Every weekend I go on a bike ride in Irvine, which has more than 100 miles of protected bike trails, though there are occasional unprotected parts. This past Saturday, I was 5 miles into my ride when a car plowed into me.

The driver was evidently in a hurry to cross a street to get from one parking lot to another (perhaps the first lot was full?). He was focused on the cross-traffic he had to avoid and not paying attention to the hikers and bikers in front of him. Five hours later, I was in a trauma care center having one of my hips replaced.

After the operation, bedridden with plenty of discomfort and lots of time on my hands, I thought about the significance of luck in our lives. If I had been a few seconds earlier or later, the driver would not have hit me. On the other hand, if the driver had been driving a bit faster, I would now be dead.

The Paris Olympics, which finished on the weekend I was hit, provided many examples of how important luck can be. When Katie Ledecky won the 1500-meter freestyle by more than 10 seconds, she was clearly the best swimmer in this event — and has been for a long time. She hasn’t lost a 1500-meter freestyle race in 14 years. She has not merely been lucky.

In other Olympic events, the difference between gold and silver was a fraction of a second, a fraction of a centimeter, a fraction of a point. Noah Lyles won the 100-meter race by just five-thousands of a second, which is hardly convincing evidence that he is the “world’s fastest human.” Instead, he was no doubt lucky.

One way to think about the relative importance of skill and luck is to consider the consistency of the outcomes. If Ledecky swam the 1500 against her top competitors ten times, she would no doubt win every time. If Lyles were to race his top competitors ten times he would surely not win every time. He might win only once or twice.

Applying this metric to other sports

Thus, the relative importance of luck and skill can be assessed by the consistency of performance. For example, let’s compare how well Major League Baseball (MLB) teams do before and after the All-Star Break, which is roughly halfway through the season. If wins and losses are determined solely by skill, there will be a +1 correlation between the teams’ winning percentages before and after the break. If wins and losses are entirely due to luck, the correlation will be 0.

Ask yourself or a baseball enthusiast to estimate the correlation between first-half and second-half winning percentages. Most people recall some teams (like the Atlanta Braves) that win a lot of games and teams (like the Colorado Rockies) that lose game after game, and guess that the correlation is around 0.7, 0.8, or even 0.9. I looked at the 2023 season, and found that the correlation is only 0.59.

What about the National Basketball Association (NBA)? Is the correlation of team winning percentages before and after the All-Star Break higher or lower than in baseball? It seems that there is more randomness in baseball, with pitchers and batters playing guessing games, balls being hit directly at fielders or slightly out of reach, and much more. On the other hand, the baseball season is twice as long as a basketball season, and luck is more important in shorter seasons. I looked at the 2023‒2024 NBA season and found the correlation to be only 0.36. We are getting surprisingly close to 0.

For my last team sport, I looked at the National Football League (NFL). Most fans and bettors believe that teams that are winning will keep winning while losers will keep losing. The evidence contradicts that assumption so I was not surprised that, when I compared the team winning percentages for the first nine and last nine games of the 2023 NFL season, the correlation was the lowest yet: 0.32.

Most sports enthusiasts are surprised by how far these correlations are from 1. The surprising reality is that teams that have won most of their games often benefitted from good luck (that is part of the reason that they have won most of their games), while teams doing badly have had more than their share of bad luck.

One final correlation…  

Team sports can be affected by injuries and roster changes over the course of a season. Let’s look at golfers, specifically the 50 or so golfers who make the cut after two rounds of play in the annual Masters tournament — the one major tournament played on the same course every year — and see how well they do in the third and fourth rounds. These rounds are generally played on consecutive days (Saturday and Sunday). Injuries are rare and there are no roster changes. What do you expect the correlation to be between these top golfers’ scores in the third and fourth rounds? Many people think the correlation is higher than in the MLB, NBA, or NFL, especially since officiating vagaries are absent. They reason that golf is surely a test of skill, pitting each golfer against the course.

The correlation for the 2024 Masters is, in fact, negative, though, at -0.10, so close to 0 as to be essentially random. Yet we celebrate a golfer who wins one of the four major tournaments (Masters, US Open, British Open, and PGA Championship) as the “best golfer” in the world because we ignore the role of luck. In each tournament, any of a dozen or more golfers might win. Who does win is largely a matter of luck. That’s why there are so few repeat winners. As of August 2024, a total of 233 golfers have won at least one of the four major golf championships; 144 (62 percent) won once, and never again.

We should aspire to be more humble about our successes by recognizing that we likely benefitted from some good luck. We should aspire to be resilient after setbacks, recognizing that, sometimes, it was just bad luck and we need to move on.