How much is an NHL power play worth?
Here's a piece by hockey analyst Alan Ryder, who tallies up some statistics on NHL power plays.
Ryder looks at teams' conversion rates with the man advantage, and finds that a full two-minute power play results in about .27 of a goal. That works out to 7.9 goals per 60 minutes, "the usual expression of scoring rates" when analyzing hockey. That 7.9 figure is "more than 300% the rate of scoring during even-handed play."
(I wish Ryder had also told us the even-handed rate directly.)
With a two-man advantage, there's less data, so Ryder had to smooth out the curve. His chart shows a 50% conversion rate after 80 seconds of 5-on-3 play (compared to about 17% for 4-on-3). So the second penalty, on a second-by-second basis, is worth twice as much as the first penalty. Of course, the two penalties are seldom simultaneous. If the second infraction comes a minute after the first infraction, it would be worth one-and-a-half times as much; that would be one minute of 4-on-3 followed by another minute of 5-on-3.
Ryder estimates that a two-man advantage results in about 25 goals per sixty minutes. Yesterday, in the World Juniors, Canada beat Kazakhstan 15-0. That's approximately the equivalent of playing with a two-man advantage for two periods.
If a (single man) power play is worth .27 goals, and that's three times the normal rate, then the one-man advantage is worth about .18 goals. However, add in the fact that the other team probably won't score, and you have to add back in the .09 defensive savings. That means the PP is indeed worth the full .27. At least approximately – this doesn't take into account that the average power play doesn't go the full two minutes, so maybe the .27 should really be only .25 or something. And there are shorthanded goals, so maybe it's now .24. But these are just estimates.
Back 20 years ago in the days of the Hockey Compendium, I think Klein and Reif adjusted players' points for power play goals against while they were in the box. It might once again be interesting to figure out how to do that once again. I'd use *expected* PP goals against rather than actual, and I'm not sure how I'd make the adjustment. But I'm curious as to whether players are costing their teams a lot of goals this way.
Good stuff as usual from Mr. Ryder.