# TOI% Correlations with Rel Stats

Yesterday I looked at what statistics TOI% correlates with which will give us an indication of how coaches distribute ice time to their players. It has occurred to me that TOI% is really a “Rel” statistic in the sense that TOI% gets handed out to players based on how the players compare to the rest of the team and not the rest of the league. So, in comparing TOI% to overall stats such as GF%, CF%, Sh% I am not really comparing apples to oranges. TOI% is a statistic relative to the players teammates while those other stats are relative to the league. In this post I plan on getting around this by looking at those other statistics relative to the players teammates where the Rel stats are calculated  by On Ice – Off Ice. Here is what we get.

 TOI% vs R^2 GF60Rel 0.612 GF60 0.568 CF60Rel 0.547 Sh%Rel 0.484 CF%Rel 0.458 Sh% 0.453 GF%Rel 0.392 CF60 0.340 GF% 0.309587 CF% 0.157341 GA60Rel 0.132 GA60 0.104 Sv%Rel 0.095 Sv% 0.089 CA60 0.003 CA60Rel 0.002

In most cases the Rel stats have a higher correlation than the straight stats which makes perfect sense. A bad team still needs to give ice time to some not so good players and a great team will be limiting ice time to some relatively good players. When we compare players to their teammates and not the league as a whole we would expect the correlation with TOI% to get stronger and we do.

As we saw yesterday, we also see how poorly the defensive statistics correlate with TOI% and the Rel statistics are no different. This chart shows this observation really well.

There are no pure defensive statistics to the left of the red line and every statistic to the right of the red line is a pure defensive statistic.

Yesterday I postulated that coaches might view defense as driven more by systems than individual performance and thus individual performance doesn’t impact coaches decisions as much on the defensive side of the game. With that said though, we often hear about players getting benched or having their ice time limited because they aren’t “doing the little things away from the puck” which often gets interpreted as not being defensively responsible. I have previously wondered whether coaches just struggle with identifying what makes a player good defensively. It is far easier to identify the guys who is a great passer or the guy who has a great shot because it gets converted into goals. It is far more difficult to identify the guy who is positionally sound to inhibit scoring chances because there are no stats directly measure “goals that would have been scored if he were not so good defensively”. Regardless of what you are looking at the “it could have been worse” argument is always the most difficult to make.

It is clear to me that hockey analytics needs better measures of defensive performance which should help us better evaluate both defenders and goalies. It is a big gaping hole in hockey analytics but it also seems likely that there is a major inefficiency in how coaches utilize their players. I just can’t believe that with ideal player utilization that there should be that large of a disconnect between ice time and defensive results.