (.208) in the lineup, so I made that move for Clint Hurdle. Likewise, I let Drew and his .268 take the fall in the no-DH sweepstakes. This is a .540 Boston advantage, so our totals are now at a 12.7 percent chance of a Boston sweep, a 34.5 percent shot of there being a 3-1 Boston lead, 34.9 percent for a 2-2 tie, 15.4 percent for a 3-1 Rockies lead, and 2.5 percent possibility of a Colorado sweep.


Game Five, in Colorado
Colorado vs. Beckett      Boston vs Francis
Taveras     .210          Pedroia      .285
Matsui      .233          Youkilis     .272
Holliday    .271          Ramirez      .336
Helton      .292          Lowell       .276
Atkins      .241          Varitek      .266
Hawpe       .280          Crisp        .255
Tulowitzki  .223          Ellsbury     .200
Torrealba   .198          Lugo         .226
Average     .247                       .269

The rematch doesn't have the DH, and this time we'll assume that Ortiz (.233) sits out and that Crisp plays over Drew (.188), letting the defense get the maximum value by having both Crisp and Ellsbury out there. This breaks .605 Boston's way, so we now have a 20.9 percent chance of Boston in five games, a 34.7 percent likelihood that they're up 3-2, 23.1 percent chance that Colorado leads 3-2, and a 6.1 percent that the Rockies are cracking champagne corks at this point.


Game Six, in Boston
Colorado vs Schilling     Boston vs Jimenez
Taveras     .225          Pedroia      .264
Matsui      .246          Youkilis     .279
Holliday    .290          Ortiz        .412
Helton      .309          Ramirez      .261
Atkins      .258          Lowell       .282
Hawpe       .296          Drew         .323
Tulowitzki  .239          Varitek      .302
Spilborghs  .228          Ellsbury     .304
Torrealba   .211          Lugo         .221
Average     .260                       .301

No change from Game Two seems like an obvious choice by both managers to me, so let's repeat it. What that translates into is a 67.5 percent Boston advantage, which means that Boston takes Game Six to clinch 23.4 percent of the time, we're tied at three games apiece 26.9 percent of the time, and Colorado just won the whole shebang 7.5 percent of the time. (The remaining 42 percent of the time the Series is already over).


Game Seven, in Boston
Colorado vs. Matsuzaka    Boston vs Fogg
Taveras     .235          Pedroia      .284
Matsui      .254          Youkilis     .300
Holliday    .304          Ortiz        .378
Helton      .318          Ramirez      .281
Atkins      .270          Lowell       .304
Hawpe       .305          Drew         .297
Tulowitzki  .250          Varitek      .277
Spilborghs  .239          Ellsbury     .279
Torrealba   .222          Lugo         .237
Average     .269                       .296

Adding the DH back into the mix doesn't help the Rockies this time around, as they don't have the spare bat to take advantage of it-a common problem for National League teams. Game Seven breaks .617 Boston's way, which translates into 16.6 percent of the total, while the Rockies win in seven 10.3 percent of the time.

The grand total across all of the variable outcomes works out to a 73.6 percent chance that Boston wins the World Series, against Colorado's 26.4 percent shot. So there you have it, my best estimate at a ridiculous amount of matchup detail.

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