What if? Shooting at 5-on-3 or with the goalie pulled...

I've really come to like the "what if?" shooting analysis. Sunny Mehta put the idea in my head in his guest post on Forward vs Defense shooting percentage over at Irreverent Oiler Fans. The idea of "what if?" is to ask if a particular group of shots were taken under different circumstances, how would the shooting percentage change? My first attempt looked at what would happen if all of the shots taken by defensemen were taken from the same locations by forwards. My second was a look at shootouts vs even-strength, power-play and short-handed shooting. Expanding on this, I'd like to look at 6-on-5 Empty Net shots, and 5-on-3 power-play shots and see what would have happened if they had been taken at 5-on-5 and 5-on-4.

First, some basic shooting percentages, including missed shots:
Shooting% Rebound%
ES (5-5) 5.78 5.67
PP (5-4) 9.13 6.58
PP (5-3) 16.2 8.32
EN (6-5) 8.25 8.04
SO (1-1) 33.6 N/A

In terms of raw numbers, shooting percentage with the goalie pulled is a little lower than if each team has one fewer player (the 5-on-4 PP), while more shots result in rebounds - presumably because having an extra player on the ice allows your team to get to more rebounds. A 5-on-3 power-play bears no resemblance to regular hockey - shooting percentage goes way up, along with rebounds.

Now let's look at what happens if we assume that the EN, 5-on-3 PP and SO shots were taken at 5-on-5 and 5-on-4. In an attempt to put shootouts on equal footing, this table considers only initial shots - and not rebounds:

ES (5-5) PP (5-4) Actual SPCT Shots/Yr
PP (5-3) 6.16 7.86 14.79 1112
EN (6-5) 6.19 7.23 7.24 1120
SO (1-1) 11.74 12.70 33.63 993

The way to read this is: you take the set of shots taken at 5-on-3, for example, but assume they were taken at 5-on-5. Shots taken from these locations went in 6.16% of the time at 5-on-5, but at 5-on-3, they actually went in 14.79% of the time. Shots at 5-on-3 don't come from what would normally be considered dangerous locations - the average shot at 5-on-5 goes in 5.78% of the time - the set of shots taken at 5-on-3 would have gone in 6.16%of the time. But the two-man advantage makes these shots more dangerous, and they go in 14.79% of the time.

We can see that Empty Net shots, on the other hand, are basically the same as shots taken 5-on-4. Shots from the same locations as the EN shots went in 7.24% of time, and had they been taken at 5-on-4, we would have expected them to go in 7.23% of the time.

Shootout shots, however, are taken much closer to the net and would consequently be more dangerous regardless of whether it was a power-play or empty-net situation.

What's really interesting is that a typical shot is 2.4 times as likely to go in on a 5-on-3 as it is at 5-on-5, while a shot in the shootout - a breakaway - is just 2.86 times more likely. So the relative risk level for a shot going in from a particular spot is just 20% higher when there are no defenders on the ice versus three defenders who have to deal with five opponents. Once you include rebounds, a shot from a given location is just as dangerous on the 5-on-3 as it is on a breakaway. Of course, you don't usually get to slowly skate the puck right into the crease when you've got a two-man advantage.

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