Puckerings archive: Playoff Scoring Levels (16 Mar 2001)

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 March 16, 2001 and was updated on April 8, 2002.

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Playoff Scoring Levels
Copyright Iain Fyffe, 2002

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Playoff hockey is often seen as being tight-checking and low-scoring, and there is some truth to that. Playoff hockey does not suffer from the same bullshit that the regular season brings; for instance, goons do not play during the playoffs, and fighting is therefore extremely rare. But the question is, how much lower are scoring levels in the playoffs?

The answer to this question has been sought before, by Klein and Reif (KR). Unfortunately, their analysis is flawed. Their point is valid, but they make a mathematical error. Here is the passage:
“The most pervasive belief surrounding hockey is that it is much tighter than the regular-season variety of the game. “Playoff hockey” is the phrase, and it automatically triggers the image of a close-checking, conservatively played 2-1 or 1-0 game. The truth is, though, that the average playoff game features only about 13 per cent fewer goals that the average regular-season game.” (pp.196-198).

A bit overstated, if you ask me, but the point is valid. There is a belief that playoff games are lower-scoring, and it is indeed true. KR mention that playoff games have about 13 per cent fewer goals than regular-season games, although the numbers they present actually suggest the figure is 12 per cent. How do they calculate this? The same way that everyone calculates this figure: they compare regular-season goals-per-game averages to playoff goals-per-game averages. This is a very common error. This method is too simplistic.

The problem is that not all teams make the playoffs. Therefore, if we include all teams in one group (regular-season), but limit the other group to only some teams (playoffs), bias can occur. I will show KR’s data, with additional data that excludes non-playoff teams from the regular-season goals-per game calculations.

I have limited my analysis to the years used by KR. The table presents the following figures:

RSGPG: The regular-season goals-per-game average, as calculated by KR.
PLGPG: The playoff average, per KR.
PLRat: The ratio of playoff GPGA to regular-season GPGA.
FRGPG: The regular-season goals-per-game average, excluding teams that did not make the playoffs. To be honest, I did not calculate these directly, because I’m too lazy (but this extremely small inaccuracy does not affect my point). I used KR’s numbers for GPGA and the total goals in the NHL for that year to compute total minutes, and then calculated an average minutes per team and used that as my minutes for playoff teams in the regular season. he distortion this would cause is negligible.

FRRat: The same ratio as above, calculated using the Fair GPGA.

Year	RSGPG	PLGPG	PLRat	FRGPG	FRRat
1936-37	4.75	3.48	.733	4.62	.753
1937-38	4.88	3.81	.781	4.89	.779
1938-39	4.91	3.54	.721	4.98	.711
1939-40	4.84	4.04	.828	4.78	.839
1940-41	5.12	4.16	.811	5.03	.827
1941-42	6.05	5.24	.866	6.02	.870
1942-43	7.20	5.58	.776	6.95	.803
1943-44	8.17	5.51	.675	7.44	.741
1944-45	7.35	4.73	.643	7.35	.643
1945-46	6.69	6.13	.916	6.56	.934
1946-47	6.32	4.87	.771	6.06	.804
1947-48	5.86	5.69	.972	5.72	.995
1948-49	5.43	4.26	.785	5.28	.807
1949-50	5.47	4.07	.745	5.09	.800
1950-51	5.42	3.80	.701	5.20	.731
1951-52	5.19	3.82	.735	4.89	.781
1952-53	4.79	5.40	1.128	4.74	1.139
1953-54	4.80	4.18	.869	4.64	.901
1954-55	5.04	4.61	1.112	4.86	1.154
1955-56	5.07	5.57	1.100	5.09	1.094
1956-57	5.38	5.51	1.024	5.36	1.028
1957-58	5.60	6.05	1.081	5.60	1.081
1958-59	5.77	5.91	1.024	5.80	1.019
1959-60	5.90	5.10	.866	5.65	.903
1960-61	6.00	4.65	.774	5.85	.795
1961-62	6.02	5.54	.921	5.87	.944
1962-63	5.95	5.69	.956	5.63	1.011
1963-64	5.55	4.79	.863	5.43	.882
1964-65	5.75	5.06	.880	5.61	.902
1965-66	6.08	5.30	.881	5.89	.900
1966-67	5.96	5.25	.880	5.77	.910
1967-68	5.58	5.34	.957	5.55	.962
1968-69	5.96	5.56	.933	5.84	.952
1969-70	5.81	6.00	1.033	5.77	1.040
1970-71	6.24	5.93	.950	6.37	.931
1971-72	6.13	6.04	.985	5.98	1.010
1972-73	6.55	6.27	.957	6.55	.957
1973-74	6.39	5.68	.889	6.32	.899
1974-75	6.85	6.07	.887	6.84	.887
1975-76	6.82	5.65	.828	6.82	.828
1976-77	6.64	6.24	.939	6.63	.941
1977-78	6.59	5.67	.860	6.29	.901
1978-79	7.00	6.02	.860	6.95	.866
1979-80	7.03	6.51	.926	7.07	.921
1980-81	7.69	7.77	1.010	7.67	1.013
1981-82	8.02	6.99	.872	8.05	.868
1982-83	7.73	7.45	.964	7.67	.971
1983-84	7.80	6.21	.796	7.76	.800
1984-85	7.68	7.34	.956	7.65	.959
1985-86	7.86	6.43	.818	7.81	.823
1986-87	7.25	6.13	.845	7.17	.855
Average	6.18	5.44		6.07

There are 51 years here. Of these 51 years, the FRGPG is lower than the RSGPG 40 times, higher 7 times, and the same 4 times. So clearly, there is a degree of distortion in KR’s numbers. The difference is generally minor, but it is still there.

What can we learn from this? Really, only that bad teams tend to play high-scoring games, usually because they allow a lot of goals. When you remove them from the mix, goals-per-game figures drop. But that’s not really the point.

The point is that when you do statistical analysis, you should strive to get it right. It is very easy to lie with statistics, as they say, so it is critical to eliminate flaws in your analysis. It’s ironic, because if KR had performed their analysis the proper way, it would have provided somewhat stronger support for their assertion that playoff scoring isn’t as low as many people think. By my analysis, playoff scoring is 10% lower; by theirs, it’s 12%. So you see, doing the numbers right can get you stronger support for your position.

Reference

Klein, J. and K.E. Reif. The Klein and Reif Hockey Compendium (revised edition). Toronto: McClelland and Stewart, 1987.