Monday, August 3, 2009
Guarantee Revealed
Back on April 27, I made the following proclamation.My bold prediction: The Yankees will beat the Red Sox at least once this season. Book it.
The Yanks had dropped their third straight game against Boston in 2009 at that point. Of course, they've since lost another five games, and are winless in eight games. If we assume the two teams are essentially equal talent-wise, the odds of that happening are around one in 250.
Anyway, since we're all getting antsy about the Yankees ever beating Boston, I figured I should take my guarantee one step further and reveal the game the Yankees will win. I've decided it will be part of the upcoming four game series at home.
I could have just done this using POOMA, but I think it's better if I go about it empirically. So the first thing I did was re-project the starting lineups for both teams going forward, then figured out how many runs per game we would expect each lineup to score in an average game based on these new projections.
| Lineup | PA | AVG | OBP | SLG | BR | Outs |
| jacoby ellsbury | 5 | .294 | .343 | .414 | 0.7 | 3 |
| dustin pedroia | 5 | .306 | .366 | .448 | 0.7 | 3 |
| victor martinez | 5 | .285 | .364 | .450 | 0.7 | 3 |
| kevin youkilis | 5 | .291 | .394 | .515 | 0.8 | 3 |
| david ortiz | 5 | .265 | .367 | .508 | 0.8 | 3 |
| jason bay | 5 | .265 | .366 | .490 | 0.8 | 3 |
| j.d. drew | 5 | .264 | .375 | .458 | 0.7 | 3 |
| jason varitek | 4 | .234 | .336 | .421 | 0.5 | 2 |
| nick green | 4 | .246 | .285 | .391 | 0.3 | 3 |
| total | 42 | .272 | .355 | .455 | 6.0 | 27 |
I'm giving the Red Sox their best possible offensive lineup here, which means sitting Mike Lowell for Victor Martinez and Jed Lowrie for Nick Green. That lineup projects to score around 6.0 runs per game.
| Lineup | PA | AVG | OBP | SLG | BR | Outs |
| derek jeter | 5 | .308 | .378 | .430 | 0.7 | 3 |
| johnny damon | 5 | .280 | .357 | .460 | 0.7 | 3 |
| mark teixeira | 5 | .285 | .383 | .532 | 0.8 | 3 |
| alex rodriguez | 5 | .273 | .393 | .540 | 0.9 | 3 |
| hideki matsui | 5 | .268 | .359 | .468 | 0.7 | 3 |
| jorge posada | 5 | .280 | .369 | .485 | 0.8 | 3 |
| robinson cano | 5 | .303 | .340 | .473 | 0.7 | 3 |
| nick swisher | 4 | .240 | .361 | .452 | 0.6 | 3 |
| melky cabrera | 4 | .276 | .334 | .407 | 0.4 | 2 |
| total | 43 | .279 | .364 | .472 | 6.3 | 27 |
This version of the Yankee lineup looks to be a touch better than the Red Sox's over 27 outs, at 6.3 runs per game. And yes, I'm aware that the starters won't play all four games for both teams, but this is all hypothetical anyway.
The Yankee defense has actually been better than Boston's this year, according to both ZR and UZR. However, I've incorporated the defense into the pitching projections that follow so I won't treat it separately here.
The next thing to do is estimate runs allowed per game by the pitching staff. The assumption here is that each starter will pitch around their average innings pitched per start in 2009 while allowing their re-projected runs allowed pro-rated to those innings. Remaining innings to get to nine will be filled by the top relievers on the team, using one inning for closer, one inning for setup man, then remaining innings to be adjusted accordingly. Obviously, the top relievers won't pitch in every game, but they should pitch in any game with a lead. Since I'm trying to figure out the probabilities of winning each game, I'll stick with the top relievers exclusively.
