Wednesday, August 21, 2013

TOIComp Effects, Part 1

When I ran the numbers for TOIComp, I was a little disappointed—but not surprised—that the spread between top and bottom competition (for valuable regulars) was so small. After all, we observe the same thing for Corsi Rel QoC, and differences at the season level in that metric don't appear to appreciably alter players' results. I felt that a similar study on TOIComp would be more work for the same result, but I'll do it anyway (after prompting from @garik16 and @pcunneen19).

Hopefully, there's something interesting in the data this time.

The simplest way to tackle this problem is to separate players into buckets. We need to develop two bucketing systems: one for individuals, and one for groups of players. (Why? The spread of group averages will be smaller than the spread for individual observations that form the group.) So first, let's take a look at individuals:

We have six seasons of data here—about 5300 player-seasons (excluding goalies). When we sort players into buckets, we need to keep this in mind. We want the first bucket to contain the smallest values and the last bucket to contain the biggest values, with all buckets having a decent sample size. (I could aim for equal sample sizes, but I'll go for equal bucket width instead, which makes it easier to sort the players and change the number of buckets, if need be.)

I calculated the F TOIComp for each 5v5 Corsi event and tabulated those values here, and since the totals were getting quite big, I used percentages instead. (I really should have tabulated the F TOIComp based on actual shifts, not Corsi events, but this is just to get an idea of the spread and what bucket sizes I can use. I don't think using ice time would change the results all that much.)

I decided to separate competition into half-minute buckets, starting from 11 minutes and ending at 22. For even spacing for individuals, I spaced the buckets every two minutes, starting at nine and ending at 21, forwards only. The numbers are not zone start-adjusted, and I intentionally squeezed the scale to focus on the differences in this range (and not the terrible results of low-TOI enforcers against top-six forwards).

The graph is a little crazy. Each line is a span of individual TOI/60. There's a clear downward trend—not as clear as with Corsi Rel QoC, obviously, since TOIComp isn't directly based on Corsi like Corsi Rel QoC— with some sample size issues near the ends. As for differences, we're looking at around 56% for top players versus bottom players, and more like 47% for top players against a line of top players. Several other groups of players look like they experience a ~10 percentage point drop from competition of ~12 minutes to competition of ~19 minutes as well.

None of this should be surprising. In general, though, the spread of F TOIComp for an entire season isn't 12 to 19. For forwards with at least 200 minutes played in a season:

That spread only goes from ~14 to ~17. In our chart above, that looks like only a two or three percentage point difference in Corsi%, and that's at the extremes.

To put it visually, let's compare the percentage of ice time spent against each bucket for three 2007 Devils: Jay Pandolfo (who is the one player falling in the 17-17.5 range above), Patrik Elias (who is a little over 16 minutes), and Mike Rupp (who is one of the few players in the 14-14.5 range):

Rupp, an enforcer (unsurprisingly among enforcers in F TOIComp) has a high point at nearly 20% of his ice time coming against sub-11min F TOIComp competition. Pandolfo also has lots of ice time against top-tier opponents. This is pretty much the most extreme chart there will be.

Here's one with the top-ranking forward in F TOIComp with at least 1000 5v5 minutes played in 2007, John Madden (16.91), versus a middling player from that list (Dustin Brown, 16.03) and the bottom forward of the 68 (Matthew Lombardi, 15.52):

From the link above:
Using the curve for the average player on the first chart, we can calculate that Nodl’s 95th percentile usage is only harsh enough to bump an average player’s Corsi down to 49.5%, while Betts’ 13th percentile usage would be soft enough to allow an average player to post a 50.6% Corsi.
Using our average Corsi% graph, a player can expect a ~52% Corsi against 14-14.5 minute F TOIComp. Regular (i.e. better than 4th-liner) NHLers, at the low end, can expect between 50% and 51% Corsi in their 15-16 F TOIComp. At the high end, a 16-17 minute F TOIComp player can expect to go a little under 50%. It's hard to slap a precise number to describe effect of F TOIComp, but the effect of going from the top to the bottom appears to be in line with what Eric T. found earlier.

That being said, we haven't looked at D TOIComp like this, and I think we need to check both F TOIComp and D TOIComp against on-ice shooting and save percentages as well. Tyler Dellow has also been examining Corsi% after a faceoff versus in "open play," and it's possible that differences in quality of competition are more important, say, after a faceoff than otherwise. There's also the issue of good players suppressing other good players' numbers, making the effects of quality of competition seem smaller than they actually are. Stay tuned.

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