## Friday, 10 October 2014

### Puckerings archive: The Cost of a Penalty (18 Oct 2002)

What follows is a post from my old hockey analysis site puckerings.com (later hockeythink.com). It is reproduced here for posterity; bear in mind this writing is over a decade old and I may not even agree with it myself anymore. This post was originally published on October 18, 2002.

Theory: the Cost of a Penalty
Copyright Iain Fyffe, 2002

The value of odd-man play is often debated. In the mass media, much ado is made about the power-play (and, to a lesser extent, penalty-killing), calling it a key to success. Others, such as Klein and Reif, downplay its importance, noting that even-strength play is better for predicting success.

This essay takes a conceptual approach to this problem. What, in theory, is the importance of odd-man situations? To examine this question, I will examine a theoretical team, one which is average in all respects.

This team plays in three types of situations: even-strength (ES), power-play (PP) and short-handed (SH). Examining each of these situations reveals the answer we are looking for.

Even-strength: The team is completely average. Therefore, they will score exactly as many ES goals (ESGF) as they allow (ESGA). Thus, their expected net goal differential per minute of ES time (ESMIN) is calculated as follows:

( ESGF - ESGA ) / ESMIN

Which, for reasons discussed above, is zero.

Power-play: On the PP, a team scores about three times as often as at ES, while goals against are cut in half. PP time (PPMIN) produces a net goal differential as follows, using 1998/99 figures:

( PPGF - SHGA ) / PPMIN
= ( 1533 - 220 ) / 16326 ... minutes figure is estimated
= 0.08

Short-handed: Since PP time for one team is SH time for another, SH situations produce the converse of PP, or -0.08 goals per minute.

Taking this all together, as average team will have a winning record if they can obtain more PP opportunities then they give. That's badly phrased, since a team with a winning record cannot be average, but you know what I mean. This is most easily accomplished by taking as few penalties as possible, since you have rather limited control over your opponent's actions.

From this perspective, odd-man situations are extremely important, as they decide games. The team taking fewer non-coincident penalties should win, on average.

If this perspective is valid, then we should be able to predict success based upon PP opportunities for and against. I tested the coefficient of correlation between net PP opportunities and standings points for a selection of recent seasons:

 1990/91 0.11 1991/92 0.26 1994/95 0.02 1995/96 -0.02 1998/99 0.63 1999/00 0.23 average 0.21

The correlations provide, on average, some support for the theory. They are generally positive, but not that strong (aside from 1998/99, which is very strong). But remember, we are not considering the quality of the teams, unless you consider taking few penalties to be a quality (which you should.) So there is some evidence that this theory is valid.