June 1, 2006

Schrodinger's Bat

Quantifying the Comeback

by Dan Fox

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"It was a crazy night, an outstanding game, and it shows character and heart. We have to keep it in our mind, and continue playing."
--Yankees closer Mariano Rivera on their May 17th comeback win

Who doesn't like a big comeback?

Even if you're not a rabid Yankees fan, you have to admire the tenacity and fight--not to mention the drama involved--when a team overcomes a 10-1 deficit in the third inning to come all the way back and record a 14-13 victory in front of the faithful on a walk-off home run in the bottom of the ninth with two out. It doesn't get much better than that.

With that in mind, some readers may be wondering--given the drama and human interest that is so deeply embedded in such sports spectacles--why we have to ruin these performances by introducing a bunch of esoteric numbers. Doesn't the quantification of the game make it less interesting? And further to the point, doesn't this obsession with performance measures and probabilities in the end reveal less a love for the game than a love for playing around with numbers?

This attitude was summed up by Buzz Bissinger in the preface of his book Three Nights in August when he says the following regarding living in a post-Moneyball world:

"front offices are increasingly being populated by thirty-somethings whose most salient qualifications are MBA degrees and who come equipped with clinical ruthlessness: The skills of players don't even have to be observed but instead can be diagnosed by adept statistical analysis through a computer...It is wrong to say that the new breed doesn't care about baseball. But it's not wrong to say that there is no way they could possibly love it...They don't have the sense of history, which is to the thirtysomethings largely bunk."

The short answer to these questions is that we humans quantify (and then classify) in order to make sense of the world around us. And, as it turns out, the ability to do so has proven to be quite successful in a whole host of human activities.

Rather than diminish our appreciation for achievements on the field, quantification--used effectively--serves to put these events into perspective and, in many cases, multiplies our reverence. Contrary to Bissinger, quantification serves as a framework for historical evaluation and yes, may even enhance our passion and respect for the history of the game (including among thirtysomethings like myself).

It is in that context that today we take a look at the biggest comebacks of the past 35 years. Quantitatively, of course.

Method to the Madness
Earlier this week we took a look at quantifying high impact performances using the Win Expectancy (WX) framework developed by Keith Woolner. Using that tool, we found that with a few caveats in mind--including the limitation of not being able to perform a what-if type analysis and the limitations of the technique when applied to defense--the highest impact plays of 2005 raised the win expectancy around 70%, most all of which were late inning home runs. We also showed that approximately 90% of the plays on the diamond affect the win expectancy by less than 8%. For the most part, wins are created through the accumulation of many plays over the course of a game.

But in considering the five highest impact plays of 2005, the Yankees/Rangers game mentioned earlier, although truly remarkable, would not have made the list. The reason is that while Jorge Posada's home run raised the Yanks' WX some 54%, their probability of winning was still 46% before the home run since they only trailed by one with the tying run on second. As improbable as the home run and win were, what was far more improbable was that the Yankees won at all given that they were trailing 10-1 entering the bottom of the third inning.

So today, we'll take a look at the three greatest comebacks in terms of WX from 1970 through 2005 (excluding 1999 since the data used for this article comes from Retrosheet). In other words, we've calculated the WX at each event in every game for those 35 seasons and culled out the lowest WX values for teams that eventually went on to win the game.

(For a different spin on comebacks using run differential take a look at this excellent post by Mike Carminati over at Mike's Baseball Rants.)

As a result, we hope that this provides some historical context, and yes, appreciation for these feats.

The Games
The following games rank as the biggest comebacks of the past 35 years in terms of WX.

• August 5, 2001 - Seattle at Cleveland. I'm sure many readers remember this game fondly since it is both fairly recent and was broadcast on ESPN (and rebroadcast thanks to the miracle of ESPN Classic). Ichiro Suzuki hit a two-run single in the top of the second to give the Mariners a 4-0 lead. They extended their lead to 12-0 in the top of the third by plating eight runs by starting the inning with six straight hits, a hit batsmen, and a sacrifice fly. The Indians also contributed a walk and an error by Omar Vizquel that let in two additional runs.

  In the fifth, they picked up two more runs matching those scored by Cleveland in the bottom of the fourth. The game stayed at 14-2 until the bottom of the seventh when Russ Branyan homered off of Aaron Sele to make it 14-3. It was at this point that the Indians, probabilistically, faced their biggest challenge. With two outs in the bottom of the 7th and trailing 14-3 their chances of winning stood at .0256%, or 1 in 3,905, the lowest point for any team that went on to win the game in the past 35 years.

