Randomness and sports
You following the comments on my Super Bowl post? Stephen tried to troll for, like, a really long time, but after that didn’t work out for him he got down to business and took me to school on football analysis. You should read that. It’s good.
I have difficulty accepting Stephen’s assertion that a team could (in the real world) have (before a game begins) an 80% chance of winning that game. I am insufficiently competent at math, analysis, and intelligence even to know how to begin solving this riddle, but I would like to explore it for a bit. One caveat before we begin: I am not swayed by appeals to authority. No need to bother telling me that lots of experts say so. I like logic and data.
To start with, let’s take a look at Tangotiger’s mind-bending analysis of the role of luck in baseball standings (Note to long-time Darien fans: I finally found this goddamn article! Why I never thought to Google "tangotiger luck" defeats me). First, I’d like to mention that you can be sure this is strictly scientific because of the line "they are identical because god told you." God comedy aside, I’ve examined the math and the data, and it’s all correct to the best of my ability. I can see no way of avoiding Tango’s conclusion: 40% of a team’s record is luck.
Now, football is not baseball. The season is only 16 games long, for one thing, which will inevitably increase — dramatically — the effect of luck on the final standings (anecdotally, as a Bears fan who watched the Bears shitheadedly cling to that division championship last year in the face of an obviously superior Packers team, I can attest to the value of luck in really annoying the Packers fans I work with). But we’re not talking about standings — we’re talking about one game. And this is where I end up sailing completely out to sea.
Football is not baseball in one other very important way: there is no bat. The way the ball is put into play in football is far, far less random than in baseball — in most cases, the ball goes pretty much where it’s meant to go, whereas in baseball there’s no way to tell beforehand. So I can accept that football is, at the individual-game level, less random than baseball. But by so much that we can go from 40% luck to < 20% luck? Or am I understanding the math wrong here? Is there some way that the season standings can be 40% luck without the average individual game also being 40% luck?
These are for-reals questions, by the way. I’m not trolling. Based on my extremely feeble grasp of statistical theory, it seems extremely unlikely that a team can even approach 80% likely to win a game before it starts. So what am I missing?
