By Chris Litsas/ info@eurohoops.net
One of the most memorable EuroLeague finals is that of 2012 between Real Madrid and Olympiacos Piraeus. The beginning of that game found Madrid having full control and leading by 17 points early in the second quarter.
On the other hand, Olympiacos had many problems to solve; one of them was that their leader, Vassilis Spanoulis, didn’t manage to score a single point in the full first half.
Do you remember what happened in the second half? Vassilis Spanoulis started off by hitting three 3-pointers in a row showing everyone that his hand is getting hot. He finished that game with 22 points and most importantly helped his team to win the EuroLeague trophy.
One explanation for Spanoulis’ historic performance is that after he hit a series of field goals he developed a ”hot-hand”; a psychological boost making his shot even more effective than usual. This interpretation sounds valid especially because psychology in basketball is considered to be one of the most impactful factors driving the players’ performance.
In this article, we will try to prove or reject the impact of the “hot-hand” in European basketball. To tackle this task we compare the field goal percentage of each player under the following situations:
- Shots following a hit (i.e. when the player has a “hot-hand”)
- Shots following a miss (i.e. when the player has a “cold-hand”)
We also repeat this for longer streaks of successes or misses to get a broader view of the phenomenon.
Checking the data
We analyzed 1.510 EuroLeague games starting from October 2015 until the ongoing season (last game date: 26 February of 2021). For the analysis, we used the play-by-play logs of each basketball game, post-processed by 3StepsBasket. We found 323 players with more than 50 “hot-hand” and 50 “cold-hand” moments which was the minimum requirement for a player to be included in the experiment.
An example of the data and the analysis can be seen in the image below, where we show how we treated the shots of Luka Doncic in the first game of the 2017-2018 EuroLeague season.
The red rows correspond to the shots Doncic took after he hit a shot, while the blue rows are the shots following a miss. For example, the first red row is a shot he took after hitting the shot he attempted before, so we count this attempt as a “hot-hand” attempt.
In that game, Luka Doncic averaged 40% in his “cold-hand” (blue) field goal attempts but a strong 75% for the shots taken with a “hot-hand” (red). This increase of 25 percentage points comes to support the hot-hand effect on shooting.
The -surprising- results
After splitting the players’ shots in “cold” and “hot-hand” we tried to see how much of a difference it makes for a player to shoot in each situation and we got the following results:
- The average shooting percentage for a player with a hot-hand is 46.2%
- The average field goal percentage for cold-hand shots increases to 48.2%
- The average shooting percentage without preconditions is 47%
Consequently, when the players shoot with a cold-hand they have on average 2 percentage points higher chance for success, compared to their field goal percentage when they have a hot-hand!
This result comes in full opposition to the common belief that a streak of successful shots helps the player to shoot even better than usual. In conclusion, we can state the following paradox:
The hot-hand has a negative effect on the shooting percentage of a player!
As we mentioned in the introduction we didn’t only check shoots following only one hit or miss. We repeated the experiment for longer streaks of shoots. And without any surprise now we noticed that the same pattern holds for the shoots following two consequent hits or misses. Again the shots following two misses are more accurate than the ones following two hits. Shooting percentage after 2 misses: 47.8%, percentage after 2 hits: 45.5%.
Wondering what happens after a streak of 3 hits or misses? The same pattern again, percentage after 3 misses: 47.4%, percentage after 3 hits: 44.0%.
The next table lists some of the players with a strong increase on shots following one miss:
| Player | FG% after hit | FG% after miss |
| Luka Babic | 29.0% | 51.2% |
| Tim Abromaitis | 39.3% | 57.1% |
| Amine Noua (ASVEL) | 38.9% | 56.2% |
| Pero Antic | 22.4% | 37.3% |
| Adrien Moerman (Efes) | 40.5% | 51.5% |
| Pierre Oriola (Barcelona) | 48.3% | 59.4% |
| Semih Erden | 54.8% | 65.5% |
| Shaq McKissic (Olympiacos) | 41.8% | 51.9% |
| Rudy Fernandez (Real) | 33.4% | 42.3% |
| Howard Sant-Roos (Panathinaikos) | 30.9% | 39.6% |
| Nikola Mirotic (Barcelona) | 47.0% | 55.5% |
| Vladimir Lucic (Bayern) | 50.2% | 58.2% |
In total 64% of the players shoot better after a miss than after a hit. Although, as not every player follows the rule of the increased percentage after a miss, here are some players that can claim they have a working hot-hand:
| Player | FG% after hit | FG% after miss |
| Austin Daye | 52.2% | 33.8% |
| Evgeny Voronov (Khimki) | 48.1% | 36.4% |
| Kyle Kuric (Barcelona) | 54.1% | 43.6% |
| Paul Zipser (Bayern) | 50.7% | 41.2% |
| Edy Tavares (Real) | 75.1% | 66.4% |
| Dyshawn Pierre (Fener) | 61.0% | 52.6% |
| Kostas Sloukas (Olympiacos) | 47.2% | 42.2% |
| Nikola Milutinov (CSKA) | 66.4% | 61.9% |
| Wade Baldwin IV (Bayern) | 46.9% | 42.8% |
These results may come as a surprise, although this is not the first time such an experiment has been conducted in basketball. In 1985 Gilovich, Vallone and Tversky organized a similar experiment and they measured the percentage shift of the Philadelphia 76ers players based on the outcome of the shot they had taken before. Their results were identical with ours; the 76ers players experienced a decreased field goal percentage when shooting after one or several hits but an increased percentage on shots following misses.
So the next time you see a player hitting a series of shots don’t be surprised in case he gets benched soon. Just remember that the “hot hand” he just experienced gives no guarantees of what is about to come. Contrariwise, as we have shown, he will most likely shoot next with reduced accuracy compared to his usual standards. Either his excessive confidence or the reaction of the opponents’ defense will soon force him to miss a shot.
* Technical note: We also applied a two-sided t-test on the paired samples of shots after hits vs. shots after misses, which resulted in a p-value of 0.007e-7 which gives strong significance to our findings
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