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Luck vs Shot Quality in Shooting Percentage

We're back to talking about "shot quality" (which I liked to call shot location) yet again (it's definitely my least favorite "statistical" topic...) We looked at Defense-Independent Goalie Rating last week and re-visited it yesterday in our discussion of shot distance against. A couple of open points came up yesterday that required a little more inquiry - first, here's the regression to the mean and R^2 of various quantities, looking at odd and even shots (road EV data only):

M R^2
Shot Distance 0.7481 0.5149
Shot Location 0.6717 0.453
Shooting % 0.228 0.0478

There's an interesting contradiction here: even though shot distance and shot location/quality are persistent, shooting percentage is very luck-driven. That means these results are in no way surprising:

Shot Distance 1.00
Shot Location 1.36
"Luck" 2.84
Observed Shooting % 3.08

Don't forget what luck is: I flip a coin a huge number of times to model a league where every shot is equally likely to go in (at the league average shooting percentage.) I then look at the standard deviation of shooting percentage over the course of 1340-shot samples (1340 is the average number of road even-strength shots per team over the last six seasons.) The observed range of team shooting percentage against is barely larger than what we see in our pure luck league - luck is 85% of the observed range.

Bottom line: shot distance/location/quality is just a tiny sliver of shooting percentage (both for and against.) When you factor in the 33% regression to the mean we see in odd and even samples, shot quality accounts for just under 10% of team shooting percentage.