# The Puck Stops Here

## Parity Is Exaggerated

One of the stories of the first round of the playoffs is that of parity in the NHL.  Some of the strongest powers in the NHL are facing elimination.  These teams include the two-time Presidents Trophy winning Vancouver Canucks and three of the last four Stanley Cup winners in the Chicago Blackhawks, Pittsburgh Penguins and Detroit Red Wings.  Last year’s Stanley Cup winner the Boston Bruins are tied in their series.  This shows that any given team can win on any given night.  There are no superpowers in the NHL.  While there is some truth to that, this level of parity is a fluke.  These playoffs so far have been closer than statistical expectations.

The simplest way to see this is by looking at a simple model.  Let’s assume that each game is a coin flip.  It is a long drawn out dramatic coin flip that takes about three hours, but a coin flip nevertheless.  There cannot be more parity than this situation where each game is truly a 50-50 shot.

In this model, one of the first round series should end up as a sweep.  One of the teams will win the first game and that team has a 50% chance of winning game two, a 50% chance of winning game three and a 50% chance of winning game four.  If that team wins all of games two through four they will sweep the series.  There is a 1 in 8 chance that this will happen.  Should the series be less even than a fair coin flip that can be modelled as well.  Instead of each game being 50-50 it can be 55-45 or 60-40 or whatever the odds we need.  In these cases the odds of a sweep increase from 1 in 8.  There is no way to have a less than 1 in 8 chance of a sweep.

We have eight playoff series underway, so odds are at least one will be a sweep.  None have been.  This shows that the series have been more even that would be expected by chance alone.

If we look at the results so far, the top seed has a record of 17-15.  This is one game from being a true .500 record.  However the seeding of teams in the playoffs is not based upon point totals in the regular season.  Both conferences number three seeds had fewer points than the number six seed they are playing against.  Chicago had more points than Phoenix and New Jersey had more points than Florida.  Thus we can say that the team with more points in the regular season actually has a losing record in the playoffs at 15-17.  It is easy to see the Detroit vs. Nashville series as being another example where the top seed is not actually the better team.  Detroit has a much better record in the regular season and playoffs in the last several years.  In the standings, the teams were separated by two points.  Both teams had the same number of wins.  Regulation tie points are what make up the difference between these teams.  Detroit had a better team +/- this season, so it is quite likely they were actually the better team.  Reversing the Detroit/Nashville results gives us an even more lopsided record for the better teams.

Home ice advantage is a well established effect in the NHL.  Home teams have an 11-21 record thus far in the playoffs.  That is another number that is clearly an unsustainable fluke.  Had more home teams won (even at a 50% rate), the favorites would be doing better this season.

If we use shots differential to look at the series, we see Chicago and Detroit are the two teams that have most dominated their series by shots.  Both of these teams are losing 3-1 in their series.  Boston has the third best shots differential and is tied 2-2 in their series.  The other series are closer by shots differential, but have Vancouver, St Louis, Ottawa, New Jersey and Pittsburgh leading them.  Should that be the results in the actual series, we would not be discussing parity at all.  It is a bit of a shock that Ottawa is outshooting the New York Rangers, but most of the shots leaders in the series have been predictable.  It is the win leaders that have not been so predictable.  Of the five series that are not tied only St Louis has outshot their opponent and the margin is only two shots per game.

One story of the first round is unpredictability.  This unpredictability is being used to assert parity in the NHL.  When we dig a bit beneath the top layer of the numbers, we see that this is a clear case of unpredictability, but it does not show parity as well as we first might have guessed.  The results of the first round have been unlikely.  In many games the team that carried the play did not win.  That can happen sometimes, but over the long term it will not last.  The playoffs are short best of seven series so unlikely improbable events will occur.  There have been more improbable results in the playoffs so far than one would expect to have seen.

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One of the big differences is the absence of any home ice advantage.  Arenas were once like baalparks each unique in it’s own way.  They are all the same now.

Perhaps the league should allow teams the option of making their rink bigger if they wish.  Then you would again have teams constructed to play in different size arenas, thus a home ice advantage would be created.  Also the game might become a little less dangerous with more space to maneuver in.

Posted by 13 user names on 04/20/12 at 08:07 PM ET

There is no need to arbitrarily change rules to create a home ice advantage.  It exists over any long period of time.  In the short term (the playoff games so far are a short term) unlikely events can occur.  Home ice advantage will show itself over a longer term.

If your issue is making the game safer with larger ice surfaces that is another issue we can address and I can support it under some circumstances.

Posted by PuckStopsHere on 04/20/12 at 09:43 PM ET

I think you’ve made a mistake in your calculation.  I think the chance of a sweep where the outcome of each game is 50/50 is 1/16th.  1/2 ^ 4.  Sweeps are much more common than this because the probabilities are often substantially in favor of one team over the other.

Also the Senators were 12th best in the league in Fenwick close and the Rangers were 14th so it shouldn’t be much of a surprise that they are outshooting the Rangers.

Of course goaltending is very important but there is no reason to think that it is more important in the playoffs than in the regular season.  Having said that I really believe that Marc-Andre Fleury had a terrible series and that is why the Penguins lost.  The Penguins have such a great team its a shame to see them eliminated so early.

Believe it or not the Kings were a better possession team during the season than the Canucks were.

Nashville baffles me.  They were 2nd to last in the league in Fenwick close.  Rinne is an elite goalie but I don’t think he alone can explain their success.  Do they have a way of creating higher quality shots?  I just don’t understand their success but its gone on too long for me to attribute it to luck.

Posted by Bossy_Rules on 04/23/12 at 02:48 AM ET

I stand by my calculation.  Team A has a 1/16th chance of sweeping and team B has a 1/16th chance of sweeping.  So a sweep occurs 1/16 + 1/16 = 1/8 of the time.

Posted by PuckStopsHere on 04/23/12 at 03:20 AM ET

Right, each team has 1/16 so its 1/8th for a sweep.  You could have just said that instead of   “I stand by my calculation”.

Posted by Bossy_Rules on 04/23/12 at 04:04 PM ET

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Smileys

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