## Contemplating "Streakiness": Does a win streak predict itself?

Win Streaks are a common occurrence in baseball, as are losing streaks. The 2010 Tampa Bay Rays won 96 games last year with a maximum win "streak length" of 7 games. Despite having the best record in the American League, however, the Rays still had many many losing streaks, the longest of which was 5 games. The question at hand is whether these streaks are meaningful in a predictive sense.

We here announcers insist that "the team's on a hot streak so the opposition better watch out" or that a team's lost several games in a row so they "aren't playing well" all the time, implying that a team on a hot/cold streak is more/less likely to win their next game. That being said, we hear the same things said about hitters all the time, but as The Book showed, they have little to no predictive value.

First some notes about how streaks are going to be examined and some implicit assumptions.

• Games can be part of more than one streak, i.e., if the Rays win games 1, 2, and 3 then games 1 & 2 and games 2 & 3 constitute two different streaks.
• The season's total win percentage is being used as the team's true talent win percentage. Although this is probably not true, it's probably at least reasonably close.
• Opponent team's strengths are being ignored. Although this is the biggest flaw in the methodology, the computation simply gets to be too complex if attempts are made to account for this.

To evaluate "streakiness", we will first look at the raw number of win streaks versus the expected number. It stands to reason that if streaks are just the product of random variation, they won't happen at a rate too different than what is expected. To calculate the expected number of streaks if each game was an independent event, binomial distribution is used.

 Streak Length Rays xStreaks 2008 Rays Streaks 2008 Difference Rays xStreaks 2009 Rays Streaks 2009 Difference Rays xStreaks 2010 Rays Streaks 2010 Difference 2 58 58 0 43 47 4 58 57 -1 3 35 31 -4 22 25 3 35 34 -1 4 21 17 -4 11 13 2 21 22 1 5 12 9 -3 6 5 -1 12 13 1 6 7 4 -3 3 3 0 7 6 -1 7 4 1 -3 2 1 -1 4 2 -2 8 3 0 -3 1 0 -1 3 0 -3

The table above is pretty clear. In almost all circumstances, the number of streaks is almost identical to the expected number, and indeed is lower in most cases. This suggests that streaks for the Rays haven't occurred anymore than we might expect if each game was an independent event.

More directly, we can examine the Rays' win percentages immediately following a streak. If streaks are in any way predictive, we would certainly expect a team to win games more often when they're "running hot".

 Streak Length 2008 Rays WP After 2009 Rays WP After 2010 Rays WP After Total 2 53.4 53.2 59.6 55.6 3 54.8 52 64.7 57.8 4 52.9 38.5 59.1 51.9 5 44.4 60 46.2 48.1 6 25 33.3 33.3 30.8 7 0 0 0 0 8 N/A N/A N/A N/A

The columns above show the Rays' win percentage in the game immediately following a streak of length in the left column. The results here are pretty clear: in none of these situations have the Rays found themselves significantly more likely to win a game than their 57 win% over the last three years would suggest, and in many cases the Rays win less often following a win streak than they do in an average game.

When a fair coin is tossed 162 times, even it can be expected to have one streak where it lands heads more than 7 times in a row. And yet, after it has landed heads 7 times, no one would claim that the coin has "momentum". Although this can't disprove the notion that a win-streak is predictive, based on the information we have, there's no reason to believe that the Rays have had any more momentum than a coin that lands heads 57% of the time.

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