David R. Henderson  

Sports Outcomes and Randomness

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One thing I notice in most sports commentary about the game I love watching most on TV, NBA basketball, is how little awareness there seems to be about the role of randomness. The Golden State Warriors and the Cleveland Cavaliers are clearly first-rate teams and are clearly better than the Philadelphia Seventy-Sixers, the New York Knicks, and the Los Angeles Lakers.

But are the Cleveland Cavaliers better than the Golden State Warriors? That's hard to say, just as it's hard to say that the Golden State Warriors are better than the Cleveland Cavaliers. In their 7-game playoff, each team won 3 games by wide margins. By the end of 6 games, each team had scored exactly 610 points. In the one very close game, the 7th game, Cleveland won by 4 points. And if Kyrie Irving had not made an incredible 3-pointer in the last minute, the game would have been tied.

Warriors' coach Steve Kerr, being the gentleman and good sport that he is, said in the press conference afterwards that the better team won. I don't think that's clear. And if the Warriors had won by a thin margin, I would also not have said that the better team won.

Randomness happens.

I wrote about randomness in sports earlier here.


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COMMENTS (16 to date)
Matthew Moore writes:

Depends what you mean by 'the better team', and by 'random'

In sport, the better team usually means the better team on the day. This isn't a tautological statement. There is substantial within-team variation in quality from day to day, due to reasons that are probably largely group-psychological, but not random.

My introspection leads me to think that, if a pair of teams play 100 times and each win 50, the best team probably won about 80% of the time. In the overall series, maybe the teams do have the same average ability. But in any one day, there is probably a substantially better team.

Walterb writes:

If a clutch 3-pointer is a random event, the players should just sit on the bench and watch the ball randomly propel itself through the hoop.

Michael Byrnes writes:

Walter wrote:

If a clutch 3-pointer is a random event, the players should just sit on the bench and watch the ball randomly propel itself through the hoop.

It is random in the sense that Kyrie is a very good career 3-point shooter... and he still misses more than 60% of his attempted threes. He's been better in the playoffs though (shooting 44%)... but still has missed more playoff threes than he has made.

David R. Henderson writes:

@Walterb,
If a clutch 3-pointer is a random event, the players should just sit on the bench and watch the ball randomly propel itself through the hoop.
No. Because if they’re on the bench, the probability that they will score, or defend against a score is zero. 0 is less than 40%.

Mark Bahner writes:

More games were played at Golden State, but Cleveland still took the series. (Hooray!)

But I'll certainly admit Cleveland's offense looked terrible...especially in the last quarter or so. Too much standing around (and a long way from the basket!) without the ball.

It has to be one of the most improbable team come-from-behind situations of all time.

P.S. Steve Kerr is a class act.

P.P.S. And what a killer he was in the last seconds with the Bulls. In those days, if the Bulls were down by less than 10 points with 2 minutes to go, I'd know they were going to win.

Walterb writes:

David, if they sit there long enough, there is a probability of 1 that the entire game will play itself without their intervention.

Brandon Berg writes:

True, but right or wrong, there's no way for the coach of the losing team to say that and not look like a sore loser.

Andy writes:

Vegas lines know which teams are the best because sentimentality loses them money (though bettors sentimentality makes them money). And we can use prices to aggregate all the information directly instead of doing very loose descriptive statistical analysis like this post.

The Warriors were 5 point favorites at home and 2 point underdogs in Cleveland. They would be favored in a neutral arena though it would be close. They were the best team this year.

Floccina writes:

One reason that I do not like the 3 point shot is that I think it increases randomness to above the optimum level. There were wider margins in finals this year, I think due to the 3 point shot.

David R. Henderson writes:

@Andy,
Vegas lines know which teams are the best because sentimentality loses them money (though bettors sentimentality makes them money). And we can use prices to aggregate all the information directly instead of doing very loose descriptive statistical analysis like this post.
Take out the word “know” and soften it a little and this is a really good point.
The Warriors were 5 point favorites at home and 2 point underdogs in Cleveland. They would be favored in a neutral arena though it would be close. They were the best team this year.
Good point again.

jj writes:

When you say randomness, do you really mean unpredictability? I don't see how true randomness (e.g. Brownian motion, dice throws) affects basketball.

David R. Henderson writes:

@jj,
When you say randomness, do you really mean unpredictability?
I mean that it’s probabilistic.

mike davis writes:

I suspect that sports commentators, especially former athletes, are very aware of the role of randomness. They just don’t talk much about it because sports fans just don’t want to hear much about it. Why that might be true is an interesting question.

As I understand it, cognitive psychologists are convinced that we have a strong tendency to underplay the role of luck in our lives, at least when it comes to success (“I got that job because I’m awesome. The fact that the guy who would have ripped my job talk to shreds had the flu on the day of my seminar had nothing to do with it.”) Of course we overplay the role of luck when things go badly, but apparently these are not symmetric—on average we overweigh the importance of skill. I’m pretty sure, too, that the evo-psych crowd has a good story to explain this. (People hard-wired to overestimate the role of skill are going to try harder than people who think life is one big crap shoot. People who try harder get to have more sex.)

Teams become an extension of ourselves. That’s weird but also kind of nice, since it makes watching sports so much fun. Given that we project our own psychological characteristics to the teams we admire, we should expect most sports talk to be about skill, not luck.a

Thomas Sewell writes:

The probabilistic randomness of sports outcomes is the chief (serious) argument made for not increasing goal size in soccer.

Based on the number of "almost" goals, shots off the post, etc..., it's empirically clear it would increase the number of times the "better" team wins if the goal was made larger (width and/or height), up to some constraint related to ability to shoot successfully past a typical goal keeper from longer and longer distances.

The reason I've been given why a change in goal size isn't adopted is that in order to have fans in general (not just fans of the best team) more engaged and have a more enjoyable experience, it's preferred that there is as high a chance as possible the not-best team can win, consistent with keeping the overall impression the game isn't so random that skill doesn't matter.

I find this empirically true, in the sense that everyone paying attention knew Venezuela was the better team against the US the other day, but US fans are right to watch anyway, just in case that miracle occurred.

At the same time, the US plays Columbia for 3rd place today, after having lost 2-0 to them in the group stage (despite winning the group overall). Who is the better team? The US has the opportunity today to prove or disprove the earlier result as the "fluke" in fan's minds (despite the fact that it'd take many more trials to really prove it).

It's similar to the reason board games with some randomness are preferred, vs. totally deterministic games. People like to feel like they have at least some chance of winning, even if they aren't the best. Think Cataan vs. Diplomacy.

David R. Henderson writes:

@Thomas Sewell,
Interesting points. I think you mean Argentina, not Venezuela.

Thomas Sewell writes:

@David R, Henderson,

Yes, meant Argentina. For some socialist-related reason I had Venezuela on the mind while writing that. :)

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