Basketball Statistics Blog

Friday Press Clippings:
The “Hot–Hand” Theory in Basketball

From The University of Toledo
By Rexanne Bruno, John Reay, Eric Stade and Pat Tarrant
Download source here: ' The “Hot–Hand” Theory in Basketball: A Model Project For Statistics Students ' by Rexanne Bruno, John Reay, Eric Stade and Pat Tarrant

"... Namely, we address the “hot–hand” theory in basketball. According to this conjecture, a player has a better chance of hitting a shot after a hit than after a miss. Of course, the phrase “better chance” is subject to interpretation, and already in the literature several different takes on this phrase have been considered: one may study only free throws for an individual player, or field goals for an individual player or for a team, or attempts that are limited to one quarter of continuous playing, or attempts that may span a whole game
or different games over several days. ..."

"... Entire sequences of each selected player’s field goal attempts (two and three point shots) were recorded, noting whether each shot was made or missed. The raw data for each player thus consisted of a string of 0’s (missed shots) and 1’s (made shots).

Anasterisk (“*”) in a string was used to indicate that a player left the game, and upon his return a new sequence, not considered contiguous with old one, was started for the player.

This was done to avoid the possibility that an A–team member might miss the actual point at which a player returned, and thus might create spurious relationships between shots. ..."

"... Finally, a runs test was conducted on each of the three longest observed sequences: one of 17 consecutive shots by David Robinson of the Spurs; one of 14 consecutive shots by Shaquille O’Neal of the Magic; and one of 12 consecutive shots by Hakeem Olajuwon of the Rockets.

The objective of such a test is to detect an unusually high, or low, number of “runs” in the data, a run being (in our case) a sequence of one or more consecutive 0’s or consecutive 1’s.

Again the conclusion was the same: there was no statistically significant dependence of one shot on the previous one. ..."

"... Even to quite permissive levels of statistical significance, our data do not indicate a dependence of the success of a given shot on the outcome of the previous one. This result is consistent with much of the literature, although some authors have argued that there is evidence of such a dependence.

(Perhaps the lesson to be learned by this apparent discrepancy is that, before using statistics to answer a question, one should make sure that one has asked the question precisely. Again, we found that this particular project led to many discussions that, while pen–ended, were still quite educational.) ... "

"... Beyond the gathering and analyzing of data, and the drawing of conclusions from the game, there are many ideas to be gleaned from the process of completing the above (or a similar) project.

We think it best that students be asked to look up and retrieve the articles themselves, rather than receiving photocopies or the like.

We hope that, by the time they are nearing completion of the project, they would be eager to find what others have written; moreover, beginning (and other) students will learn from this experience of looking up related research articles. ..."

"... Finally, the students might be asked to explain why and how different researchers can come up with opposite conclusions, when looking at (for example) the hot–hand problem.

The students should clearly report on whether these apparently conflicting conclusions are due to statistical flukes in the various observed data sets, or to the measuring ofdifferent quantities, etc.

Questions of this type should lead the students to reconsider their own analysis, and to determine exactly what questions they tried to answer, and what alternative, related questions could have been asked. ..."

Read more articles in The University of Toledo.

To read today's 'Press Clippings' in Spanish, click this week above on the 'Español' tab or afterwards click here: ' Scouting en baloncesto. Información para ganar ' by Juan Carlos García Gómez.

You must be logged in to read or post a comment. Register

tags:  basketball  ~  statistician's digest   ~  basketball analysis  ~  hot–hand” theory in basketball
visit:  eBA Portal  ~  eBA Forums  ~  eBA Encyclopedia  ~  eBA Clinics