Brad Marchand, despite being one of the league’s biggest pests, is a highly skilled two-way winger who can play in all situations. He is both one of the best power play weapons for the Bruins and a key part of their penalty kill. So it is interesting to consider his prowess for getting calls and putting his team on the man advantage as well as for being called and sitting in the box while the Bruins play shorthanded. I plan to estimate the net  “penalty effects” on the Bruins from Marchand’s penalty taking and drawing abilities.

Marchand and Penalties

Marchand has often been both the among the leading penalty takers and penalty drawers for the Bruins. His penalties taken (PF) numbers have been top three on the team in 2010-11 (3rd), 2013-14 (1st), 2014-15 (1st), and 2015-16 (t-1st). In the penalties drawn (PA) category, he has had top three finishes on the team in 2010-11 (1st), 2011-12 (1st), 2013-14 (2nd), 2014-15 (1st), and 2015-16 (1st). This has led to a large spread in how Marchand effects the amount of time that the Bruins special teams receive over the season:

Season	GP	PD	ATOI	PD60	Rank	Boston PP-PK TOI
2009-10	20	0	12.01	0.00	n/a	-18:28
2010-11	77	0	14.13	0.00	5/19	+11:07
2011-12	76	+6	17.59	+0.27	2/19	-07:30
2012-13	45	+2	16.95	+0.16	3/17	-76:40
2013-14	82	-5	15.89	-0.23	11/20	-70:22
2014-15	77	-11	17.14	-0.50	18/20	-43:00
2015-16	52	+2	18.33	+0.13	3/20	-74:25

GP = games played
PD = penalty differential (PF-PA)
ATOI = average time on ice per game
PD60 = PD per 60 minutes of ice time (PD/[GP*ATOI]*60)
Rank = PD60 ranking on the team that season among players with 30+ GP
Boston PP-PK TOI = difference in PP TOI and PK TOI for the Boston Bruins

Generally speaking, Marchand has been very good at drawing more penalties than he has received, but he has had a few odd years where the opposite has been true. This is crucial for the Bruins as they have been consistently been the team with one of the largest disparities between PK time and PP time to their disadvantage. Between 2010-11 and the present, the Bruins have had a PP-PK time differential of -260:50. The next closest team, the Capitals, sit at -216:33 in that same time span. So relatively speaking even a +2 PD for Marchand is a big deal because the average Boston player had a negative PD in any given year. Calculating relative PD60’s for Marchand would put him in a much better light than he currently is cast in the table above for many of his seasons (and I might do so in a future post).

Situational Penalties

Not all penalties are created equal. Taking a penalty on the PP and on the PK are two incredibly different beasts. In one situation you are ruining your team’s opportunity to sustain heavy offensive pressure while in the other situation you are putting your team at a major disadvantage as you sit in the box with a teammate. Marchand’s PD60 varies by situation as follows:

Season	ALL	5V5	PK	PP
2009-10	0.00	0.00	0.00	0.00
2010-11	0.00	-0.13	+1.02	+1.40
2011-12	+0.27	+0.35	+0.59	-1.14
2012-13	+0.16	+0.40	0.00	-0.79
2013-14	-0.23	-0.33	+0.47	0.00
2014-15	-0.50	-0.57	+0.52	-1.71
2015-16	+0.13	-0.33	+3.50	0.00

It is quite clear that Marchand has a penchant for returning games to even strength when playing on either the PP or the PK. His 5v5 game has been a bit variable over the years, but the last three have been noticeably in favor of penalties taken for him.

Putting It Together

It should actually be little surprise that Marchand is so good at drawing penalties on the PK. This year he already has 3 shorthanded goals and 2 shorthanded points. This has given him a +6 penalty differential in only 103 minutes. In fact, Marchand is 2nd among players with 500+ shorthanded minutes since 2009-10 (there were 246 such players) with a CF (Corsi for) of 19.0%. This is both because he has the 2nd best CF60 at 20.1 and the 8th best CA60 (Corsi against per 60) at 85.7. At all three measures he is even better than his Selke winning partner Patrice Bergeron. Marchand is an astoundingly skilled penalty killer both because of his ability to stifle the opposition and to generate rushes, which result in either penalty draws or high-quality scoring chances more often than almost every other player in the league.

