FanPost

PDO is a bad metric, from an analytical standpoint. Math Proofs inside.




When I first started to get into advanced hockey statistics, some of them didn't sit well with me. And in almost every case I've come to see that I had a Don Cherry shaped monkey on my back for most of those opinions, and that they were a different way to look at the game. That was fine. Yet, after all this time, one of them continues the bother me. PDO.

So I started really thinking about it, and came to a startling realization. Its not because its against ingrained old school beliefs.

"PDO is an advanced statistic in hockey that combines save % and shooting % in an effort to measure overall performance of a team and highlight teams with outsized "luck".

The basic idea is that teams on average should be around the 1.000 level as each shot is either a goal or a save teams that are relatively higher are producing above expectations and should regress back to the 1.000 level and teams that are relatively lower are producing below expectations and should regess up to the 1.000 level." (Definition taken from sportingcharts.com)

Its because its bad math, bad statistics, and oversimplifies something that we should be able to state with a reasonable degree of confidence.

PDO is by nature a zero sum game, something that makes it difficult to draw conclusions. For instance the PDO of two teams playing each other is always one. There's inherent problems in combining two interrelated numbers to draw a conclusion, and this analysis would be more accurate if I broke down shooting and save percentage separately, but I'm both lazy and this is already going to be a chore to read, so I'll let the simplification stand.

Last season over 82 regular season players took 74300 (approximately) shots over last year. That means over 148600 individual events were used to calculate the PDO of the 30 NHL team's that I will be using for this analysis last year. (PDO numbers from http://www.sportingcharts.com/nhl/stats/team-pdo-numbers-save-plus-shooting-percentage/2013/)

Now, the numbers for PDO are all ugly things to work with, so I'm going to simplify them for visual purposes, by undoing the percentage form which they are based on. Using Boston as an example, I first subract the sample mean 1.00, to get 0.027 as an adjusted PDO. Now I multiply by 100, to get Boston's final adjusted score of PDOa 2.7. Nice easy way to say that the Bruin's didn't deserve to win the President's trophy.

I do this for all the NHL teams to get a spread of numbers ranging from Boston's +2.7 to Florida's -2.6.

Is the formula I'm going to use to calculate the stand deviation.

Thats a very complicated looking way of expressing how this actually works. We want to calculate the amount a team can expect to differ from league average PDOa of 0. This formula shows us how to calculate σ. Which is the amount of difference we see between the expected PDOa and actual PDOa for teams.

In our case the capital N in the equation is 30, and represents the number of NHL teams.

i =1 is telling us that we are calculation the deviation for one single NHL team.

The fancy E looking symbol under the square root sign is sigma, and it tells us to take the total of all the teams deviation.

X stands for any of the teams, lets calculate for the Montreal Canadiens.

(Xch - u)^2 = (1.1- 0)^2 = 1.21. This calculates how much Montreal contributed to the deviation for the whole NHL.

So we now go through this calculation for each individual NHL team the total all the results, divide by 30, and take the square root of all those results to calculate the expected standard deviation in PDO for any NHL team in a year.

I punch my PDO numbers into this http://www.calculator.net/standard-deviation-calculator.html to generate a nice easy to read table.

Sample Standard Deviation, s: 1.2275384208703
Sample Standard Variance, s2 1.5068505747126
Total Numbers, N 30
Sum: 0.2
Mean (Average): 0.0066666666666667
Population Standard Deviation, σ 1.2069060536024
Population Standard Variance, σ2 1.4566222222222

If it follows the normal distribution
The 68.3% measure confidence range, σ -1.2208717542036 - 1.2342050875369
The 90% measure confidence range, 1.645σ -2.0126340356649 - 2.0259673689982
The 95% measure confidence range, 1.960σ -2.399308638239 - 2.4126419715724
The 99% measure confidence range, 2.576σ -3.1554723054951 - 3.1688056388284

The second half of the chart states how much confidence you can have in the numbers, using another equation and proof

based on a normal distribution Its a fairly basic stats proof, but one that takes a long time to work out, and can be found here for those curious (http://en.wikipedia.org/wiki/Central_limit_theorem)

So what we can conclude here is that teams have a 68.3 chance of their PDO regressing 1.2 towards the mean.

In Vegas 68.3% odds of predicting anything gets you bounced from a casino.

So yes, there is something to PDO. But regressing all the way to league average PDO should not be expected. For instance, league leading negative PDO team , the Florida Panthers,has a 95% chance of fiinishing next season below 1.00 PDO, and by the same measure the league leading Bruins have a 95% chance of finishing above 1.00 pdo.

Bad news. The Habs PDO was within a single deviation from the mean (barely), meaning that their shooting percentage and save percentage is very likely to regress (68.3% likely) and was not indicative of exceptional talent.

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