By Benedict Brady
Basketball is considered by many to be a streaky and psychological game. Analysts and fans use terms such as “hot” and “cold” to describe shooting performances. But do players get in their own head? After they miss a shot, are they inclined to defer for a few possessions to rebuild their confidence? Conversely, do players build confidence when they make a shot, and look to continue their hot streak on the next possession? A logical way to test this is to look at what a player does the possession directly after a shot attempt. If there was some sort of psychological effect from a miss, players would be less likely to call for the ball and shoot again after a miss than after a make. In this blog post, we will explore this phenomenon in depth in the NBA.
The first step in this analysis is to gather play by play data and box scores from Basketball Reference, for every game played in the 2016-2017 season up until January 9. After that, we then can be narrowed down the play data to just field goal attempts. Finally, we can create a matrix indexed by player name and the team they are on, and chart the result of each shot, make or miss, recording whether or not the same player took the team’s next shot. This gives us the data set that we will analyze.
The first question is whether or not we can see significant evidence of a difference league-wide between the chance that the shooter stays the same after a make and after a miss. The null hypothesis here is that players have the same chance of shooting again after either a miss or a make, and the alternative hypothesis is that the chance increases or decreases based on the result of the previous shot. The league average comes out so that the same player shoots again 22% of the time after a make and 16.5% of the time after a miss. A two sample t-test yields a p-value of 2.2e-16, which is means this difference is highly significant, and there is a very low probability that it is due to random variation.
It is worth noting here that this specific conclusion is not original analysis, it has already been demonstrated here by HSAC alumnus John Ezekowitz. For the rest of this article, we will try to further his analysis by considering how this effect manifests in individual players and teams.
So, how does this apply to individual players?
This graph gives us insight into four measured variables. On the x and y axes, we have the chance that a player takes the next shot after he makes versus after he misses. The color of the bubble is the difference, or “spread,” between the two values (make minus miss). And finally, the size of the bubble is number of shots that the player has taken in the season up until this point. This graph is restricted to players who have both made and missed more than 50 shots up until this point in the season.
A few things to note. Most of the players in this chart exist above the y = x line which means that they are more inclined to shoot after a make than a miss. We also have a group of players that exists pretty far below the line, including players such as Willie Reed, Rudy Gobert and DeAndre Jordan. This group highlights one slight flaws in this analysis. Tall centers are fairly likely to get their own rebound on a close layup and try to put it up again. This does not play into our intuition of the hot hand, because they are nearly forced to put the shot up again as it is obviously the best team option. Still, despite this anomaly, the overwhelming majority of players are subject to this “hot hand” effect.
In addition to this chart, we can look at a list of players ranked by the difference between their probability of taking a shot after a make and probability after a miss, or “spread” for short.
When organized by spread, the point guards and shooting guards are more likely to be on the top half of the list, and the power forwards and centers are more likely to be on the bottom half of the list. One possible explanation was mentioned above, that taller players are more likely to get their own rebound and put it directly back up without restarting the play. The other theory is that smaller players shoot a higher number of jump shots, which could potentially have more of a psychological effect due to higher variance.
The player analysis is clearly going to be subject to a fair amount of random variance. An interesting extension would be to check and see if players were highly correlated year to year under this metric. Also, we are not accounting for quarter changes and when a player subs out, so this data could be cleaned up further.
Once we have established that this is a significant phenomenon, and broken it down by individual players, the final point that we will explore is the distribution of teams.
Every single team is positive under this metric, but to varying degrees. Teams like Cleveland and Oklahoma City have a high chance of the same player shooting after both a miss and a make, probably due to fewer players dominating the ball. The full team results are as follows:
It is interesting to note that the top half of this list is composed of stronger teams than the bottom half. It is not a perfect correlation by any stretch, but it is strong enough that there is probably some underlying cause.
From this analysis, we get an interesting insight into how skewed the league is on this, and which players and teams suffer from it the most. With the current literature suggesting that the hot hand does not exist or exists to a small degree, this analysis highlights two possible inefficiencies in the NBA. First is that a team may be potentially forcing the ball to someone they think is “hot” over someone who has missed a few shots, even when they are guarded more heavily. Conversely, teams on defense could be shifting toward players like John Wall after a make, and shifting away after a miss, as his shot selection is greatly influenced by his previous shot. Regardless, it seems that NBA players are not perfectly rational actors.