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?
I don’t have the time to do any analysis — I think we can get sometime order of magnitude estimates pretty quick — but what I was saying is that a worst case match up could favor a team by 4:1. That doesn’t mean that on average you’re that much ahead — most games are more evenly matched. It’s probably 5 or fewer matchups per year that result in 14+ point spreads.
Comment by Stephen | 8 February 2012
Also the it seems like baseball allows for more situations where a single very random event decides the game. A homer with bases loaded and two outs is game changing compared to getting an out there, amd it seems like the home run is an extremely hard to achieve “lucky” event.
The only equivalent I can think of in football is a hail mary, but you’re not going to see that more than once per game usually. But batters try to get HRs all the time in baseball. It seems like this random element that doesn’t have a clear analog in the NFL
Comment by Stephen | 8 February 2012
PS Fuck you, my trolling was great.
Comment by Stephen | 8 February 2012
For what it’s worth, ability to hit home runs is very much a reproducible skill, as is (pitching) ability to prevent home runs. There is of course a good deal of luck involved, but I’m not really comfortable labeling it a “random event” to a significantly greater extent than any other outcome of a given PA.
A truly totally luck-determined event in baseball would be something like a triple play. That requires a pretty unlikely confluence of events in order to happen; no matter how good you are, you aren’t turning three without two men on, and if you can do it with those two men not on first and second I’m very surprised. Then you’ll need a smashed line drive right at a fielder, and you need the runner coming from first to get so far up the line he can’t get back in time. And, of course, you need your dudes all to do the right things.
Comment by Darien | 8 February 2012
Yeah I spoke poorly. Let’s say it’s a skill based probabilistic event with high variance. So any given at bat is unlikely to result in a homer, but you can hit two in one game or go 10to games without and neither is crazy unlikely.
There’s really nothing similar in football that I can think of. There are things like a pick six that are huge game changers so maybe that’s similar?
Comment by Stephen | 8 February 2012
Also I just realised something I’ve been getting super wrong. When we say that 40% of a team’s record is luck, that’s not a range from neutral to high luck — it’s a range from very poor to very good with neutral in the middle. So you’d expect an overpowering favourite to win 80% of the time rather than 60%, since luck can only tip negative by 20%. I think.
Math is hard.
Comment by Darien | 8 February 2012