Golf Performance and Regression to the Mean

Regression to the mean is a statistical principle that was first discovered when studying the size of seeds and the height of parents in relation to their offspring. So, what does this have to do with sport performance? Why does statistical probability fool us into lowered confidence, misinterpreting reason and wrongly jumping to conclusions?

Regression to the mean states that if a variable is extreme on the first observation, it will be closer to the average on the second measurement, it will regress toward the mean. For example a professional golfer’s average score is 70. In a tournament one golfer shoots 63 and another golfer shoots 77.

63 —> 70 <— 77
Extreme —> Mean <— Extreme

Regression to the mean states that the next time these golfers play, both their scores will be closer to their average than their original outliers. The more extreme the original score, the more regression you can expect. The reason for this?

Performance = Ability + Luck

We like to explain performance through ability. The golfer who has the most fluid, powerful swing and a delicate touch around the greens. But what is often ignored and underrated is the role luck and randomness plays. A lucky few bounces or a few putts that drop in the edge of the hole rather than lipping out.

This is because our mind is strongly biased towards cause and effect explanations rather than rational, statistical probability, otherwise called a:

Narrative fallacy – A tendency to explain things through stories

One famous example of this is the Sports Illustrated jinx – An athlete who gets on the cover of sports illustrated becomes jinxed and performs badly the following season. When this happens, it triggers our associative memory to search for explanations that result in this poorer performance, such as increased pressure, overconfidence, fame and distraction. But regression to the mean provides a simpler explanation. To get on the cover of Sports Illustrated you must perform exceedingly well through high ability and a reasonable amount of luck. While ability remains pretty stable, luck and a whole host of unimaginable uncontrollables also play a role which means performance does not stay the same forever.

The narrative fallacy also creates a problem with feedback. Negative feedback is often followed by better performance and positive feedback followed by poorer performance. This leads to conclusions being drawn that negative feedback helps performance and positive feedback is ineffective, but what is most likely is that performance is unaffected by the feedback. It is simply that to receive either positive or negative feedback, the performance was extreme and either much better or much worse than usual and the next attempt is just closer to average, it regresses to the mean.

How can you make this principle work in your favour?

Bob Rotella wrote about Stuart Anderson, a high school basketball player who knew he was a 50% shooter:

“After I missed one, I figured the next one was likely to go in. After I missed two, I was overdue. By the time I’d missed five, I figured the next one absolutely had to drop. Every time I missed, I figured the odds were increasing in my favor.”

“Okay,” the student said. “If that’s how you think when you miss your first shots, what do you think if you make your first six or seven in a row?”

“That’s totally different,” Stuart said. “You decide that tonight’s your night, you’re on a hot streak, and you’re going to make everything you look at.”

“That’s ridiculous,” the student said. “You can’t have it both ways.”

“Of course you can,” Stuart said.

The golfer should imitate this mentality. If you miss a few putts, it can only mean you have a higher chance of holing the next one, you will regress to the mean. But if you make a few, trust you’re on a hot streak and ignore this statistical principle.

Rational when performance is poor. An optimistic outlook and a protective mechanism for confidence.

Irrational when performance is good? Perhaps, but great athletes create their own reality. Elite athletes shift the rules to seemingly work in their favour so positive thinking becomes a self-fulfilling prophecy.

For more on how to improve your Mindset, Confidence and Performance, get in touch!