How Much Does Luck Matter In Sports?

Luck, especially in reference to sports, is an extremely subjective term. Everyone has different views of luck, and as a result, it’s hard to agree on which teams might have gotten the most or least lucky. My goal was to create something that would remove the subjectivity from luck and instead turn it into an objective formula. Let’s get right into it.

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1. The Formula

With this goal in mind, I created something I like to call the LUCA rating, which stands for Lucky vs. Unlucky Classification Average. (Yes, I tried to name it after Luka Doncic, but there aren’t many words that start with K.) The rating measures how much a specific team’s season was affected by luck in terms of win percentage. For example, if luck gave a team three extra wins throughout a nine-game season, its LUCA rating would be .333. You get the point.

The formula mainly stems from Bill James’ Pythagorean Winning Percentage, which determines the number of games a team should have won, in a specific season, based on points scored and points allowed. James’ formula goes as follows:

Points Scored = PS

Points Allowed = PS

Win Percentage (more on this later) = wPCT

Pythagorean Win Percentage = p-wPCT

Absolute Value (more on this later) = | … |

MLB p-wPCT: PS¹.85 / (PS¹.85 + PA¹.85)

The equation is simple- reward teams with a big run differential and punish teams without one. However, the exponential number depends on a number of things: how many games are in a specific sport’s season, the average number of runs scored per game, and numerous other factors. As a result, the overall formula is different for every sport. Here are the values for each of the “Big 4” American sports (if you’re looking for the MLB’s, scroll up):

NBA p-wPCT: PS¹⁹.31 / (PS¹⁹.31 + PA¹⁹.31)

NFL p-wPCT: PS².37 / (PS².37 +PA².37)

NHL p-wPCT: PS² / (PS² + PA²)

Once I figured out these formulas, the rest was pretty simple. To determine how much different the Pythagorean winning percentage was from the regular, we just had to subtract them. Finally, we had to take the absolute value of our answer, because for this article’s sake (or at least for the beginning of it) luckiness and unluckiness are treated the same, it just depends on how much of it you have.

So there you have it! Here are all of the final formulas:

Got it? I hope so. Let’s move on.

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2. The Questions (and Answers)

There were three main questions that I wanted to answer by the end of this experiment, and I’ll answer them one-by-one with the data I found using the formula. First off, I wanted to find out which sports were the most and least luck-dependent. I thought it would be interesting to try and find out if certain sports were more luck-dependent than others, and why that might occur.

In order to find this out, I calculated every single team’s LUCA rating (which can be found on this spreadsheet), added up each league’s teams, and divided it by the number of teams in each league (30 for the NBA and MLB, 31 for the NHL, and 32 for the NFL). That gave us a league-wide average LUCA value for every single sport, which would show how much a random team’s winning percentage would be affected by luck.

The most luck-dependent sport was the NFL, as according to the data, about .077 of a given team’s winning percentage had to do with getting lucky or unlucky. Out of every single league, the NFL’s season is by far the shortest, which likely played a big role in it placing first in our rankings. With a longer season, it’s a lot more likely for the luck to even out by the end of the year, which would bring its final rating closer to zero.

One other thing about the NFL that differentiates it from other sports is its overtime rules. In the NBA, NHL, and MLB, both teams have a chance to get the ball in overtime, but in the NFL, if the first team scores a touchdown it’s over. As a result, a lot of overtime games are decided by a single coin flip, which certainly qualifies as luck.

The second-most luck-dependent sport was the NHL, with a .057 final rating. Hockey games are typically pretty low-scoring, so a lucky goal or two would end up playing a huge role in a game’s final score. The NHL’s seasons are also the second-shortest, as each team played only 56 games throughout the entire season.

Finishing just behind the NHL was the NBA, with a league-wide LUCA rating of .052. NBA refs have been under massive pressure as of late with players like James Harden and Trae Young doing their best to draw every foul call they can. As a result, a lot of referees can make bad or unnecessary calls, leading to a couple of easy points.

And finally, the least luck-dependent sport was the MLB, running away with the title with a league-wide rating of .041. Unlike the other three sports, there are no referees calling fouls or penalties. (Yes, umpires can affect the game, but usually on a much smaller scale than your average NBA or NFL ref.) Baseball also has the longest season of any sport, nearly ten times as long as the NFL, and most games are decided by three or four runs, not one.

The next question I wanted to find an answer to was which teams got the most and least lucky this past season. To find an answer to this, I just had to remove the absolute value signs from the initial formula, because luckiness and unluckiness wouldn’t be treated the same anymore.

In the NBA, three of the luckiest teams in the league were the Cavaliers, Magic, and Kings. On the complete flip side, some of the more unlucky teams this season were the Raptors, Jazz, Nuggets, and Clippers. I found it interesting that a lot of the lucky teams were near the bottom of the standings and the unlucky ones were near the top of the standings because I thought it would be the other way around.

The NFL, however, ended up in a completely different way, and the way I was expecting. Most of the lucky teams were near the top of the standings- not to say that all good teams got lucky, just that it’s more common to see a lucky team make the playoffs than miss it. Teams like the Titans, Bills, and Packers, all division winners, were extremely lucky this past season, while the Jaguars, Texans, and 49ers were some of the NFL’s most unlucky teams.

The NHL and MLB both followed similar trends, as both their unlucky and lucky teams were spread all throughout the standings. Some standout teams included the Wild, Panthers, and Mariners (lucky), and the Capitals, Diamondbacks, and Twins (unlucky). Again, you can find the full list here if you want to look at a specific team.

The one final thing I wanted to learn was what causes teams to get lucky. I touched on this earlier in the article in relation to each sport, but I’ll list some of the more prominent things that can affect a team’s final winning percentage.

• Overperforming/underperforming expectations
• Umpires calling balls and strikes
• Foul calls by referees
• Length of a season
• Length of a game
• Dropped passes
• Coin flips
• Errors
• Etc.

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3. The Conclusion

My main takeaway from this is that luck really does matter. Of course, it isn’t as important as having a good team or performing well, but it can definitely impact a team’s performance a lot more than you might think. There are plenty of external factors that can affect your team’s luck as well, such as what referee or umpire shows up to your game, a certain type of weather that might hurt your performance or a fluke injury.

However, luck is becoming less and less prevalent with the introduction of new technology. A bad call by a referee is likely to be overturned by instant replay. Even the MLB is starting to move to robot umpires, with many independent leagues already making the switch. Only time will tell how prevalent luck will be in the future, but for now, it’s as important as ever.