The hot (invisible?) hand: can time sequence patterns of success/failure in sports be modeled as repeated random independent trials?

Abstract

The long lasting debate initiated by Gilovich, Vallone and Tversky in [Formula: see text] is revisited: does a "hot hand" phenomenon exist in sports? Hereby we come back to one of the cases analyzed by the original study, but with a much larger data set: all free throws taken during five regular seasons ([Formula: see text]) of the National Basketball Association (NBA). Evidence supporting the existence of the "hot hand" phenomenon is provided. However, while statistical traces of this phenomenon are observed in the data, an open question still remains: are these non random patterns a result of "success breeds success" and "failure breeds failure" mechanisms or simply "better" and "worse" periods? Although free throws data is not adequate to answer this question in a definite way, we speculate based on it, that the latter is the dominant cause behind the appearance of the "hot hand" phenomenon in the data.

Figure 1. The two trends observed in the data.

Panels a and c(individual and aggregated levels respectively) show how the chances of hitting a free throw increase with the number of throws taken in a row (until a set of three throws). This increase is evident in both individual and aggregated levels (a and c respectively). The last two values of the axis represent sets of two throws taken only by individuals who had at least one three throws set. These values resembles the values of the first two throws in a three throws set. Panels b and d show the success rates of the second throw in a two throws sequence following a success/failure in the first throw. These panel shows a major finding of the current paper: “hot hand” statistical traces - success rates in the second throw are higher when the throw attempt followed a success in the first attempt rather than a failure. In this case as well, the results are present both in the individual level and in the aggregated level (b and d respectively).

Figure 2. Comparison of the individual 's across seasons.

This plot shows the individual in one season vs. the value of the same individual in the following season (in cases where the player had finite values in both seasons). The color code refers to the total number of two throws sets taken in both seasons. The numbers (in black) in each quartile are the number of observations that fall in each of them. This random pattern of the (see text for more quantitative support for this statement) values across seasons suggest that the individual “hot hand” is not a characteristic of the player but rather something that can vary from one season to another for the same individual. This fact leads us to suggest that this phenomenon is caused by whithin-season nonstationary probability of success rather than psychological reasons which are connected to positive/negative feedback loops.