I’m a football fan… well, more specifically the NFL. I hear that colleges other than the one I went to actually have their own teams and that quite a lot of people think that the outcomes of these “college football games” are important, but I never saw the appeal. Anyway, as I said, I follow the NFL. This year, as the season has proceeded, I’ve found myself noticing quite a few long winning and losing streaks occuring this year. With 2 teams reaching 10-0, and a few teams having streaks of 6 and 7 wins (or losses), I decided to track the actual numbers and determine just how abnormal this season is.
Using one of the many available NFL statistic sites, I was able to compile the number of streaks that occured at each of the 10 lengths available at week 11 (which was just completed). Note that only 10 games have been played by each team at this point, and that I ignored the bye week, allowing streaks to continue through the bye uninterrupted. The following are my results:
Now, to determine how abnormal this year is (so far), I first have to determine what the expected count for each of the streak lengths is. I must admit, I had to seek outside help determining what this should be, as my first few attempts bore rotten fruit. Luckily, there are some helpful folks at MathOverflow, one of which was able to find a solution:
|I know, these numbers seem small, given that I’d expect HALF of the 2-game sequences to be a 2-game streak. The trick here is know that every 3-game streak has two 2-game streaks inside it which don’t count!|
Now, let’s compare the two sets of values. I’ve found a great little charting tool for small sets of data over at Google. Here’s what it comes up with:
Hmmm, these don’t seem to be very different, do they? As you can see, it seems this season isn’t very abnormal at all; with only moderate drops in the number of 1- and 2-game streaks to account for the obvious outlier of having 2 undefeated teams this late in the season. Each streak length is very close to the expected count for that length.
There would seem to be several reasons one could come up with for why long streaks should occur in football: the literally outstanding talent on certain teams compared to others, the non-random nature of scheduling often pitting teams against obviously “unfair” set of opponents, even the difference between having to play certain teams at home or at the away park with largely varying weather. Yet it seems that the schedule is “fair”, that the teams are well matched. The math we’ve done here has shown that my anecdotal musings of unusually large streaks are without basis. How cool is that?