Eugene Fisher October 12, 2018

If you were to put sports and games on a continuum, where the outcomes reflect pure skill on the right side, and pure luck on the left side, where would the big team sports go? Somewhere in the middle right? But in what order? There’s actually a way to estimate that using statistics, and this is where they end up.

“What you find is the NBA is the sport that’s farthest away from random, and then you go down the line and hockey is actually the sport that’s closest to randomness.” Michael Mauboussin did these calculations for his book, The Success Equation, and his findings remind us what we love so much about these sports. Mauboussin’s continuum is based on the regular season for each league. And he found that skill explains less than half of the season standings for the NHL.

But that’s not to say hockey players are any less skilled. “All these athletes, all these players are amazing. Amazing. Almost inconceivable how good they are.” The continuum doesn’t tell us how skilled the players are, it’s more like how well their sport measures their skill.

So a big factor is the sample size, or the number of games in a season. Major league baseball teams play 162 games. Compare that to the NFL, where teams play only 16 games.

The small sample size pushes football toward the luck side of the continuum, since it’s harder for skill to emerge from the noise with so few trials. But the number of games doesn’t explain everything. Both the NHL and the NBA play 82 games in a season. So their placement has more to do with the dynamics of the game itself.

Like the number of chances teams have to score during the game– that’s another type of sample size. “Basketball, they’re coming down, and they have a shot clock and they have to take lots of shots. They’re forced to take shots, so there’s a lot of samples that go back and forth. Ice hockey of course is much more fluid, possessions are much less discrete.” They don’t even have a way to measure possessions in hockey, which gives you a sense of how little sustained control those players have.

The number of players matters too. Tennis is a sport where skill plays a much bigger role, in large part because there simply aren’t many people involved. That’s why Serena Williams could hold the number one rank for 186 consecutive weeks from 2013 to 2016. When skill dominates, outcomes are more predictable. In a sport like swimming or sprinting, the activities are even more individual.

Essentially racing a clock. There’s nothing standing between the athlete’s skill and their ranking. But in team sports you have more players and lots of interactions. And what matters isn’t just how many are on the field at a time, but how possession is distributed among a team’s players over the course of the game. Baseball requires the nine hitters on a team to take turns at bat. “Ideal would be, wouldn’t it be awesome if our best hitter hit every time?

And our weaker players never play at all. In basketball, in a sense, you can do a little bit of that. I mean, not quite, but you can have LeBron James playing most of the game, whereas the very best hockey player, Sidney Crosby, is going to be on the ice 22, 23 minutes per game. He’s their superstar.

Hockey is inherently really fast and erratic, so even the best players need to rest, putting some limits on how much their skill can influence the results. Whereas in football you have the quarterback involved in every offensive play. “I think football does boil down to a few skilled players, typically. And I would say probably the quarterback – head coach combination becomes the most important determinant or predictor of success.” And then you have the question of the talent pool. Basketball inherently rewards unusually tall players. This chart shows the height and weight of different positions in different leagues.

These are NBA players, and here’s the height of the average American man. “So what happens is you shrink your sample size, in anything, a small sample size, you get a lot of variance. So saying that differently, there are 7-ft players that are really skillful, and there are 7 foot players that are not quite as skillful, and they’re both in the NBA by virtue of their height.

As a consequence you get more variance and so skill tends to assert itself more.” Soccer and hockey don’t require such an outlier body type, so you’d expect less variance in player skill. And that leaves more to luck. To understand what that means, you have to see how Mauboussin calculated all this. “I learned this, by the way, from the sports analytics guys, so I wasn’t clever enough to come up with this myself. But there’s a really interesting concept in statistics called pythagorean theorem of statistics.” It says that you have two random, independent variables, then you can add their variances.

Variance is a measure of how spread out a dataset is. For our purposes, the equation looks like this: The variance of the observed, real life results equals the variance of skill plus the variance of luck. Skill plus luck equals everything that happened. “So you think about how do we apply this to sports, and we’ll use basketball as an example. So what do we know? We know the actual variance of win loss records of all the professional sports teams right?

Basketball teams. So that’s a known.” Over a season, some teams win about half of their games, some do a lot better than that, some a lot worse. So if the variance is a measure of how spread out those win-loss records are for the league, you can see that you have more variance in basketball than hockey. The other part of the equation estimates what the results would be in an all-luck world.

“So if instead of playing every basketball game, the teams just went out and flipped a coin, and whoever won the coin toss, and they went back and took showers and went home.” The variance of luck varies from sport to sport depending on how many games are in a season. More games mean lower variance of luck, just like the more times you flip a coin, the closer your data gets to 50-50. “Now we have two out of the three pieces of the equation, and what that allows us to do is then estimate the contribution of the other distribution.” Basically what this asks is: how different does the real world look from a world in which the winners are just chosen at random? He averaged the results of 5 seasons for each sport, and that’s how he placed them on the continuum. If you were to look at just the playoffs rather than the regular season, you might get a different result. According to one analysis, baseball playoffs are the worst at ensuring the best team wins.

Which raises the question of what we want our sports to do. Do we want to measure skill as precisely as possible? Or do we just want to feel alive?

“We’re there to enjoy the journey, right, to have both the highs and lows, and having the highs and lows is kind of what makes it engaging as a fan. I think that’s part of the whole human condition that makes it really fun for us to watch.