The Bruins benefit from these penalty draws by having to spend less time shorthanded and gain more time at even strength. Just in 2015-16, the Bruins have had a GD60 (goal differential per 60) of -4.8 while shorthanded and +0.2 in even strength situations. So drawing a penalty on the penalty kill results in an immediate +5.0 GD60 swing for the remainder of the would-be penalty kill. In addition, the offset between the original penalty and the penalty drawn by Marchand results in a PP opportunity, during which time the Bruins have dominated with a +7.9 GD60, which is a 7.7 GD60 increase over even strength. So if we just go with the assumption that Marchand’s six extra drawn penalties on the PK this year have each occurred with one minute of the PK remaining, we will arrive at a scenario where he has converted 6 mins of PK into ES and 6 mins of ES into PP. Using these numbers, the goal differential swing is +0.50 goals from the PK → ES and +0.77 from the ES → PP conversion. So Marchand’s PD on the PK can be estimated to increase Bruins’ goal scoring by +1.27 goals this season.

Meanwhile Marchand has had a PD of 0 on the PP and -4 at 5v5 play. The null PP PD leads to no change in goals. The 5v5 PD leads to an estimated eight extra minutes of PK for the Bruin’s, which is estimated to result in -0.64 change to the GD. Overall, these penalties result in +0.58 goals for the Bruins. However it is likely that the PK performs less favorably if Marchand is in the box so that number is likely an overestimate by some amount.

Below are the estimated effects of Marchand’s penalty differentials each year on the goal differentials of the Bruins:

Season	5v5 ΔGD	PK ΔGD	PP ΔGD	SUM ΔGD
2009-10	0.00	0.00	0.00	0.00
2010-11	-0.33	+0.34	-0.18	-0.17
2011-12	+1.22	+0.19	-0.57	+0.84
2012-13	+0.60	0.00	-0.13	+0.47
2013-14	-0.94	+0.20	0.00	-0.74
2014-15	-1.80	+0.18	-0.37	-1.99
2015-16	-0.64	+1.27	0.00	+0.63

Closing Notes

The first thing I would like to note is that I am not at all the first person to try and do this sort of analysis. War-on-Ice has already beat me to the punch with their Goals Above Replacement (GAR) calculator, which covers their entire player database going back to 2005. The results they have for Marchand can be seen here:

A few things are very evident at a quick glance. First off, it looks like this whole penalty issue is pretty insignificant, but the ranges for [penalties] drawn GAR and [penalties] taken GAR are -4.00 to +8.52 and -7.04 to +8.34, respectively. The range of GAR per win ranges from 6.15 to 6.55 so it’s accurate to say that over the course of a season, some players can effectively get their team an extra win just based on their ability to draw penalties and avoid taking them. So the seeming insignificance of penalty GAR does not necessarily apply to the whole league. Secondly, my numbers clearly differ from those of WOI. Well, there’s an easy explanation here: They are an incredibly smart group of people who have created a much more sophisticated model than I have. This newbie blogger just went off somewhat unrefined numbers (see below) while those smart cats have defined a “replacement player” and made all analysis relative to that theoretical entity through fancy algorithms.

Now my model does use very rudimentary numbers. My numbers don’t account for 5v3, 3v5, allows penalties for and against to cancel out within the same situation (which for most teams they simply don’t), doesn’t account for offsetting penalties, etc. These are the sort of assumptions that will reduce the accuracy of the results, but have allowed me to quickly run through the numbers by hand as a sort of proof of concept. It would take some level of programming to create a more rigorous model for Marchand’s penalty effects on the Bruins and it would likely need to also analyze the whole league to create some absolute points off of which all players would be relatively judged (ie, generate meaningful context). Effectively, I would need to recreate what WOI has done. Maybe one day.

Finally, sample size is always an issue when dealing with special teams, especially within a single season and even moreso when dealing with a single player. In some of the years, Marchand’s PK and PP time could be under 50 minutes for the season. So there is the potential for a lot of noise in the data.

Ultimately, I hope I have introduced the idea that players can create “penalty” effects on their teams. While the results for Brad Marchand were less significant than I anticipated when I decided to do this post, it did let me highlight a player who I think is overlooked as one of the best defensive wingers in the game.