That's a pretty decent introduction, and it would definitely leave an impression on someone who hadn't heard about heuristics and biases before. Sadly, they left out one bias that greatly affects the accuracy of sports commentary: ignorance of regression to the mean.
I played high school football in Indiana and was also very good academically. I suffered quite a bit of heckling from teammates for being a "nerd." I also have a friend who is a grad student with me now that had a similar experience growing up in Colorado and he had a very good way of describing the typical coaching strategy:
Say you are a basketball coach with 4 players all lining up to practice their free throws. Suppose all of them usually have an accuracy of about 85%, which is pretty good. In the first 10 attempts, though, it could easily be the case that Player 1 happened to miss a lot and only made 4 shots, Players 2 and 3 happened to make 7 and 8 shots respectively, and player 10, through statistical oddity, happened to make all 10 shots.
The coach will usually do the following: because Player 1 made the fewest shots, the coach will yell or offer some kind of critical instruction. Because Player 4 made all 10, the coach will offer praise and positive comments. The other two players are more or less where they should be, so the coach won't really single them out for extra attention.
Due to regression to the mean, as the number of free throw attempts gets large, all the players will converge to their expected percentage of 85%, making between 8 and 9 shots out of every 10. What will the coach believe has happened?
Yelling or being critical of the player who randomly got off to a bad start must have caused that player to improve and pick up the slack and get back up to the usual level. Praising the player who randomly got off to a good start caused them to slack off and drop back down to the normal level. Not saying anything to the two who got off to a normal start ultimately had no effect.
So, if you're a coach, yelling makes bad players do better and praising makes good players do worse. Thus, regression to the mean will reinforce the idea that you should just yell at the people doing below average. I found this to be a particularly illuminating way to look at it. This may also be true for bosses in a typical work environment.
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.
Basically, your athletic skill only matters to get you into the pro game. Once you're there, the statistical settings of the playing surfaces makes it essentially a random competition. This is less true in college sports where talent distributions are more skewed, but still plays a role.
The rationalist in me wishes we would just have competitive coin flipping and get it over with.
The rationalist in me wishes we would just have competitive coin flipping and get it over with.
That would be awesome. However, it would not have the results you expect at all. I can bias a coin that I flip to about 60%; some professional magicians can do 95%+.
Basically, your athletic skill only matters to get you into the pro game. Once you're there, the statistical settings of the playing surfaces makes it essentially a random competition. This is less true in college sports where talent distributions are more skewed, but still plays a role.
Perhaps, but the data you present don't constitute evidence for this proposition. In fact, the only reason they appear to support the above statement is because of cognitive anchoring to talking about probability and especially the probability 1/2, which somehow feels more random then other probabilities. If anything, having the pitcher's distance set so that on average 1/2 the runners make it to first base makes tiny differences in skill more significant.
Agreed, this conclusion is a non sequitur. Regardless of what the average success rate is, some players and teams are more skilled than others and will consistently succeed at a higher rate. People are much better than 50-50 at predicting which team will win a game (and there is a large industry centered in Las Vegas which depends on accurate estimates of these probabilities), which shows that it's not just random.
But there's already much more than a tiny variation in skill among the 50% of runners who make it on base. I think the statements indicate a broader trend: among athletes who are collectively within the same skill class, the arrangement of the playing surfaces play a more dominant role than individual variation in athlete skill.
I think the statements indicate a broader trend: among athletes who are collectively within the same skill class, the arrangement of the playing surfaces play a more dominant role than individual variation in athlete skill.
This is trivially true of you define skill classes narrowly enough. If the non-trivial claim your trying to make is that the class of all professional athletes is such a skill class, you have yet to present any valid evidence for your claim.
I am taking all pro athletes to be in the same skill class purely as my own approximation. I haven't supplied any evidence because I don't have any and I didn't claim that I did. I only have the loose statistics that my friend showed me in a few charts for the presentation he is making. I thought it was obvious from my post that I was speculating a plausible explanation given what appears to be evidence that the physical parameters of games have evolved to produce certain statistical regularities in performance.
When you move away from professional caliber athletes, these statistical regularities go away (i.e. pro baseball has a total on-base percentage of about 0.5 but high school baseball is much less). My personal experience playing high school and college sports leads me to believe that as the skill level increases, the variance among the participants goes down rapidly. I felt it was reasonable to extrapolate from this for the sake of an anecdotal comment on a discussion post.
But by all means, if you need every statement I made to be qualified with direct evidence, you should seek better sources than my off the cuff remarks. I never claimed otherwise.
I felt it was reasonable to extrapolate from this for the sake of an anecdotal comment on a discussion post.
It would if the anecdotal comment was at least Bayesian evidence for the claim in question.
But by all means, if you need every statement I made to be qualified with direct evidence, you should seek better sources than my off the cuff remarks. I never claimed otherwise.
I didn't expect scientific evidence. What I do expect is for valid evidence of some kind, even anecdotal. Your statement was a complete non sequitur. Sorry, if this wasn't clear.
Agreed, this conclusion is a non sequitur. Regardless of what the average success rate is, some players and teams are more skilled than others and will consistently succeed at a higher rate. People are much better than 50-50 at predicting which team will win a game (and there is a large industry centered in Las Vegas which depends on accurate estimates of these probabilities), which shows that it's not just random
This is not relevant at all. I am saying that there will be a 0.5 OBP for the game as a whole, not for specific players or teams. The statistics I am talking about having nothing to do with predicting variations in talent within the game.
