Every fan of any team in the history of team sports has said the following phrase after a loss: "We just got unlucky tonight." How much merit does this statement have? I personally don't really believe in luck. I think instead in terms of variance. Imagine this example: if I were to flip a coin four times, there is a 50% chance I would get heads once and tails once. There is a 25% chance I would heads twice, and a 25% chance I would get tails twice. If I repeat this experiment over the sample of 100 coin flips, the probability of me getting heads less than 45 times is 18.41%, while the probability of me getting heads more than 55 times is the same. In the NBA, every possession is worth about 1.1 points, and there about 100 possessions per game. We can use these numbers to assume that scoring on a possession is worth about 2.2 points on average. So, back to the coin flip example. If we look at scoring on a given possession like flipping a coin (as the chance of scoring on a possession is about 50%), then we can see why people might say their team got "unlucky." 18% of the games (about 21 per season), your favorite team will give lose about 11 points in a game based on shooting variance. 18% of the games, the opposing team will also gain about 11 points based on shooting variance. These swings can not only change singular games, but they can swing entire seasons.
The game that I will show you to understand how much this can swing a game is the Rockets-Spurs game from Thursday. In that game, the Rockets won 109-105. However, the Rockets had an Effective Field Goal percentage of 56.4%, while the Spurs had a 50.5% eFG%. The Rockets shot 13-33 (39.4%) from 3 and 12-19 (63.2%) from the free throw line. The Spurs, on the other hand, shot 9-31 (29%) from three and 12-16 (75%) from the free throw line. It would be easy for a Spurs fan to say they lost simply because they suffered from bad luck just by looking at these numbers. However, the Rockets are also just a better shooting team than the Spurs, they pick their spots more effectively, and they got to the line more often for more efficient points. When looking into the numbers and adjusting the score for expected overall team shooting by zone (including shots at the rim and short vs. long mid-range shots), I calculated the Spurs would have scored 108.738 points and the Rockets would have scored 109.089 points if both teams shot at their team average from each zone on the court.
That number I just listed is inherently flawed. Different players shoot different shots at different percentages. The Rockets were also missing high usage players in that game, so the team numbers aren't necessarily indicative of what we should expect from that team. To get a more accurate picture of what an "average" night should have looked like, we need to adjust the numbers based on who was shooting the ball and where they were shooting. Doing this is fairly simple, it just takes a little bit of effort. When looking at the game this way, I found that the Spurs were expected to score 108.15 points if all their players shot their average percentage, but the Rockets would have only scored 106.985 points. This means that on an average shooting night all around, the Spurs would have won this game. Now picture this across the sample of an entire season. Shooting variance can cause a team to win 5-10 games more or less than they should. Not only does shooting variance have a huge impact on individual games, but it has a huge impact on individual seasons.
Single game shooting variance has an even greater impact at the college basketball level. With fewer possessions and lower offensive ratings, shooting variance is often the reason why we see so many college basketball upsets. It is also a big reason why the best team in the country almost never wins March Madness. A good example to show this is last Thursday's Indiana-Purdue game. In that game, underdog Purdue defeated Indiana by a score of 81 to 69. Purdue led the whole way through, and at face value it seemed like a dominant performance. And it was. However, Indiana shot the ball worse than we could've expected and Purdue shot the ball better than we could have expected. I am only going to use 3-pointers and free throws for this game because I don't have access to shot location data inside the arc. Indiana as a team shoots 32.4% from 3 (216th), and Purdue shoots 37.4% from 3 (50th). From the free throw line, Indiana shoots 66.6% (265th) and Purdue shoots 69.3% (198th). Obviously, Purdue is a far superior team to Indiana in terms of shooting, and that was very obvious just from the eye test. However, Indiana shot 3-18 (16.7%) from 3 and 16-29 (55.2%) from the free throw line, which is worse than expected. On the other side, Purdue shot a ridiculous 11-17 (64.7%) from three and a slightly below average 20-31 (64.5%) from the line.
When adjusting the overall team stats for shooting variance, the game looks a lot different. If Indiana shot their expected team percentage, they would have made 5.832 of 18 threes and 19.314 of 29 free throws. If Purdue shot their expected team percentages, they would have made 6.358 of 17 threes and 21.483 of 31 free throws. With those adjustments, Indiana would have scored 11.81 more points while Purdue would have scored 12.443 less. So, if both teams shot their average percentages Indiana would have actually won 81-69. Again, a calculation like this is inherently flawed because it doesn't take into account who was taking all of those shots. When we account for who was taking the shots, we still get fairly similar results. Indiana scored 11.855 points less than expected while Purdue scored 14.644 points more than expected. Adjusting the shooting using this more accurate measure, the final score would have been about 81 to 66 in favor of Indiana. In all fairness to Purdue, they shot far worse from inside the arc then their team average (about -6%) while Indiana shot far better than their team average from inside the arc (about +4%). So, while the new adjusted score might be jarring, it does not tell the whole story from a statistical standpoint (when adjusting for inside the arc, Indiana wins by about 10 still, but I don't put much stock into that because I don't have accurate shot location data). The numbers also don't adjust for shot quality, such as open vs. contested threes or off the dribble vs. spot up threes.
It's really easy to look at these numbers and say your team lost because of luck. While shooting variance does play a big role in winning or losing individual games, it does not tell the whole story. At the end of the day, Purdue played better than Indiana in the game referenced above. Matt Painter ran a lot of interesting actions to get Trevion Williams the ball wherever he wanted, and Archie Miller didn't have a counter. At a certain point, you have to something to adjust and stop letting the other team’s best player do what he wants. He could have switched cross and back screens, fronted the post and loaded baseline, gone zone, or done other creative things to lessen Williams' impact on the game. Purdue also got far too many open looks. Players on Indiana were caught in no man's land too often, rotations were sloppy, there weren't consistent double's or dig's on Williams, and when they did double they did it from one pass away (big mistake). Miller didn't adjust, and that is a large reason as to why Purdue shot so well. Miller also didn't adjust on offense. There is no way they can operate with Jackson-Davis, Race Thompson, and Trey Galloway on the floor at the same time. It was painfully bad to watch. With five minutes left in the game, Miller finally took Galloway out, but it was too late. Purdue so easily loaded up to Jackson-Davis' left hand (where he wants to do everything) because they always had two players they could help off of. Miller did a bad job of putting his players in a position to succeed, and that was a bigger reason as to why his team lost.
Shooting variance can be a big factor, but it doesn't nearly tell the whole story to any game. Coaching decisions, schemes, and how the players play outside of scoring (defense, passing, etc.) affect the game to a greater extent. But that doesn't mean shooting variance can't change the outcome of any given game or season. Because it definitely does on a nightly and yearly basis at every level.
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