## The Penalty Kill - Luck, Effectiveness and Being A Leaf

### Regression of GA/60 and GD/60 vs Various Factors

The regression of Goals Against every 60 minutes (GA/60) and Goal Differential (Goal For minus Goal Against) every 60 minutes (GD/60) on PK play vs different factors from 2007 to 2011 is shown in the chart below for

1. GA/60 or GD/60 vs SV%

2. GA/60 or GD/60 vs SV% + SH% + SF/(SF+SA)

SV% is the goalie SV% when the team or players is on the PK. And SF/(SF+SA) is the ratio of shots for divided by total shots (shots for + shots against) during the PK. SF/(SF+SA) is a proxy for how well the team clears their zone on the PK. That is, they are more likely to get a shot for (and minimize shots against) if they can clear the zone and hence more likely to minimize GA/60. Good Pkillers are able clear their zone. Note that these shot totals were used instead of a more advanced statistic because I couldn't find a database for players and team with both home and road PK shots or home and road Fenwick Tied or Fenwick Close. The regression could very likely be improved by doing this analysis with a more advanced shot statistic but the above regression did quite well to explain PK goal variability.

The best average results for Rsquared with the lowest standard deviation for GA/60 is given by 85% SF/(SF+SA) + 15% SV%. That is, the variability in GA/60 on the PK is 79.5% explained by team 0.8 SF/(SF+SA) + 15% SV%. The variability in GD/60 on the PK is 89% explained by this multiple linear regression 96% SF/(SF+SA) + 0.5% SH% + 3.5% SV%.

### What Is With These Strange Weights?

Rounding this implies teams or players that do well on the PK tend to based on

- 20% based on Random Chance (or some yet unidentified skill)

- 80% based on a skill metric (85% SF/(SF+SA) + 15% SV%)

This can also be stated that team that tend to do well on the PK do based on

- 20% based on Random Chance (or some yet unidentified skill)

- 68% based on ability of the team to clear the zone [SF/(SF+SA)]

- 12% based on goalie SV%

The weights are given by a simple multiple linear regression and can possibly improved a few more percent. The key point is the average Rsquared is higher then SV% and with a lower standard deviation for over 4 years of data. And the metric can better explain the variability in GA/60 on the PK then SV% on it own.

Goaltending while a player on the ice is important to GA/60 but players that clear their zone tend to be better penalty killers. Using the penalty killers on ice SV% is not useful because the player can't influence goalie SV% (someone may argue that they can obstruct shooters to give the goalie easier saves and clear the crease from players trying to deflect or screen). That said, a player can more easily control how well they clear their zone (measured by how well they out shoot the opposition relative to other NHL Pkillers). 0.85 SF/(SF+SA) + 0.15 SV% better describes the variation in GA/60 for different players or teams that get the same level of SV% from the goalie on the PK. The reason seems to be players that can clear their zone are able to limit scoring chances against and minimize GA/60. And so good Pkillers don't depend on the their goalie.

### Do Hockey Gods Matter Less on the PK?

For any one penalty kill - the variance is quite high (100%) or can be explained entirely by luck. However as a team kills more penalties the effect of luck decreases to near zero and true skill becomes more important. There is a probability that the team is having an "unlucky" penalty kill streak but the that probability drops to almost zero after a number of a large number trials.

That is, the league average PK is 80% (varies between 80 to 83% for the last several years). Think of the penalty kill as a loaded coin that lands heads 80% of time (no goal) and tails 20% of the time (goal against). If a team after a a hundred trials has a 72% probability of killing off a penalty (heads) the chance that random variation is the source is almost zero. The chance that skill (be it coaching, goaltending or skater) is the source of variation is practically 100%. That is, the team probably has a coin that lands heads (no goal) 72% of the time rather then league average. Chances are it is not luck but rather skill (be it coaching, goaltending or skater) that is limiting a teams PK for the leafs.

### GA/60 vs GD/60

Different factors become important on the PK if the goal is to prevent goals (given by GA/60) or to prevent being outscored (GD/60). If the task is obtain short handed goals and prevent goals against, then SV% becomes even less important and the shot factor (SF/(SF+SA) and SH% become more important. If the goal is to prevent GA/60 then outshooting opposition and SV% become important.

### What the heck is this measure (or clearing the zone on PK is important)?

This measure should not be surprising. Basically a good penalty killer outshoots and minimizes shots against versus other penalty killers (and gets some benefit from goaltending). But the statistic is also is proxy for how well a player or team can clear their zone on the PK. That is, if they are getting shots on the opposition net then the puck is not in their own zone. The weights are bothersome but there maybe some better reasons to question this metric, namely because it doesn't give credit for a player like

- Tim Brent who is known to blocks shots on PK (even clearing the zone or icing the puck is not rewarded)
- Mike Brown who will skate circles around an opposing player and eat up PK time
- Colby Armstrong that can create a turnover and/or trap a puck along the board with his skate and eat PK time.

Those type of players may appear to be poor on the PK by this statistic however the statistic does explain 80% of the variability over four years, so if a player is giving up GA/60 on PK then something is not working in their game.

### By Player 2011

The light grey lines mark the average intersection of play for the statistic and GA/60. Players higher to the left, give up fewer GA/60 on the PK and outshoot other penalty killers. Players to the bottom right give up more goals and are outshot. Note that Tyler Bozak is above average on the PK and all other leaf players are below league average. Even Connolly who for his career was a better then average PK has now to below average as a leaf. At this point it is hard to say if the reason is

1. That he has worse team mates and goaltending
2. Poor PK Coaching and PK Strategy that does not set him up to succeed
3. Toronto Blue & White PK mental disease is festering in the locker room
4. Still too small a sample size for Connolly specifically

Though the evidence points to #2.

### Leafs Compared to the Average NHL Penalty Killer

The Leaf on the PK are 6.6% worse then the league average measured by the weighted SF/(SF+SA) + SV%

 League Leaf Difference % Average 132.1 123.4 -6.6% Forward 131.9 123.1 -6.7% Defense 132.2 123.6 -6.5%

### PK Effectiveness of Players on Leafs or Their Other Teams

The chart below gives a perspective of players who played on the leafs from 2007 through 2011 and joined other teams or who have recently joined the leafs. The "Change In" figure represents how well they are playing on the PK relative to their "non leaf" team. In all cases, the player is playing worse on the leafs then they did on other teams. There is not one exception of a player who is a better PK on the leafs then another team.

This data suggest that PK coaching on the leafs do not get the best out of the penalty killers. However it is impossible to state definitively if the problem is:
- The players (some of them who are quite capable on other teams) cannot implement the leaf PK strategy
- The PK strategy itself is "below league average" in effectiveness
- A strange confluence of factors make penalty killers ineffective when they dawn the leaf uniform.

The - 6.3% performance drop that players see in their Pkilling when they move from other team to the leafs (or from the leafs to other teams) matches closely the difference in the current leafs players to average NHL PKillers (-6.6%).

PensionPlanPuppets.com is a fan community that allows members to post their own thoughts and opinions on the Toronto Maple Leafs and hockey in general. These views and thoughts may not be shared by the editor of PensionPlanPuppets.com.

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