I actually conjecture that the two of you are committing a non-sequitur by bringing in gambling odds. Do you have statistics about how successful gambling odds have been at predicting the winner or the point spread? Just because there is a business that dreams up the odds does not mean that those odds wind up actually being good predictors of the game. Why do we have million-to-one upsets every season if this is true? Wouldn't we have to wait for millions of games to have upsets of that magnitude?
The statistical regularities I am talking about are properties of the whole competition itself. And I specifically mentioned that one of my premises is that talent distribution is more balanced in pro sports than in college. How accurate are these odds predictions in pro sports? And how much more accurate are they in college? If college is significantly more accurate than pro, then that certainly is Bayesian evidence for my claim.
The fact that a large gambling industry regularly sets odds for games other than 1:1 is one piece of evidence that the outcomes depend on skill and are not essentially random (analogous to a coin flip). The Vegas favorite does win substantially more than 50% of the time (I could look up a citation if you really doubt that), but there are also plenty of other pieces of evidence besides gambling odds. For instance, teams' winning percentages have more variability than you'd expect if they followed a binomial distribution with p=.5 (as they would if games were a coin flip). Teams' winning percentages one season are strongly correlated with their winning percentages the next season. Similar patterns hold true for other statistics that are kept for teams (like points per possession) and for statistics that are kept for individual players. There are also some teams that are consistently successful year after year (like the Yankees, Lakers, and Patriots), and some players whose statistical performance is consistently impressive (like Albert Pujols, LeBron James, and Peyton Manning).
Of course randomness also plays a significant role in the outcomes, but that doesn't mean that skill is irrelevant. In sports like baseball, basketball, and football, a game consists of many little events with a moderate probability of success where a player's skill influences their chance of success by a few percentage points. Over the course of a game, these differences accumulate so that the more skilled team wins maybe 70% of their games on average (more when there is a wider disparity in skill, less when the teams are more evenly matched). There are differences between sports based on the nature of the game (in baseball the better team wins more like 60% of the time) and there are differences between levels of competition (as you say, there are wider ranges of ability at the college level and so the better team wins more often). Over the course of a season, the best teams are generally able to emerge and win enough games to make the playoffs (some average but lucky teams make the playoffs as well). Luck plays a large role again in the playoffs, since there are fewer games and teams are often more evenly matched.
The way to go beyond this analysis is to look more closely at the data, as has been done (e.g.) here.
My only point was to speculate that the playing surfaces are engineered to bring about an "optimal" amount of randomness. The link you provided seems to support that the randomness is actually there. Whether it's perfect 50/50 or instead 42/58 is just splitting hairs. I still believe that my reasoning was sound. Given that I see random outcomes in sports, the arrangement of the playing surface is a reasonable candidate explanation. Under the premise that athletic talent does not vary widely enough for talent to be the better explanation (which, whether right or wrong, was the premise I had been assuming), it makes organization of the playing surface a more likely candidate. This is why I disagree about it being non sequitur.
I was not claiming that the playing surface dictates every microinteraction within a game and that all of them come out as 50/50, just that the game is engineered to be a sellable product, and without randomness it would not be as marketable. I was claiming that talent is not the primary factor, but to be clear, I think that if talent comprises only 58% of the explanation for a team's record, as the link you provide suggests, that my conclusion is totally appropriate. Talent might be a larger piece of the explanation than chance, but if it is not much much larger than chance, then it's fair to use natural language to describe talent as not being the primary factor. If you want to split hairs over my linguistic choice to embed thresholds into that statement, that's fine. But it's still a reasonable conclusion.
The rationalist in me wishes we would just have competitive coin flipping and get it over with.
My understanding is that controlling a coin flip is an existing magic/sleight-of-hand technique; might not be a very good spectator sport, though.
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.
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.
The rationalist in me wishes we would just have competitive coin flipping and get it over with.
+1 for making me laugh.
The rationalist in me wishes we would just have competitive coin flipping and get it over with.
You may be onto something here.
Sports is not a good example, because it's entertainment (fun!), so logic is not the most important thing there. Even a rationalist needs to let go sometimes and allow his/her cognitive biases run wild on occasion. Being Spock 100% of the time is boring. This applies only to fans and commentators, not coaches.
On a totally unrelated note, Go Canucks, Boston sucks!
I'd take fighting out of hockey.
That's not an action. "If I were commissioner, I would write a rule suspending anyone who engaged in what I or referees considered to be fighting for ten games on each offense," describes an action one not fighting could perform - writing - that would influence the situation.
Not discussing the mechanism you'd use makes the argument too nonspecific. It's like saying "If I were President, I'd fix the economy."
I did not elaborate because it would be too far off-topic. Yours is one way to do it. There are many other way to make the utility of fighting negative for everyone involved. In any case, getting rid of fights is infinitely easier than fixing the economy (European and international hockey does quite well without them, showing that it is not that hard).
Being Spock any of the time is boring, but being rational about things doesn't demand killing their entertainment value.
Being Spock any of the time is boring, but being rational about things doesn't demand killing their entertainment value.
No way. You can do badass martial arts. Bring on the Spock!