Tuesday's Numbers: Improving on shot metrics...

This will be a pretty short post today, unfortunately, however I wanted to direct your attention to a pretty good bit of math done over by our SB Nation buddies over at Broad Street Hockey yesterday. Eric T., who is a pretty good follow if you're a hockey fan and on Twitter, upon noticing how much better the Washington Capitals were with the score-tied at even strength than they were in any other game state, decided to look at adjusted shot metrics for every game state, not just score-tied.

For those new at this, the measure I use to determine the quality of a team is their score-tied Corsi rate or score-tied Fenwick rate. Corsi and Fenwick rates are shot differential equations. They're best counted with the score tied because the game wildly changes with one team up by one or two goals: the team that is behind will press more, creating more shots and scoring chances. We don't exactly know why yet, but the stats tell us these things happen, and the stats never lie.

Never ever ever.

So, Eric asked himself "doesn't it seem inefficient to throw away all of the results from when the score isn't tied? Can't we find a way to correct for the score effects instead?" Which kinda makes sense. The Vancouver Canucks have fallen down the ladder in score-tied Fenwick rank over the last month or so, but they aren't playing a lot of games with the score tied. They play 16 minutes out of 60 with the score tied, so we're throwing away a good chunk of data to make our decision.

Eric's method of adjustment was simple.

Thanks to the Fenwick tabulations at Behind the Net, we can see that over the last four years, the average Fenwick for a team that's behind by two goals is about 56%. So if a team gets 57% of the shots when they're trailing by 2, that's 1% better than average -- just like if they had 51% of the shots in tied situations. Similarly, the average for a team that's behind by one goal is about 53.9%, so a team that gets 52.9% when down by one is 1% worse than average, like a 49% Fenwick Tied.

For those interested in the math he did...

Ideally, we'd merge the corrected Fenwick scores based on how much time a team spent in each game state; the more often a team leads by 2, the larger the up-by-2 Fenwick sample size will be and the more weight it should receive. However, since the TOI numbers at Behind the Net are buggy, I've used the league average TOI instead. The average team spends 3.75 minutes per game down by 2 goals, 8.46 minutes down by 1, and 17.94 minutes tied, giving us the following formula for Score-Adjusted Fenwick:

Score-Adjusted Fenwick = [3.75 * (Fen_up_2 - 44%) + 8.46 * (Fen_up_1 - 46.1%) + 17.94 * (Fen_tied - 50%) + 8.46 * (Fen_down_1 - 53.9%) + 3.75 * (Fen_down_2 - 56%)] / 42.36 + 50%

Still with me here? Good.

While the Washington Capitals are certainly a team whose rank would change given game state because they are only real good with the score-tied, so are the Canucks. While they're 11th in overall Fenwick rank with the score tied, they are 2nd when down by 1, and 4th when up a goal. Something I've noticed with this team is they are extremely adept at shutting down the flow of play when the situation requires it: if they're up late in a game, they don't give up scoring chances.

Score-adjusted Fenwick rank after 40 games correlated slightly higher to the final standings than score-tied Fenwick did (Eric found an r-squared value of .36 versus .34) and, we know that shot differential metrics can predict the final standings better than the standings so I think that the adjusted Fenwick can become the new "industry standard" for power rankings and such.

So, really, this is a terrific bit of work done by Eric, and he also took the liberty to do a full on adjustment for all 30 teams. Here are the top 10:

Team	Score-Adjusted Fenwick	Fenwick Tied	Fenwick Close
DET	57.0	56.5	56.8
STL	56.2	56.5	56.1
PIT	55.5	54.9	55.4
CHI	53.0	53.9	52.7
VAN	53.0	50.8	51.4
BOS	52.9	52.4	52.7
SJ	52.3	51.6	51.1
PHI	51.1	48.0	50.9
LA	50.9	51.8	51.3
WPG	50.8	50.4	51.1

He called Vancouver and Nashville "badly underrated" by the "tied" or "close" standard that are commonly used by stats guys. However, Nashville, who are 29th in score-tied at 44.3%, are also 29th in score-adjusted at 46.0%. I checked last night and saw that their on-ice shooting percentage as a team is 8.2%, which I think is ridiculously high given the low-event game that Barry Trotz prefers to play.

So, if I'm a betting man, the Predators are the next team to regress to the mean. Don't take it personally, because I love our plucky Tennessean rivals.