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March 29 marks the second anniversary of my first article here at HockeyZonePlus. To commemorate the occasion, I thought I’d write a larger, more complete article than usual; I’ve noticed my recent articles tend to be quite short. Since the article is so much larger than usual, it’s broken up into three parts; this also means I don’t have to type it all at once, which is nice. But what to write about? Well, with the playoffs nearly upon us, it’s an appropriate topic to discuss, in an analytical way.

Media and fans alike seem to enjoy nothing more come playoff time than a Cinderella story. The history of the Stanley Cup playoffs is replete with these feel-good stories. The Canucks made the finals in 1982 after finishing 11th overall in the regular season. They did it again in 1994, this time after a 14th-place finish. The North Stars also wore the glass slipper twice: in 1981 (9th overall) and 1991 (16th). Another 16th-place team has made the finals: Carolina in 2002. Los Angeles finished 11th overall in 1993 and made the finals; Anaheim did the same in 2003.

What do all these teams have in common? They were all underdogs that fought their way to the Stanley Cup finals, defying the odds. But the more observant of you may have noticed that I only mentioned making the finals, not winning the Cup. That’s because they all have one other thing in common: they all lost. For all the warm and fuzzy feelings, there’s not a single Cup win among them. In fact, no team ranked lower than 7th overall in the regular season has won the Stanley Cup since the advent of 16-team playoffs in 1980. Okay, that’s not literally true. When the Devils won the Cup in 1995, they had placed only 10th overall in the regular schedule. But there are very good reasons not to consider the 1995 Devils a 10th-place team, as we’ll explore in Part 3.

The fact is, these Cinderella stories are really the result of the very flawed playoff system used in the NHL. The purpose of determining a league champion is to recognize the best team in the league. With that being the case, having a playoff system such as the NHL’s actually decreases the likelihood of achieving the goal. This is because the short-series nature of the playoff system introduces all kinds of blind luck into the proceedings, allowing lesser teams to defeat greater ones with relative regularity.

It’s all about probability. Things can happen in a set of four to seven games that cannot happen in a set of 82 games. Poor teams can seem great for brief periods, and if that brief period happens to coincide with a playoff series, then suddenly the poor team has defeated a good team, sending the more-deserving players to the golf course early.

When you think about it this way, playing an 82-game schedule seems ridiculous if you’re just going to decide the champion using a short-series playoff system. Over 82 games, luck has a much greater chance to even out, allowing the better teams to finish with better records than the poorer teams, most of the time. Even with the unbalanced schedule the NHL uses, it is far better than the playoffs at determining which team or teams are the best.

Okay, so the regular season is better. But just how likely is a playoff upset? How great an effect does this luck thing have? Obviously, it depends on the relative quality of the teams. Let’s make a rough estimate of the chance that Team A will defeat Team B in a playoff series, given that Team A will win 60% of its games against Team B. This is a significant edge; it’s something like a 90-point team going up against a 70-point team. I’m not sure exactly, I haven’t done the math.

There are four ways to win a best-of-seven series: 4-0, 4-1, 4-2 and 4-3. There is only one sequence that results in a 4-0 win (WWWW). There are four sequences that result in a 4-1 win (WWWLW, WWLWW, WLWWW, LWWWW). There are 10 sequences for 4-2, and 20 for 4-3.

The probability of the 4-0 sequence occurring (from Team A’s point of view) is calculated as:

.6 x .6 x .6 x .6

Which is .1296. This means that in 12.96% of the series in which a team can expect to win 60% of its games against its opponent, it will win the series 4-0.

The probability of each of the 4-1 sequences is:

.6 x .6 x .6 x .6 x .4

Which is .05184. Multiplying this by four gives us a 20.736% that Team A will win the series 4-1. Similarly, we expect Team A to win 20.736% of the series 4-2, and 16.589% of the series 4-3.

Adding these probabilities up tells us that Team A should win this playoff series about 81% of the time, which is a four-in-five chance. What this means is that for every five playoff series in which one team has a 60/40 edge over its opponents, one superior team will lose, due to random chance.

There are 15 playoff series in the NHL each year. If all matchups were 60/40 (which they’re not, many are much closer), we would still expect three upsets to occur from sheer luck.

So many people still do not realize this. When an upset occurs in the playoffs, it is often attributed to the better team choking, or the lesser team having more character, or desire, or grit, or heart, or simply “knowing what it takes” to win. Well, what about this? Do some teams really perform better than expected in the playoffs? Are Cinderella teams the product of good chemistry rather than good luck?

You may immediately think of the Devils; hold on, we’ll get to them in Part 3. For now let’s just look at the big picture.

If there were teams that perform better (or worse) in the playoffs than in the regular season, we would expect it to show up in the playoff results. If it were the case, then the breakdown of finals appearances by regular-season rank would not be a clear function of their regular-season success. But look at the data since 1980, where Rank is a team’s regular-season rank and Finals is the number of final series appearances by that rank:

Since we are dealing with a relatively small sample, some aggregation is appropriate. Here Range is the range of regular-season ranks, from the table above, Number is the number of teams in each range, and Average is the average number of finals appearances by the ranks in each range:

Even competing against teams just below them in the standings, first-place teams are by far the most likely team to make the finals in any given year. As the ranks get lower, the chance of making the finals plummets. The correlation coefficient between the regular-season rank and the finals appearances is –0.75, which indicates a very strong relationship between the two: the lower you rank, the less likely you are to make the finals.

The point is, this relationship is far from random. Even with the luck involved in the playoffs, the chance that a team making the finals is predictable based on its regular-season standing. The clear pattern in this data does not support the notion of “playoff teams”.

Part of the problem is a bias of perception. If something has a 1-in-10 chance of occurring, but you happen to witness that 1-in-10 chance the only time you observe it, then you will tend to estimate the chance of that event happening as being greater than it actually is; perhaps as high as 100%.

So when a lesser team (let’s call them Anaheim) defeats a greater on (say, Detroit), it’s common to attribute it to something in the nature of the event, not to random chance. But if that particular series were replayed, Detroit would win most of the time. Of course, that particular series cannot be replayed; that doesn’t even make sense. We are then stuck with but the single observation, and a single observation is not nearly enough to make any kind of meaningful inference.

As fun as the playoffs might be, they do not do anything to determine who the best team is. That is accomplished in the regular season.

Next time, we’ll look at how often great teams are able to overcome the randomness of the playoffs to claim their rightful places as league champions.