Friday, 27 June 2014

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.


Playoff Scoring Levels
Copyright Iain Fyffe, 2002


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.

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