The Falconer posed an interesting question last week: "[what is the] effect of a PK going to the box? I did a post on "costly penalties" a couple of years ago. J.P. read my post and noted that it seemed like whenever a member of the Thrashers PK unit took a penalty the opposition was more likely to score. Sure enough that is the case, the opposition PK% rose to something like 25% when an Atlanta PKer went to the box. I'd love to see a breakdown of this for the entire NHL..."
I'm going to approach this from a slightly different perspective - if a regular penalty-killer goes to the box, how does that change the rate of shots allowed by the penalty-killing team? Because there are so many more shots than goals, shot rate gives you a better sense of the opponent's offense.
So far, I ran this analysis for 2008-09 - I picked out every forward who played more than two minutes at 4-on-5 per game, played more than 70 games, and didn't change teams. I then looked at the following quantities:
1) Shot rate against at 4-on-5 when this group of players was in on the ice.
2) Shot rate against at 4-on-5 when this group of players was not on the ice - but not while they were in the box and only in games that they actually played in.
3) Shot rate against at 4-on-5 when this group of players was not on the ice - but only in the 120 seconds following one of these players taking a penalty.
And the results:
| On-Ice ShA/60 | Off-Ice ShA/60 | TOI On/G | TOI Off/G | |
| In Box | 78.7 | 0:18 | ||
| Not In Box | 72.5 | 70.8 | 2:37 | 3:46 |
We see several effects here - the first is that the opponent's shot rate is substantially higher when one of these penalty-killing forwards is in the box. So The Falconer's insight is correct - when a first line PP unit goes up against a PK unit that's missing one of its top players, we should expect more shots on goal.
The second might be surprising: the shot rate against the our top penalty-killers is worse than against their lesser teammates. But this is a reflection of the drop-off in talent on the opponent's 2nd-line PP relative to the 1st line, as opposed to the PK unit's performance.
***Update***
I mentioned below in the comments that PK save percentage is mostly luck. To elaborate on that - if you take the individual team save percentages at 5v4 over the last two seasons (just G and SOG, but excluding missed shots), the average shooting percentage is 12.67%, with a team standard deviation of 0.01892. If I run a simulation of random shooting over 10000 seasons - where I assume every shot has a 12.67% chance of going in - the standard deviation of shooting percentage is 0.01603. So 72% of the variance of shooting percentage is due to luck, and 28% to other factors.
You can read much, much more about this at Objective NHL.