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The "Hot Hand" in Basketball
First I'd like to personally say I did not write this. I think it's interesting, though.
An example of post-hockery is the widespread belief in the streak shooting of basketball players. You would be hard-pressed to watch an entire televised game without at least once being told that so-and-so has the "hot hand."
The term "hot hand" is used and understood in a predictive sense: The player with the "hot hand" is engaged in a streak shooting that is expected to continue. Ninety-one percent of fans, coaches, and players reported that a player has "a better chance of making a shot after having just made his last two or three shots than he does after having just missed his last two or three shots." Eighty-four percent reported that "it is important to pass the ball to someone who has just made several shots in a row".
These statements clearly imply two testable propostions: 1: long streaks of hits (or misses) frequently occur and 2: success breeds success. To test these hypotheses, Gilovich, Vallone, and Tversky analyzed the shot-by-shot floor shooting records of an entire season of the Phil 76ers and the free-throw shots of the Boston Celtics, along with additional experimental research on the "hot hand" phenomenon. The results were clear and consistent:
1. Are there more or longer streaks than would be expected by chance?
No. In analyzes counting the number of streaks of various lengths, it was found that the observed number coincided very closely to what is expected purley by chance.
2. Are players more likely to make shots after having made previous shots than after having missed previous shots? No. The relative frequenices of making shots after having made or missed the previous, one, two, or three shots were counted. The shootings percentages after three misses (56 per), two misses (53%), one miss (54%), one hit (51%), two hits (50%), and three hits (46%) reveal a trend that directly contradicts the hypothesis. Players were more likely to make a shot after having missed previous shots than after having made previous shots.
3. Does the outcome of a given shot relate postively to the outcome of the previous shot? No. Consistent with the trrend above, there was a small negative correlation across shots (-.04).
4. Do players have unexpedectally varying "hot" and "cold" games? No. Anaylses found that day-to-day performance variations coincided wel with statistically expected flucutations.
5. Are players more likely to make a second free-throw shot after having made the first than after having missed the first? No. The relative frequencies are virtually identical.
6. Can players at least sense when they themselves have the "hot hand?". No. Cornell Univ varsity and junior-vars players made shot-by-shot wagers (indicating confidence) as they took shots around an arc equidistant from the basket. As expected, players appeared to hold the "hot hand" belief: Their wagers were higher following hits and lower following misses. However, these wages were totally unrelated to the outcome of the shots. Thus, player's perceptions of being "hot" or "cold" as measured by their own wagers, predicted nothing.
7. Is there a "momentum" effect such that success follows success more closely in time than it follows failure? No. The time interval between two successful hits did not differ from the time interval from a hit to a miss. It made no difference whether this comparison was made across all 83 players in the study or within individual players.
In conclusion, Despite the unshakable belief of players, fans, and coaches, the "hot hand" is an illusion.
An example of post-hockery is the widespread belief in the streak shooting of basketball players. You would be hard-pressed to watch an entire televised game without at least once being told that so-and-so has the "hot hand."
The term "hot hand" is used and understood in a predictive sense: The player with the "hot hand" is engaged in a streak shooting that is expected to continue. Ninety-one percent of fans, coaches, and players reported that a player has "a better chance of making a shot after having just made his last two or three shots than he does after having just missed his last two or three shots." Eighty-four percent reported that "it is important to pass the ball to someone who has just made several shots in a row".
These statements clearly imply two testable propostions: 1: long streaks of hits (or misses) frequently occur and 2: success breeds success. To test these hypotheses, Gilovich, Vallone, and Tversky analyzed the shot-by-shot floor shooting records of an entire season of the Phil 76ers and the free-throw shots of the Boston Celtics, along with additional experimental research on the "hot hand" phenomenon. The results were clear and consistent:
1. Are there more or longer streaks than would be expected by chance?
No. In analyzes counting the number of streaks of various lengths, it was found that the observed number coincided very closely to what is expected purley by chance.
2. Are players more likely to make shots after having made previous shots than after having missed previous shots? No. The relative frequenices of making shots after having made or missed the previous, one, two, or three shots were counted. The shootings percentages after three misses (56 per), two misses (53%), one miss (54%), one hit (51%), two hits (50%), and three hits (46%) reveal a trend that directly contradicts the hypothesis. Players were more likely to make a shot after having missed previous shots than after having made previous shots.
3. Does the outcome of a given shot relate postively to the outcome of the previous shot? No. Consistent with the trrend above, there was a small negative correlation across shots (-.04).
4. Do players have unexpedectally varying "hot" and "cold" games? No. Anaylses found that day-to-day performance variations coincided wel with statistically expected flucutations.
5. Are players more likely to make a second free-throw shot after having made the first than after having missed the first? No. The relative frequencies are virtually identical.
6. Can players at least sense when they themselves have the "hot hand?". No. Cornell Univ varsity and junior-vars players made shot-by-shot wagers (indicating confidence) as they took shots around an arc equidistant from the basket. As expected, players appeared to hold the "hot hand" belief: Their wagers were higher following hits and lower following misses. However, these wages were totally unrelated to the outcome of the shots. Thus, player's perceptions of being "hot" or "cold" as measured by their own wagers, predicted nothing.
7. Is there a "momentum" effect such that success follows success more closely in time than it follows failure? No. The time interval between two successful hits did not differ from the time interval from a hit to a miss. It made no difference whether this comparison was made across all 83 players in the study or within individual players.
In conclusion, Despite the unshakable belief of players, fans, and coaches, the "hot hand" is an illusion.
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