True Shooting Percentage: How many shots does it take?

If you've ever heard me talk about hockey before, or have read this blog, or my Twitter feed, you know that I'm very skeptical of JT Miller.

via Puckalytics.com, JT Miller is shooting 12.12% this year during 5v5 play over 66 shots. Last season, JT Miller shot 14.78% during 5v5 play over 115 shots. Among players with at least 60 shots on goal this year, Miller ranks 46th in the league. Not so egregious. Last season, though, Miller ranked 9th in the league. Really, it was the explosion of goals last year for Miller that has caused me to dive into this, as 9th in the entire league does seem a bit high for JT. And it seems high, because last year's mark of 14.78% is a shooting percentage that JT didn't even touch when he was playing in the AHL. From the seasons 12-13 through 14-15, JT Miller took 235 shots in the AHL and scored on 29 of them, for an all situations shooting percentage of 12.34%

JT Miller's all-situations shooting percentage across last season and this season? 16.81% on 226 shots on goal.

The burning question remains, is JT Miller an elite shooter? Has his game evolved to that level? Or, is he getting lucky? Miller has 38 goals since 15-16, while his Corsica.Hockey expected goal total is a "mere" 23.17 goals, meaning his outpacing his expected total by 15 goals. In this sample (last two seasons), JT Miller is 13th in the league for goals scored above expected. The 12 names above him? Marchand, P. Kane, Tarasenko, Crosby, Burns, Ovechkin, Stamkos, Panarin, Hoffman, Kucherov, Weber, and Scheifele. I think even Rangers fans can admit that these are names that JT Miller likely does not belong to. Which is no shot at JT Miller the hockey player, but these are the NHL elite goal scorers.

When you couple together the names that JT exists among, and the comparison between his NHL and AHL shooting acumen, one has to wonder if we have enough data on JT to accept that this is his true shooting percentage talent. 

Thus, I've taken the following methodology to determine how many shots it takes for a player to reveal his true shooting percentage.

Stealing a page from baseball, as I often do, from this article which attempted to discover true numbers across varying metrics in baseball: http://www.fangraphs.com/blogs/525600-minutes-how-do-you-measure-a-player-in-a-year/

Following this, what I did was set a few benchmarks (500 shots on goal through 1500 shots on goal) and ran split-half correlations for each player that met these requirements on their odd games and even games shooting percentage. The author of the article above sought out a 0.7 correlation at a minimum to determine feasibility of finding truth in a metric, so I'll do the same. The results are as follows:

[data via custom query in Corsica.Hockey. The sample is only forwards, and 5v5 play to eliminate potential noise from a player receiving PP or PK time one year, but not the next. Data is from 2007-2008 through the 2015-16 season]

Since we were already at a sample size of just 50 at 1100 shots, I decided to just make the jump to 1500 as a maximum test, since we can't really discern any value from 8 players there anyway.

At no point after 500 shots on goal do we see a sample that produces a correlation of 0.7 of greater between odd and even game shooting percentage.

To round this back to the discussion on JT Miller, if we reduce the shot requirement to 225 (JT has 226 over the past two seasons) we get a correlation of 0.517 on a sample of 496 forwards.

This sort of goes against what we already believe. Where it's hard to imagine that we don't know a player's true shooting percentage after they've put 1000 shots on net in the NHL. And even after running this test, I'm still not certain that isn't true. But, I do think it is true that there doesn't seem to be this magic number of shots on net where we can definitively say that at that point, this player is a x% shooter. Well, at least not with this methodology.