Free throw percentage measures made free throws as a share of total attempts: makes divided by makes plus misses, multiplied by 100. It can be calculated separately after each length of consecutive made shots to test whether recent success predicts the next attempt. section 16.4.1
A rising percentage after longer make streaks may resemble a Laplace probability curve, but streaks alone do not establish a hot hand. Small record counts at long streaks can produce misleading 100% values, and even independent coin flips can generate long runs. section 16.3 section 16.4.1
Calculating a streak-specific percentage
For Giannis Antetokounmpo, attempts following a streak of four makes included 27 makes and 8 misses, yielding 77.1%. After five makes, the percentage fell to 66.7%, so the player-level pattern did not resemble a steady Laplace curve. section 16.4.1
giannis_tbl1 %>% mutate(pct = makes / (makes + misses) * 100) -> giannis_tbl2 print(giannis_tbl2) ## # A tibble: 12 × 4 ## streak makes misses pct ## <int> <int> <int> <dbl> ## 1 1 74 46 61.7 ## 2 2 63 30 67.7 ## 3 3 41 16 71.9 ## 4 4 27 8 77.1 ## 5 5 14 7 66.7 ## 6 6 6 4 60 ## 7 7 3 1 75 ## 8 8 3 0 100 ## 9 9 2 0 100 ## 10 10 1 1 50 ## 11 11 1 0 100 ## 12 12 1 0 100
This R output groups attempts by prior make streak, counts makes and misses, then computes the percentage for every streak length. section 16.4.1
At the NBA-wide level, pooling thousands of attempts produces percentages that generally increase with prior consecutive makes and roughly approximate a Laplace curve. That aggregate pattern should still be kept separate from a hot hand, which concerns an individual over a finite period. section 16.5