Thursday, August 5: Smoltz vs. Chamberlain
| Pitchers | IP | R |
| john smoltz | 5.2 | 2.66 |
| manny delcarmen | 0.8 | 0.34 |
| takashi saito | 1 | 0.34 |
| hideki okajima | 1 | 0.40 |
| jonathan papelbon | 1 | 0.32 |
| total | 9 | 4.06 |
And yes, I'm aware that pitchers can't pitch 5.2 innings or 0.8 innings, but innings have to add up to exactly 9 so that's how I made it work.
| Pitchers | IP | R |
| joba chamberlain | 5.5 | 2.35 |
| mariano rivera | 1 | 0.30 |
| phil hughes | 1 | 0.42 |
| alfredo aceves | 1 | 0.43 |
| phil coke | 0.5 | 0.23 |
| total | 9 | 3.73 |
Since we now have an estimate for runs scored per game and runs allowed per game for both teams, we can use Pythagenpat to calculate an estimated winning percentage, then use log5 to estimate the probability of each team winning that game.
For the Red Sox, that means their Pythagenpat exponent for this game is (6.0 + 4.06)^.287 = 1.94, and their estimated winning percentage is 6.00 ^ 1.94 divided by (6.00 ^ 1.94 + 4.06 ^ 1.94) = .681. For the Yankees, their Pythagenpat exponent for this game is (6.3 + 3.73)^.287 = 1.94, and their estimated winning percentage is 6.3 ^ 1.94 divided by (6.4 ^1.94 + 3.73 ^ 1.94) = .734. Before factoring in homefield advantage (+ 0.02 to home team winning percentage, - 0.02 to road team), that means the Yankees should have a 55.3% probability of winning this game. Add in homefield and the probability would go to 59.3%.
Friday, August 6: Beckett vs. Burnett
| Pitchers | IP | R |
| josh beckett | 6.8 | 3.10 |
| hideki okajima | 1 | 0.40 |
| jonathan papelbon | 1.2 | 0.39 |
| total | 9 | 3.88 |
| Pitchers | IP | R |
| a.j. burnett | 6.3 | 2.95 |
| mariano rivera | 1 | 0.30 |
| phil hughes | 1 | 0.42 |
| phil coke | 0.7 | 0.33 |
| total | 9 | 4.00 |
As fascinating as the detailed breakdown of the math involved surely is, I'll just put the estimated winning percentages here.
Yankees: .510, .550 HFA
Saturday, August 7: Buchholz vs. Sabathia
| Pitchers | IP | R |
| clay buchholz | 5.1 | 2.70 |
| hideki okajima | 1 | 0.40 |
| jonathan papelbon | 1 | 0.32 |
| manny delcarmen | 1 | 0.42 |
| takashi saito | 0.9 | 0.31 |
| total | 9 | 4.15 |
| Pitchers | IP | R |
| c.c. sabathia | 6.7 | 2.72 |
| mariano rivera | 1 | 0.30 |
| phil hughes | 1 | 0.42 |
| phil coke | 0.3 | 0.14 |
| total | 9 | 3.58 |
Yankees: .577, .617 HFA
Sunday, August 9: Lester vs. Pettitte
| Pitchers | IP | R |
| jon lester | 6.3 | 3.10 |
| hideki okajima | 1 | 0.40 |
| jonathan papelbon | 1 | 0.32 |
| manny delcarmen | 0.7 | 0.29 |
| total | 9 | 4.12 |
| Pitchers | IP | R |
| andy pettitte | 6 | 3.22 |
| mariano rivera | 1 | 0.30 |
| phil hughes | 1 | 0.42 |
| phil coke | 1 | 0.47 |
| total | 9 | 4.41 |
Yankees: .494, .534 HFA
So overall, here's what the numbers say.
| Game | % | %HFA |
| Sat, Aug 8 - Sabathia vs. Buchholz | .577 | .617 |
| Thu, Aug 6 - Smoltz vs. Chamberlain | .553 | .593 |
| Fri, Aug 7 - Beckett vs. Burnett | .510 | .550 |
| Sun, Aug 9 - Lester vs. Pettitte | .494 | .534 |
| Total | 2.134 | 2.294 |
Good news, as the Yankees should win 2.3 games against Boston over the weekend.
Looking at these numbers, I'm therefore going to guarantee that the Yankees win the game on Saturday August 8, with the caveat that you can't predict baseball.
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