Exploring the Hot-Hand: Player Behavior
We’ve all seen it. Stephen Curry hits a 3. He comes down on the next possession and hits another 3. On the next possession, he launches another one with a hand in his face. As the shot is in the air, you think to yourself… this is definitely going in.
We have also experienced this feeling. I know I’ve hit a couple of jumpers, felt confident, and taken a shot that even Lance Stephenson wouldn’t attempt, all the while feeling 100% confident. The worst part is, I know deep down that those shots are bad shots. But I take them because I think, “Well, I’ve made the last few, so why not?”.
For a while, I’ve wondered whether the human intuition behind the principle of the “Hot-Hand” is backed by empirical data. That is, if an NBA player hits a couple of shots, is he more likely to hit the next? To answer this question, I will be looking at NBA Shot Data from 2014 .Although this data is dated, it is of high quality. The data I used can be found here. Let’s get started.
Statistically defined, the “Hot-Hand” principle can be defined in terms of conditional probability. For example, we can think of the hot-hand as the probability of shot conversion, given the player has made his previous “n” shots. Mathematically speaking, it is P(shot “n+1” is made | player has made the previous “n” shots).
While analyzing this data, I chose to focus on only players traditionally defined as Point Guards, Shooting Guards, and Small Forwards for the following reason:
- These specific players typically score from a variety of positions. Think James Harden who is willing to drive to the basket and shoot 3’s. Traditional post players don’t display much variance in their shot selection. It is much harder to gauge the “hot-hand” if the player is mainly catching and dunking lobs.
Let’s take a look at the “hot-hand” of 2014’s perimeter players:
On the x-axis is the number of shots the player has made. On the y-axis is the field goal percentage of the next shot taken. For example, if a player has made his last 5 shots , the probability of him making his 6th shot is 25%.
Looking at the data, we see an obvious trend. Shooting percentages woefully dip after a player has made a shot. Some might argue that those included in the graph above aren’t even the NBA’s best shooters,and thus they wouldn’t contribute to understanding the hot-hand, and they would be absolutely correct. Let’s see if this data is true for 2014’s highest shooting perimeter players. According to data from basketball-reference in the year 2014–2015, Klay Thompson, Stephen Curry, and Kyle Korver were among the league’s top 3 point shooters. If we overlay their data over the league average, we see that they aren’t different from the crowd.
I’ve shortened the streak axis from 7 to 4 because each of these shooters has had one game where they have made 5 or more. However, since this sample size is so low, the graph itself does not look accurate. As we can see, on average, their FG % also dips. It’s no surprise that Ashton Kutcher’s doppleganger performs better than the league average. The man is straight cash (more on this in a future post). However, his average still takes a dip after his first made shot.
To be more mathematically rigorous, I have conducted a left-handed Z-test with an alpha value of .05 for each player displayed above using R. The results for all players were statistically significant for a streak of 1+. Now that the data has shown that for perimeter players, FG % dips, it is important to understand why this is true.
Thankfully the data set is a treasure trove. For each shot, defender distance, shot distance, and number of dribbles is given. Let’s take a look at shot distance as a player begins to “heat-up”:
Pretty clearly, there is a positive trend as players begin to feel it. But this graph could explain why there is a decrease in field goal percentage as the streak increases. Players begin to get cocky, and start pulling up from further and further. A longer distance shot, a lower probability of converting.
Enough of the general; let’s take a look at some of our favorite players:
The obvious outlier in this graph is LeBron James. Instead of moving further away from the basket as his confidence increases, it seems that LeBron begins to attack the rim more frequently. Furthermore, James Harden, is the exact opposite; he begins to move further from the basket.
It seems that as a players’ confidence increases, they begin to increase aggressive play. In James Harden’s case, his increased aggressiveness is his willingness to take riskier shots. In James’ case, his increased aggressiveness is his willingness to go to the rim. Looking at the respective FG %:
LeBron, although he begins to attack the rim more as he gets hot, his field goal percentage drops, but not as fast as the other players above. Perhaps this is the result of taking closer, but tougher shots. With no surprise, we see that Russell Westbrook’s field goal percentage plummets at a faster rate than anyone else on the list. Would I like to say that his confidence grows more irrationally than any other superstar? Yes. Does the data suggest this? Unfortunately, data doesn’t allow me to make that inference.
Let’s see how a player’s separation from his defender changes as he starts to get hot:
The y-axis does not do this picture justice. The average separation between a defender and the offensive player stays pretty constant at 4 feet throughout the scoring spree. Four feet is an incredible amount of space, if you stop and think about it. Does this tell us that if a defender wishes to stop a scoring streak, he should probably D-up a little tighter? Yes. But we already knew that. If we take a look at specific players, we can learn something more interesting.
For the most part, these players’ average separations decrease as they begin to heat up. Two immediate factors come to mind:
- The defender begins to play tighter as the offensive player begins to score more points.
- The offensive player begins to get a little cocky, and starts shooting tightly covered shots, with little regard to the defense. We’ve all seen Chef Curry jack up a contested 3 after he’s hit a few.
Regardless of which factor plays a bigger role in explaining the data above, it is clear that defender distance plays a role in explaining why field goal percentage decreases as a player begins to heat up. Tougher, more contested shots result in more misses for these specific individuals.
One last bit of analysis; let’s see if players are quick to get an isolation play after they’ve scored a few in a row. Here I am assuming that a higher number of dribbles implies an isolation scoring situation. This, of course, is not always true; we’ve seen screens drawn up for Steph Curry or Klay Thompson to shoot it when they are “hot”.
The result is somewhat of a mixed bag. Some players, like Harden and Isaiah ,excluding the 6th outlier, seem to operate at the same level. This is in part due to the fact that both Isaiah and Harden operate primarily out of the pick and roll, and use the dribble isolation quite a bit to begin with. However, it is interesting to note that Kyrie Irving dribbles less as he begins to heat up, and Steph Curry begins to dribble more as he heats up.
In conclusion, we can say that as a player begins to heat up, not only does his behavior change, but so does his defender’s. This player behavior could be responsible for the drop in FG %.
As much as we would love to acknowledge that the barrage of Curry’s 3 pointers, or Kobe’s succession of fade-away jumpers are a result of their respective hot-hands, we can and should not. So the next time you hit a couple of jumpers in pick up, do your team a favor and give the ball and your ego up, or be like LeBron and at least attack the rim.
