The Colorado Rockies were, by all appearances, an ordinary team on September 16. They’d won 76 games and lost 72 games. Since then, they’ve looked extraordinary, winning 21 of 22 games — 20 of them against teams with winning records.
They’re about to take that remarkable streak into the World Series against the Boston Red Sox. Le’ts consider just how unlikely the Rockies’ run has been.
Colorado Rockies infielders Jamey Carroll, top, and Kazuo Matsui celebrate after the Rockies finished their sweep of the Diamondbacks last week. Can the Rockies’ hot streak continue in the World Series? (AP photo)
Alan Reifman, a Texas Tech professor of human development and family studies who runs a blog called The Hot Hand in Sports, suggests using a binomial probability calculator to get a handle on the Rockies’ streak. These calculators answer questions such as, if you flip a coin 22 times, what are the chances you’ll get heads 21 times? The Rockies were, essentially, a fair coin on Sept. 16. So the probability of the run, according to a Vassar online calculator, is about one in 182,000. If we take the Rockies’ exact winning probability heading into the streak — 51.35% — we get one in 107,000.
Prof. Reifman suggests trying a different estimate that gives the Rockies more credit. What if we assume that, despite the record they actually had, the Rockies should have been expected to win 70% of their games? In that case, their streak is still a one-in-245 long shot.
No baseball team has ever had a streak this good so late in the season. That might seem to confirm a piece of baseball conventional wisdom, namely that hot teams such as the Rockies have a sort of momentum of winning that overcomes their underlying skill level and the historical record. But researches would argue the opposite: A hot streak such as the Rockies’ is just what one would expect to arise eventually if each baseball game were a flip of a coin, albeit a coin weighted according to the teams’ skill levels — just like if you flip a coin a couple hundred thousand times, you’d expect to see a run of 21 heads out of 22 at some point. And the Rockies overall have been no more streaky than you’d expect this season had their games been decided by coin flip, as Prof. Reifman wrote recently on his blog.
“These things happen,” Prof. Reifman told me. “This is one of those person-winning-the-lottery-twice kind of bizarre scenarios.” (It’s also akin to having triplets twice, without fertility aids.) That statement is supported by general research in the field, starting with a 1985 paper debunking the notion of streak-shooting in basketball, and running through a paper last year that reviewed the last two decades of research and found that “the empirical evidence for the existence of the hot hand is considerably limited.”
But there is one question such statistical techniques can’t answer: Are the Rockies merely by happenstance the team that sits on the edge of the bell curve (just lucky, as Tim Marchman recently wrote in the New York Sun), or is there something intrinsic to the team, at this time, that made it the one with the once-in-history hot streak? Prof. Reifman acknowledges that is a danger of writing off all such streaks as the product of sheer luck. For instance, he notes, the streak of 43 straight U.S. presidents being men was no accident.
What do you think? Were the Rockies lucky, or did they suddenly get much better? Is momentum in sports a real phenomenon? Will the streak continue against the Red Sox? Please let me know in the comments.
Footnote: Streakiness and momentum aren’t the only tenets of conventional baseball wisdom to collide with math. Fox analyst Tim McCarver expressed surprise during the Red Sox-Indians series upon learning that multirun innings are more likely when the leadoff batter hits a home run than when he walks. His assumption was that a runner on base affects the pitcher and batters psychologically, leading to a rally and multiple runs, while a leadoff home run makes everyone start with a clean slate. But the numbers show that it’s easier to get one more run with the bases empty, than getting two runs when starting with a runner on first base. Mike Kellermann, a Harvard graduate student, rounded up the reaction from blogs and showed that historical numbers side with the homer. Meanwhile, sports-statistics company Stats Inc. told me that in the 2007 regular season leadoff home runs led to multirun innings 28.4% of the time, compared to 27.2% of the time for leadoff walks.