October 25, 2007
Projecting the World Series
Changing Pitchers Changes Outcomes
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.