Monday, July 26, 2010
The odds of winning streaks
Posted by Dave StudemanI received an email from a THT reader the other day. It went like this...
Can anyone share research about the odds of a third W after two home wins? And after two road wins?Sure can. I pulled the results of each major league game played from 2000 to 2009, ten years of relatively consistent playing conditions. Since I'm not quite sure exactly what our curious reader was asking, here are a couple of findings:
Record of teams who had won exactly two consecutive games at home and were playing at home:
1561-1274, a .551 winning percentage
Record of teams that had won at least two consecutive games at home and were playing at home:
2857-2256, a .559 winning percentage
Interesting stuff, right? But what are we to think? Well, first of all, those winning percentages aren't as impressive as they appear. Home teams win their games about 54% of the time overall—for the time period under examination, their specific winning percentage was .542. So a .551 winning percentage is only nine points higher than average.
How should we assess those nine points? I like to use something called the Odds Ratio. You can click on that link if you want to see the mathematical details, but suffice to say that when I plugged these results into my Odds Ratio calculator and I assumed that the competition was a .500 team (on average), I found that the "underlying" winning percentage of a team that had won two consecutive games at home was indeed nine points higher than average, .509.
In other words, if you know nothing about a team other than the fact that they have just won two games in a row at home, you can assume that the team is a .509 team. If you like to think about those sorts of things.
For teams that have won two or more games in a row (and following the distribution of winning margins inherent in the 2000-2009 seasons), that .559 winning percentage in the next game indicates that a .517 winning percentage is a good assumption for the "inherent talent" of those teams.
Geeky enough for you? Well, let's get back to the second part of the question...how do road teams perform using the same criteria?
Record of teams who had won exactly two consecutive games on the road and were playing on the road:
1087-1224, a .470 winning percentage
A .470 winning percentage isn't very impressive, but if home teams play .542 ball on average, that means that away teams play .458 ball on average, right? So, once again using the Odds Ratio, a .470 winning percentage implies that the team is actually a .512 team overall. In other words, if you know nothing else about a team other than the fact that it has won two games in a row on the road, you can assume it's a .512. The comparable figure for winning two home games in a row is .509.
Winning two on the road is harder than winning two at home, .512 is higher than .509, so this result makes sense to me. And now for something that threw me off my sabermetric know-it-all throne:
Record of teams that had won at least two consecutive games on the road and were playing on the road:
1724-1947, a .470 winning percentage
Here's the upshot: teams that have won two games in a row on the road were just as likely to win the next as teams that had won at least two games in a row. The extra wins were no proof of better things to come.
Let's back up. It seems to me that there are two, maybe three, things going on when contemplating team streaks. One is the team's true talent. If the team has won a bunch in a row, that indicates that they're better than average and future results will reflect that. The other thing to consider is returning to earth, or what mathematicians call regression to the mean. Teams can't keep winning forever; at some point they're going to lose again. They're going to return to earth.
The third possible thing to consider is momentum. I don't disbelieve in momentum, but I'm someone who believes that tomorrow's starting pitcher trumps today's momentum most of the time.
According to our results, it seems that true talent and regression play out differently at home and on the road. Consider the following comparisons in winning percentage for teams that have won a consecutive number of games at home vs. on the road (the winning percentage being their record in the game following the streak):
Consecutive
Wins Home Away
0 .534 .447
1 .542 .467
2 .551 .470
3 .563 .467
4 .570 .465
5 .588 .459
6 .602 .467
7 .550 .667
8 .563 .750
9 .500 .667
10 .000 --We're talking about some small sample sizes in the upper limits here, so take these breakouts with a grain of salt. But for home teams, the subsequent winning percentage of teams on a streak goes up from one to six wins, then comes back down to earth in the outer limits.On the road, however, there's no upward trend in winning percentage once you get past two wins (until you get to the seven-game range, which means next-to-nothing because not many teams make it there). The trend is pretty much flat.
So what's happening here? Have we statistically captured "momentum?" Is it more likely to exist at home than on the road? Is there some sort of mathematical concept that I've ignored here? Are people like me ruining baseball by over-analyzing it? Has this already been analyzed people are tired of talking about it?
Let me hear ya.
Dave was called a "national treasure" by Rob Neyer. Seriously. Comments about this article can be sent to him through the miracle of e-mail.
Seems like a correlation/causation problem. Wouldn’t it seem like winning streaks become increasingly more likely because in the past the teams who were able to string together a long winning streak simply were more talented, thereby having a higher average winning percentage in any given game?