[LINK] Cognitive Biases in Sports: The Irrationality of Coaches, Commentators and Fans

On a side note, this same friend has pooled some very interesting statistics about American sports. For example, if you plot the location of the pitcher's mound as a distance from home plate and you look at how that distance has changed over time, what you'll see is basically a perfect example of the bisection method for root finding, where in the case of baseball, the number that the pitching distance controls is the percentage chance of a given batter getting on base. The current pitcher's distance causes there to be about a 0.5 probability of any given batter making it on base, which is maximum entropy (maximum surprise) from a fan's perspective. Similar results hold for the specifications for field goal posts in football and the three-point line, free-throw line, and basket height in basketball. In basketball, these settings basically cause a 0.4 field goal percentage for all shots across all players in a game... again very good for high entropy and high scoring.

A lot of these examples aren't accurate. In baseball, the distance from the pitcher's mound to home plate was fixed at its current value (60'6") in 1893 (it was moved back then and once before because improved pitching technique had shifted the competitive balance between pitchers & batters), and batters reach base about 33% of the time. In football, kickers make over 80% of their field goals. The NBA three-point line has been moved repeatedly, but the free throw line has been fixed since 1894 and the 10-foot basket height was set even before that when they were still using peach baskets.

You're mistaking the stats that I am talking about. I am talking about taking one single baseball game and computing the number of times an at-bat led to an on-base. Over a season, teams and players converge to around 0.333, but in a given game generally half of at bats lead to being on base, through all means, not just hits. A given game yields an OBP of about 0.5 on average. The stats of moving the mound are indeed from before 1893, though tinkering with the height of the mound continued into the 1900s.

I made the assumption that rim height and free throw distance were moved around like the three point line. Thank you for pointing out my mistake.

0[anonymous]15y

I stand corrected about the 0.5 OBP. It is indeed 1/3. It's possible that I have my number wrong from my friend and that his data was meant to illustrate driving the OBP towards 1/3 rather than 1/2, in which case my intuition about entropy playing a role is just wrong. It's also the height of the mound that mattered though, and that was changed a lot in the 1900s, but yes, all the data on moving it back and forth was prior to 1893. I didn't say anything about NFL kicker accuracy, just that goal post dimensions were tinkered with to achieve an effect. That effect happens to be 80%, presumably for point scoring for fans. Again, free throws were moved from 20 feet to 15, and yes it was long ago, but the rule change was specifically for field goal percentage. In fact, the rule was also changed so that the fouled player had to take the shots, to prevent teams from having a single free throw ace. Thank you for pointing out the mistakes, though. I think the larger point that playing surfaces are tuned to achieve statistical regularities in performance holds. In fact, pro sports leagues wouldn't be able to sell their products if they didn't do this, which makes it all the more interesting that fans obsess over it. You're essentially paying them good money to ensure that a particular set of physical movements will generate a sufficiently random result such that you'll be captivated by seeing it unfold. It reminds me of the Chris Bachelder novel Bear v. Shark.

1pedanterrific15y

My goodness, just look at how unsourced all that is! It's almost as though you can't trust Wikipedia.