I know many of you think that statistical analysis views all players as automatons, but we really only do that as an approximation to reality. One place where the approximation deviates somewhat from reality is in shooting.
I took every player who took 200 or more even-strength shots over the last six seasons and posted an 8% or higher shooting percentage. I then looked at the distribution of goal-scoring in every 100-shot stretch they had and compared this to the simulated distribution of goal-scoring assuming every player's shooting talent was always equal to his observed shooting percentage. What we see are fatter tails in the real distribution:
| # Goals | Actual | Sim | Ratio |
| 1, 24 | 0.145 | 0.007 | 20.71 |
| 1-2, 23-24 | 0.648 | 0.33 | 1.96 |
| 1-3, 22-24 | 1.916 | 1.512 | 1.27 |
| 1-4, 21-24 | 5.225 | 4.999 | 1.05 |
| 1-5, 20-24 | 11.381 | 11.115 | 1.02 |
| 1-6, 19-24 | 20.757 | 19.911 | 1.04 |
| 1-7, 18-24 | 33.516 | 31.052 | 1.08 |
| 1-8, 17-24 | 47.403 | 44.808 | 1.06 |
| 1-9, 16-24 | 62.329 | 59.828 | 1.04 |
| 1-10, 15-24 | 76.475 | 74.312 | 1.03 |
| 1-11, 14-24 | 88.846 | 87.152 | 1.02 |
Real players are much more likely to hit the extremes – in particular, 1, 2, 23 and 24 goals scored in a 100-shot stretch are much more likely in reality than they are in our automaton simulation. There are lots of potential effects here, including scorer bias (we often see own goals credited to some random forward; perhaps there are other issues), but the deviation in distributions likely does reflect small variations in effective shooting talent. Some of that is streakiness, but some of it can also be attributed to injury (e.g. Alex Tanguay.) At any rate, it’s good to see that humans deviate from the numbers that model them.
