Everybody knows the Leafs’ penalty kill stinks. Numerous articles have been written condemning the team’s shorthanded shortcomings (e.g. Globe and Mail, LeafsHQ, Five Minutes for Fighting, even NHL.com). Most attempt to answer the question ‘why is it bad?’ In this article I’m going to answer the question ‘how bad is it?’

Let’s transport ourselves to an alternate reality where the Leafs’ penalty kill is average. Not great, just average. The league average for PK percentage is 82.6%; if you take the Leafs’ miserable 72.3% out of the equation, the average becomes 83.0%. So, how much higher in the standings would the Leafs be with an 83.0 PK%? I’m going to use two different approaches to determine this: calculate the league-wide correlation between PK% and points; and simulate the Leafs’ season with a better PK.

Method 1: Simple Correlation between Penalty Killing and Points

In this method, my goal is to determine on average how much a team’s penalty killing proficiency affects its overall performance. To start, I charted each team’s point percentage (points divided by games played) vs. its penalty killing percentage and then added a trendline to see the correlation.

From the trendline, we can see that there is certainly a positive correlation between penalty killing and team performance: the better a team is on the PK, the better it generally does overall, which matches expectations. The trendline’s formula gives us a rough idea of the strength of this correlation: Point% = 0.54 x PK% (and we can throw away the intercept term because we’re looking at changes in PK%). In words: for every 1% a team improves its penalty kill, it can expect its point percentage to improve by about 0.54%.

Let’s apply this to the Leafs. If in our alternate universe the Leafs had a league-average 83.0%, that’d be 10.7% better than our unfortunately real universe. Using the above formula, we can expect a 5.7% (0.54 x 10.7%) improvement in point percentage. Over the Leafs’ 38 (real) games, this represents about two points in the standings.

Method 2: Subtract Power Play Goals Against from Random Games

Here I want to apply a more detailed analysis to figure out how much the Leafs’ PK is hurting them. So I examined what would happen if I randomly subtracted power play goals against from the Leafs’ season.

The Leafs have given up a power play goal in 26 of 38 games so far, and in those 26 their record is 11-11-4 (and they’re 7-4-1 in perfect PK games, which I’ll assume are unaffected by a better PK). They’ve given up 41 goals while shorthanded. If the Leafs had a league-average 83.0 PK%, they’d have given up 16 fewer power play goals against (PPGA). If we randomly choose 16 PPGA and wipe them off the board, what happens?

To answer this, I constructed a simulation that randomly subtracts 16 PPGA from Leaf games. I had to make a few simplifying assumptions: that the outcomes of games are not otherwise affected; that games that would then go to OT would have a 50/50 chance of becoming a win; and that the goal against is subtracted from the overall score rather than in a specific instance. The simulation then calculates the resulting effect on the team’s points, and repeats the process multiple times to reduce the effects of chance.

Each simulation run produced a set of game results for the 26 games in which the Leafs gave up a PPGA. Most games’ results were unchanged, but usually a few losses changed into wins. For example, in one run the Leafs won 4-3 against Buffalo on December 16 (actually lost 5-4) by allowing 1 PPGA instead of 3, and lost 3-2 in overtime November 20 against Carolina (actually lost 3-2 in regulation) with no PPGA instead of 1.

Over ten runs, the simulation added as many as eight and as few as two points to the Leafs’ total. The average improvement was five points.

Conclusion

If the Leafs had a league-average penalty kill, they’d likely have two to five more points in the standings. As of today, that’d put them anywhere from tied for 5th to tied for 8th in the Eastern Conference rather than their current 10th. If their PK remains horrible the rest of the season, it’ll likely cost them four to ten points. To put that in perspective, the average difference in points between the East’s 8th and 9th place teams the last three seasons is one point, so the PK’s poor performance is obviously a crucial obstacle to making the playoffs.

On the other hand, it’s clear that the PK isn’t the only reason the Leafs are not in a playoff position. A league-average PK the rest of the way with identical performance in other aspects of the game will only give them a handful of added points, which in the competitive East isn’t enough to guarantee a playoff spot. They need improvement across the board to lock up a place in the postseason, a point which is often missed in discussions about the penalty kill.