Concerning Playoff Cutoffs

October 29 2015, Micah Blake McCurdy, @IneffectiveMath

Among the myriad trivialities that oppress my excitable brain is the misuse of the phrase "playoff cutoff". For instance, the end-of-year 2014-2015 standings in the Eastern Conference were:

MetropolitanAtlantic
Rangers113Canadiens110
Capitals101Lightning108
Islanders101Red Wings100
Penguins98Senators99
Blue Jackets89Bruins96
Flyers84Panthers91
Devils78Maple Leafs68
Hurricanes71Sabres54

The seeded division winners are shown in bold and the wild-card teams are shown in italics.

The Penguins took the second wild-card spot with 98 points, the lowest point total among Eastern conference teams which qualified for the playoffs. It is extremely common to hear people say that "the playoff cutoff" for the east in 2014-2015 was 98 points; this is wrong. The most obvious way in which it is wrong is that the aforementioned Penguins did not need to score 98 points in order to secure their playoff spot; they could have warded off the Bruins and their 96 points with one fewer point, possibly even two fewer points and a favourable tiebreaking situation.

To arrive at a satisfactory notion of "playoff cutoff" we want a number of points above which all of the playoff teams are, and below which all of the non-playoff teams are, and which adequately captures the overall talent level of the teams at hand, so that we can compare the level of parity (artificial or otherwise) which prevails from time-to-time in the league.

A naive idea is to simply take the average of the point totals of the weakest playoff team and the strongest non-playoff team; in our above example this gives a seemingly suitable "playoff cutoff" of 97 points. However, this charming idea runs aground on the rocks of the divisional seeding, which does not appear, as of this writing, to be a purely theoretical trouble. This year (2015-2016) the Central division appears exceptionally strong, in particular, much stronger than the Pacific division. As of October 29, my prediction model Oscar suggests the following point totals for the Western conference:

PacificCentral
Kings101Predators102
Sharks97Blues102
Canucks92Stars100
Ducks86Wild98
Coyotes85Blackhawks96
Oilers82Jets96
Flames80Avalanche76

Having both wildcards go to one division has already happened (in the Central in 2014-2015, for instance) but having the sixth Central team not make the playoffs would be a novelty. It is clearly preposterous to suggest that the playoff cutoff is 92 points, the lowest among the playoff teams, since the Jets have 96 and were excluded. The unavoidable reality is that there is no such thing as a playoff cutoff for the Western conference in this scenario, there is one for the Pacific division and one for the Central.

My suggestion to resolve this frankly minor point is the following: a team is sure to make the playoffs if they do at least as well as third in their division and eighth in their conference. The minimum of these two numbers sets an upper bound for a "playoff cutoff". On the other hand, a team that does at least as bad as fourth in their division and as bad as the "third wildcard", that is, the team that comes third in the wildcard race, is sure to be excluded from the playoffs, the minimum of these two numbers gives a lower bound to any sensible "playoff cutoff". I define the "playoff cutoff" for a given division to be the average of this upper bound and this lower bound. We know it must be between these two numbers, and we have no further information, so a simple average seems to serve the turn.

In our above example, the upper bound for the Pacific is the minimum of the third-seed Canucks' 92 and the eighth-overall Jets' 96; that is, 92. The lower bound for the Pacific is the minimum of the fourth-in-the-Pacific Ducks' 86 and the "third wildcard" Jets' 96; that is, 86. The playoff cutoff for the Pacific is therefore the average of 86 and 92, that is, 89 points. This fits our intuition of the playoff cutoff measuring the required strength to qualify for the playoffs for a "notional" team -- the Canucks' 92 points is good enough but not all 92 points are required since their nearest rivals have only 86.

On the other hand, the upper bound for the Central is the minimum of the third-seed Stars' 100 and the eighth-overall Jets' 96, that is, 96. The lower bound for the Central is the minimum of the fourth-in-the-Central Wild's 98 and the "third wildcard" Jets' 96, that is, 96. Here, the playoff cutoff is exactly 96 points, which again fits our intuition exactly. After all, the Blackhawks in this scenario make the playoff with 96 points, while the Jets do not, also with 96 points; the dividing line in the Central between winners and losers is clearly 96 points.