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The League of Extraordinary Statisticians: "Good" Penalties

The League of Extraordinary Statisticians (LOES) is a weekly forum bringing together top analytical minds in the hockey world to answer a variety of questions that straddle the line between stats analysis and something you might hear floating around section 304. They have agreed to answer these questions in a few paragraphs or less, and with minimal formulae. Because this is a forum, we'd encourage you to use the comments section to answer the questions yourselves, or to discuss or debate the answers given.

The LOES is not meant to represent the entire of the hockey stats community. There are a number of people that either were too busy or too difficult to contact for the purposes of the forum.

Those who have been around the game enough have heard the term "good penalty" and, nine times out of ten, have likely thought about a defender valiantly diving to disrupt a forward who is two strides from a breakaway. Beyond that, perhaps the idea is a bit abstract, so let's make things a bit easier: think of what you might call a "dumb" or "stupid" penalty first. Then, take out all the penalties that involved action of little direct consequence to a scoring opportunity. Chances are, you are left with a pretty small number.

The point is, a "good" penalty is a value judgment, combining the perceived negative value of the penalty (a man disadvantage is clear, but even in coincidental-minor cases you might be losing an important player) plus the potential negative value had the infraction not been committed. Simple, right? Well, when posed to our LOES you can see the idea of a "good" penalty merits a bit more discussion...

The question(s) this week: In your estimation, what amount of minor penalties are of the so-called "good penalty" variety? Is taking a "good penalty" really worth it? When?

Imagine a desert. Imagine, for a moment, that the desert is filled with insects - locusts, perhaps. Somewhere, in this vast and barren desert, is a tiny lake that serves as the home of a single fish, a fish that survives by eating the occasional insect that finds it's way to the lake. The odds of any particular minor penalty being a "good penalty" are roughly equivalent to the chances of an individual member of that locust swarm dying at the hands of our aforementioned fish.

It's not that bad, but it's close. The only two instances I can think of that would qualify as a "good penalty" are when a) a near-certain goal is prevented or b) coincidental minors where the talent gap between the two players going off is wide. Given that cases of the former are often penalty-shot offences (i.e. taking out a player on a breakaway, covering the puck in the crease) and that in the latter case there will always be a bad penalty to off-set the good, this is a rare occurence indeed. As for other potential defences - i.e. "generating momentum," "sending a message," etc., the disadvantage created by going from 5-on-5 to 4-on-5 is simply too great to justify the defence.

- Jonathan Willis, Houses of the Hockey, OilersNation, & Hockey Prospectus

Very few penalties are good ones. If a player was about to put the puck directly into an open net and a defenseman tackled him, that would be a good penalty (rare), or if a defenseman took down a player on a breakaway and somehow avoided a penalty shot call, that would be a good penalty. However, an inferior player drawing a superior player into offsetting minors has some value. How often does that happen? Chris Pronger has all of four fights in six seasons, one of which he instigated at the end of OT.

- Gabe Desjardins, and, of course, Behind the Net

Generally speaking a good penalty is when you're preventing a possible goal, and the probability of that goal is greater than the probability of their team scoring on the power play. One of the caveats is time - you don't want to take a penalty when time is of the essence. Late in the game when you're trailing by a goal, it might be better to take your chances than to let your opponents use their man-advantage to easily kill two minutes.

You know, I've always felt that taking penalties is a lot like speeding tickets. In certain places and at certain times you're more likely to get a ticket - and you know that certain people in certain vehicles can more easily get away with a warning. The same is true in hockey, and you have to factor that into your calculation.

To estimate how many penalties are "good ones," I think you'd have to study game tape - I'm not sure off the top of my head how to avoid that, and do it statistically. I do know that if the purpose of a penalty is to take away a scoring chance, you'd compare scoring chances allowed against minor penalties taken. It's interesting that the correlation between minor penalties taken and 5-on-5 goals against is -0.25 so far this season. Teams that take more penalties allow fewer 5-on-5 goals, at the very least suggesting that those extra penalties are preventing goals (and are therefore "good penalties").

To study it further, I'd look at teams like New Jersey and Toronto, who take very few penalties but allow a lot of goals, teams like Pittsburgh and Montreal who take a lot of penalties but allow very few goals, and perhaps even Boston, who take few penalties and allow few goals.

- Rob Vollman, Hockey Prospectus

Once upon a time, I took a quick-and-dirty swipe at creating an Adjusted Net Penalties (ANP) stat, which put forwards and defensemen on equal footing by adjusting forwards down (they should have more opportunities to draw penalties and they should have less reason to take them) and defensemen up (vice versa) by whatever the average difference was between the positions. Somewhat along those lines of thinking, could we say that an average forward's number of penalties are appropriate for their position and that the average defenseman's number of penalties are appropriate for their position? Any more would be deemed bad penalties? Then again, I suppose it isn't reasonable to think that the average player never takes a bad penalty. Maybe it would just mean that said player was over their quota of bad penalties...

Taking a different tack, let me answer simply: if the opposing team is more likely to score on the ensuing power play than on the immediate scoring opportunity. Breakaways by any competent scorer would fall into that category, but you don't want to end up giving up a penalty shot, either.

- Timo Seppa, Hockey Prospectus

The LOES re-affirms the notion that the "good penalty" is a rare breed (of locust, perhaps) in the course of NHL play. We see that coincidental minors not only can be damaging, but on the flip side a lesser player (a pest, usually) could instigate an opposing talented player into a scrum that resulted in coincidentals. Historically, many of the better players in the NHL have recognized this tactic and avoided it, but the idea that to defend oneself is a marker of pride can sometimes cause a good player to engage the pest in question.

If nothing else, I think this LOES can stress to us an important idea: very few penalties are "good penalties." Like very few. In other words, very few penalties involve activities that offset the ensuing negativity. So when you see a player hooking down an escaping forward to prevent a breakaway, realize it might have been better for the player to keep skating and pressuring the opposition rather than essentially giving him/her a trouble-free breakaway later. When you see someone getting a holding or slashing penalty in the corner, know that the player has essentially traded one opportunity for 2 minutes of unequal pressure + opportunities (unless you're against the San Jose Sharks' power-play BOO!). Finally, when you think it's pretty cool or impressive that your team's leading scorer has over 100 PIM, realized that for as much as this player is scoring he/she is typically trading unnecessary infractions for penalty kills where the opposing shooting percentage is doubled. It kills me to watch Danny Briere and Corey Perry play sometimes because of the amount of minor penalties they commit.

For discussion: What do you think are "good" penalties? Besides Briere and Perry, which other NHL players take dumb penalties? Do you believe in the aforementioned "justice" penalties?