Many professional sports have experienced a statistical renaissance
over the past 30 years. The advanced analytics
movement has been made famous by movies like Moneyball and the popularity of
fantasy sports. It even gets a fair amount of academic attention at events
like the MIT Sloan Sports Analytics Conference.
However, the secret underlying this statistical revolution
is that most of the analytics aren’t all that advanced. Most sports have cultures of tradition (and
superstition) that have led to some poor statistical reasoning becoming an
ingrained within each game. The
analytics movement is a true introduction to statistics for a group that has been suffering from making false assumptions.
A good example comes from football. The best defenses in the NFL tend to cause a
lot of turnovers (stealing the ball away from the other team’s offense by
fumble or interception). Focusing on
fumbles, defenses that recover more loose footballs tend to do better overall
(fewer yards allowed, fewer points allowed, etc.) each season. It can even be the difference between winning
and losing a couple games, which is a big deal with football’s short length of season.
In the past, teams and fans have treated a defense’s ability
to recover fumbles as a skill and teams that caused lots of fumbles would be predicted to have a great season. But
footballs are oddly shaped. When one
hits the ground during a game, the way it will bounce is unpredictable. Analyses of fumble recovery rates throughout
history show that the probability that the defense will recover a fumble is about 50%. So historically, a fumbled football can be
treated like a coin toss. Over the
course of a 16 game season, this creates plenty of opportunities for teams to get
lucky with the way the ball is rolling, recover more fumbles and have great
season. And for the teams that are
unlucky, they get to watch the Super Bowl from home like the rest of us.
Nowadays, knowledge of this phenomenon in football can
actually be used to predict which teams will do WORSE in a given year. This
is an example of regression to the mean: the more extreme a variable is upon
its first measurement, the more likely it is to be closer to the average the
second time it is measured. The NFL season is only 16 games long, which gives a pretty small window for collecting sample data. Within this window teams are likely to
benefit from fumble recover numbers that land well above the NFL average, simply
because of luck. The next season those
numbers are likely to regress back to the mean, since fumble recoveries are essentially
random over time. So teams that benefitted from an extra win or two due to fumble luck in 2015, might not experience the same bump in performance in 2016.