  By the way, in the games studied, 4,876 teams actually found themselves at or below that probability (but not at zero) at some point in the game and the Indians were the only ones to stage a comeback.

  The rest of the story includes two additional runs in the 7th, four in the 8th, and five in the 9th to tie the game at 14 and send it into extra innings. The game-tying blow was a three-run triple by Vizquel with two down in the bottom of the 9th. Kenny Lofton then scored the winning run in the bottom of the fifteenth on a single by Jolbert Cabrera.

  The WX graph for that game is shown below.

  

• August 21, 1990 - Philadelphia at Los Angeles. This is probably a less well-known game but it is--quantitatively, anyway--almost the equivalent of the first.

  On that night, Phillies pitchers Jason Grimsley (yes he was the starter), Bruce Ruffin, and Darrel Akerfelds were rocked for 11 runs before retiring a batter in the bottom of the fifth, opening up an 11-1 lead. The low point would come with one out in the bottom of the 7th after Mickey Hatcher doubled to put runners on second and third. That low point was a probability of winning of .033%, or 1 in 3,027.

  The Fighting Phils would score two in the top of the eighth on a Von Hayes double to make it 11-3 as the game entered the ninth. In that ninth inning a walk and an error opened the door, followed later by another walk and another error (both errors by shortstop Jose Offerman, I might add). Mix in six hits and you have a recipe for nine runs and a 12-11 Phillies lead. Don Carmen came in to shut the door, recording his only save of the season.

  The graph of the game follows:

  

  Taken together, this and the previous game garner 50 of the top 60 lowest probabilities associated with events where a team has come back to win the game. In other words, from a level of difficulty perspective using WX, these two games stand head and shoulders above the rest.

• May 10, 2000 - Milwaukee at Chicago. On this day things were shaping up nicely at the Friendly Confines with the Cubs taking a 3-1 lead into the eighth inning on the strength of a nice performance by starting pitcher Kevin Tapani and solo home runs by Sammy Sosa, Mark Grace, and Willie Greene. Then the wheels fell off as the Brewers scored seven times in the eighth and ninth, the big blow a three-run homer by future Cub Jeromy Burnitz in the eighth, to give the Brewers an 8-3 lead they took into the bottom of the ninth.

  In that ninth inning, however, the Cubs' Jeff Reed and Damon Buford reached with two outs, bringing up pinch hitter Henry Rodriguez who smacked a three-run homer to make it 8-6. What was costly to the Brewers was that Buford reached on an error by first baseman Kevin Barker with two outs. However, just before Reed reached on a walk, the Cubs had nobody on base and two outs in the last of the ninth and were therefore at their lowest point, hovering at just .038%--equivalent to a 1 in 2,632 chance of winning the game. After the Rodriguez home run, three more walks and a second error by Mark Loretta on a Grace grounder scored the game-tying runs and sent the game into extra innings. All five runs in the bottom of the ninth were unearned.

  In the bottom of the 11th a walk, a wild pitch, and a Greene single to right sealed the deal for the Cubs.

  

  For Cubs fans wondering how this victory compares to "the Sandberg game" of 1984, you can see a WX graph on my blog. That game was characterized not by a larger comeback (the Cubs were "only" down 7-1 in the third inning), but by three separate comebacks in the 6th, 9th, and 11th innings courtesy of Ryno.

To round out the quantification of comebacks we'll summarize three others you may remember.

• June 10, 1974 - Pittsburg at San Diego. The Padres are down 8-0 in the top of the 8th with one out, sitting at .0812% (1 in 1,232). They go on to win 9-8.
• September 13, 1997 - Montreal at New York. Expos enjoy a 6-0 lead with two outs in the bottom of the ninth and are at .0901% (1 in 1,110). The Mets score 6 runs in the ninth, four on a grand slam by Carl Everett and go on to win 8-6 in the 11th on a homer by Bernard Gilkey.
• September 2, 1972 - New York at Houston. Mets are down 8-0 in the bottom of the 7th with two outs. Chance of winning: .1235% (1 in 810). They proceed to score 11 unanswered runs and win 11-8 in nine innings.

Against the Odds
In the end, putting numbers to accomplishments on the field helps us to understand those feats a little better. What the Indians, Phillies, and Cubs accomplished in those three games stands out both because of the drama of sport and also because of the improbability--an improbability that our human nature desires to quantify.