Figure 1.
The spatial organization of learning.
A. The spatial distribution of all 759,050 FGs in our dataset. The basket is depicted by a white circle and the upper boundary is the half court line. The color codes for the number of FGs taken from each location in scale. The black lines delineate 16 regions used in subsequent analysis. B. The averaged learning matrix
, based on 161,302 FGs attempted by 166 players that passed our selection criteria (see Materials and Methods). C. Top, Dissimilarity matrix,
, computed based on the rows of the matrix
in B such that
is the Euclidian distance between the rows
and
of
; Middle, Hierarchical clustering of the matrix in B based on the dissimilarity between the rows (see Material and Methods); Bottom, the dissimilarity matrix ordered according to the dendrogram in the middle panel. D. same as in C for the columns of matrix
.
Figure 2.
The effect of distance from the basket on learning.
A. the difference between the probabilities of attempting a 3 pt after a make and after a miss FG as a function of the distance of the first shot from the basket. FGs were sorted into 2ft wide bins according to their distance from the basket. For each bin and for each player, we calculated the average distance from the basket and the conditional probabilities and then averaged over the players. B. The shooting percentage as a function of the distance from the basket. The percentage is defined as the ratio between the number of made FGs and the number of attempted FGs. Error bars denote the SEM. The blue dots denote 2 pt FGs and the red dots denote 3 pt FGs. Analysis is based on 263,557 FGs of 300 players that passed our selection criteria (see Materials and Methods).
Figure 3.
Matching and deviations from matching.
A. The fraction of 3 pt FG attempts as function of the fractional 3 pt income, defined as the fraction of points gained by the offensive team from the time of the 3 pt shot until the time that the opposing team got hold of the ball. Each point corresponds to a single player that passed our selection criterion (same as in Fig. 2, see Materials and Methods) and the black diagonal line denotes the behavior expected from the matching law. B. The return as a function of the distance from the basket for 2 pt (blue) and 3 pt (red) FGs. The matching law predicts that the returns would be equal. Each point is an average over all players in A and error bars are SEM.