Tuesday, December 9, 2008

Scoring Probability vs Length of a 2-man advantage

I was asked recently about how the length of a 5-on-3 affects the rate at which teams score. Obviously, very few 5-on-3s run a full two minutes - it's both rare to take two penalties at once, and to successfully kill a two-man disadvantage. (In fact, it has only happened once so far during the 2008-09 season.) Here is the overall scoring rate this season for power plays versus the length of the man-advantage:

The way to read this is as follows - at 60 seconds, 30% of 2-man-advantages have resulted in a goal, while the rate is about 12% for 5-on-4s. That includes all goals scored in 60 seconds or less, and all power plays that have lasted 60 seconds or longer. If you're already on a 5-on-4 and there's a delayed penalty call against the other team, the break-even point for simply passing the puck to the other team is very low - certainly you should do it if you're looking at a 2-man-advantage of 15 seconds or longer.

This chart would look slightly different prior to the 2008-09 season. A rule change for this season puts all face-offs to start a power-play in a team's offensive zone, regardless of where the puck was touched by the offending team. In past, teams would have required another few seconds to move the puck up the ice on some power plays, and the scoring rate would have been shifted rightward in the first few seconds.


Interesting... I'd always used a rough rule-of-thumb that the percentage chances of scoring on a 5-on-3 was equal to half the length of the powerplay. Turns out I was pretty close.
(In fact, it has only happened once so far during the 2008-09 season.)

Heh, I remember this one. Obviously, the Ducks would be the only team silly enough to take simultaneous penalties (Scott N. and Beauchemin, even), and the Kings are the only team inept enough to not score during the 2-minute 5-on-3.

Well, actually the Kings scored a 5-on-3 goal later in that period, because the Ducks comically don't like learning from mistakes.
Did you run this as a failure time analysis? I've been wanting to run the powerplay/penaltykill as failure time for awhile. Just never find the time or data. It is probably only a minor issue and note important for 5 on 3 but how did you deal with the right truncation of the 5 on 4?
M_D: Not sure I completely understand what you're asking.

I'm just plotting sum(PPG(t<=T))/(sum(PPG(t<=T))+sum(PP>=T)).
Right hand truncation is when time series data is ended without the event of interest having occurred due to some other event or loss of subject (not an issue in hockey). It not really an issue with what your looking at in particular here other than it is occurring. 4 on 5 end because another penalty is called the game ends etc. 3 on 5 don't have this issue because all but one resulted in a goal. I haven't done any analysis on Survival data in awhile so I'd need to look up the specific repercussions. My gut is that it shouldn't impact the estimate just the error so it is unimportant in sports statistics. Essentially your losing sample size as the time period grows. I'll take a quick look before I go home tonight. I can see my reference from here?
ok, I see what you're saying. I think the impact is negligible. The sample size drops off rapidly beyond 60 seconds for 5-on-3; for 5-on-4, you lose very little of your sample size as time progresses.

Note: These percentages work out to basically 22 Goals/Hour. I've had this data available since 2006, when I posted in on mc79hockey. Of course fans can relate to percentages better than rates.

I think we found roughly the same thing:

is a 5-on-3 that much better than a 5-on-4?, 11/11/06.

I sent somebody the data for 2007-08 and 2008-09 last night: 20.2 GF/60 at 5v3. But it just didn't seem intuitive enough.
Just checked my reference. Raight hand truncation (censorship) isn't that big of a deal unless it is informative. So unles the a powerplay is more likely to end in a non-goal event would tell you about the probablitity of a gaol occuring sooner or latter it shouldn't be a problem. The only thing I could see as a problem would be penalties. If teams on the power play are more likely to commit a penalty would be likely to score later in the power play or vice versa. There isn't a way to detect this or deal with it(well you can start fitting more complex models but KISS). You could probably take a look at how penalties end and what teams are tending to do along with the general since of just how prevalent this is. Then dismiss it (my guess is it is real but only a small problem).
I sure hope the person who made the request for this was Alan Ryder. Otherwise, his article looks like plagiarism.

Even if it was him, should have given you some credit. Or at the very least offered to.
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