People say a lot of stuff about PDO and there are a lot of ways in which it gets attacked. It’s a weird little stat, not very commonsensical. Counter- intuitive, in fact. And whole screeds have been written to try to take it down from the base out. None of those have worked because PDO actually does what it’s supposed to do. It just doesn’t do anything more than that.
What PDO does–the only thing that PDO does–is highlight those players or teams who are getting better or worse results than they ought to be given how skilled they are. That’s all it does. That’s all it’s meant to do. It does that very easily and very efficiently.
To arrive at a PDO number, you add on-ice save percentage to on-ice shooting percentage. Most of the time we use 5v5 numbers but you don’t have to. It works a bit better that way because power plays and penalty kills have different levels of scoring than 5v5 play and every player/team sees a different mix of PP/PK and 5v5 time. So just leave the smaller chunk out. Obviously, for a team, on-ice numbers are all numbers.
With me so far? Good.
To interpret a PDO number, you look at the distance from 100. For instance, right now, 5 games into the season, Nashville Predator Filip Forsberg has a PDO of 114.7. It’s pretty high. It’s the 8th highest PDO in the league among skaters with 50 or more minutes at 5v5. Forsberg has yet to be on ice for an 5v5 goal against. He and his linemates are scoring on 14.7% of the shots they get on goal.
The greater the distance from 100, the more likely there will be a change. If it’s low, it will go up. If it’s high, it will go down. This is called regression to the mean, and the NHL (or any hockey league), the mean is exactly 100. Always. By definition. Every shot in the league is either a goal or a save. There aren’t any shots in the league that are not goals or saves. Thus league save percentage plus league shooting percentage is always and invariably 100. The average, then, is mathematically defined.
But, you say, there’s no reason for Filip Forsberg’s on-ice save and shooting percentage to equal 100. They’re not related to each other. How can the ability of his linemates to score affect the ability of his goaltenders to make saves?
They don’t. And they don’t have to. In fact, if they did–if everyone’s on-ice shooting and save percentages were always 100–PDO wouldn’t work. The value of PDO lies in it’s ability to show how far away one particular player or team’s experience is from the average. Basically, PDO takes advantage of a feature of how the numbers fall to describe a particular slice of the season.
An analogy: Imagine that you flip a coin 5 times and get HHHTH. You know that the average will be 50% heads, not 80%. The average is mathematically defined. You understand that if you keep flipping that coin, if you add data, it will–whether gradually or precipitously–move closer and closer to 50%. It will regress towards the mean. It may take 3 more flips to reach exactly 50% (all tails); it may take 20 more flips; it may take 1000 more flips. But it will get closer and closer over time.
In the meantime, that 80% heads rate tells you that randomness has had a strong effect on the outcomes you got in those first five flips.
The same is true of Filip Forsberg’s season. As he adds data, his shooting and save percentages will regress towards the league mean of 100. But just like flipping a coin, it may take 3 more games; it may take 20 more games; it may take more games than there are in a season. But, like flipping a coin, it will get closer and closer over time. In the meantime, you know that randomness in terms of the timing of goals both for and against has had a strong effect on Forsberg’s first five games.
What about talent? Some guys are better shooters than others. Some goalies are better.
Yes, this is true. However, two things are acting on PDO to bring it into line.
The first is that this is on-ice performance, not individual performance. Individual players have very little ability to consistently affect the shooting percentages of their linemates. And there are 5 players on the ice. Steven Stamkos may be able to score on 12% or more of all the shots he takes, but the 4 other guys he skates with aren’t. And Stamkos has very, very little control over his goalie’s save percentage. So as accurate as Stamkos may be, his on-ice shooting percentage will not be that high.
The second is that there’s a relatively narrow band of performance in these statistics. Goaltender performance is notoriously clustered across the league, for instance. It falls between about .895 and .939 (5v5) over a season the vast majority of the time, even accounting for goalies who don’t play much. Shooting performance occurs in a slightly larger spread, but there are still bounds to it. Only two players in 2013-14 had a personal 5v5 shooting percentage 20% or above. Only 18 (out of 792) shot 10% or above at 5v5.
Combine those two things with a reasonable level of ice time and you end up with PDO falling within a quite narrow band every year, for both players and teams.
However, almost no one gets to exactly 100. Some teams and players are in fact better at maintaining a slightly higher PDO than others. Some teams have both accurate shooters and great goaltending. Some players have both great linemates and great goaltenders. Some players and some teams are genuinely bad at both. These are players and teams we consider to be above or below average at shooting and goaltending. Their ability to be above or below average doesn’t negate the average. Nor does it negate the measuring system that shows where they are above or below average.
Again, if everyone did get to 100 every time and sit there, PDO wouldn’t tell us anything. It would be meaningless. The value of PDO lies in its ability to show distance from the mean.
If you’ve gotten this far you’ll notice that I haven’t even used the word “luck” yet. That’s because this word really seems to trip people up quite a bit. It calls up so many connotations for people: undeserved, fluky, without cause. None of those meanings are relevant here.
Instead PDO highlights the effect of randomness on a small sample. It says that if you add more data, you are more or less likely to see different results than you have so far. Filip Forsberg is more likely than not to be on ice for a goal against at some point in the 2014-15 season. It’s unreasonable to believe that he wouldn’t be. It is not reasonable to believe that the Predators will continue to see the same results from having him on the ice as they have so far.
In other words, the results that Forsberg has thus far experienced are probably not very representative of what his whole season will be, not due to anything he is or is not doing, but due only to the fact that he got a bunch of heads in a row. It doesn’t say anything about his skill, just about the difference between his sample so far and what is most likely to happen over the next 77 games.
PDO is a measure of variance more than it is of something as nebulous as “luck” or “Truth.” It’s one of the best predictors of the near future that we currently have and it really does what it says it does. It just doesn’t do anything else.
Puckology 
Thanks so much for this. The math made it make a lot more sense. Cheers.
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This isn’t a particularly effective analysis. PDO is only truly valuable on the team level. You’ll always expect Marian Gaborik to have a higher PDO than Jordan; Gaborik gets to play with better players, is a better shooter, and likely gets more time with better defensive pairings on the ice. It is different on a team level, of course. But for individual players, some can consistently shoot in the 12-14% range, while others shoot in the 9-11% range… that is a huge difference which isn’t based on luck, or randomness, or anything other than skill.
And as far as Stamkos (or anyone) having little effect on goalie SV%; that is true, to an extent, though you’d expect the Patrice Bergeron line, which is defensively sound and has lots of good players on it, to suppress shots and perhaps even SV% beyond what a fourth line might do. At the very least, though, you have to assume on-ice SV% will be constant, which means that those guys who can shoot 9% at evens will have a significantly higher PDO than those who shoot 7.5%. Again, on a teamwide basis this dissipates to an extent, but PDO isn’t particularly useful in evaluating individual performance.
You seem to be assuming PDO measures individual performance, which it doesn’t. However good any one player may be at either shooting or suppressing shots, ON-ICE shooting and save percentage takes all players on the ice at the same time. So above average shooting skill is balanced by average and below average skill. And in order to have a high PDO, a player not only has to experience high shooting percentage but a high save percentage at the same time.
Yes, some players can sustain higher PDOs than others. Yes, skill plays a role. The numbers nonetheless fall into a quite narrow range every single year, and the more minutes a player plays, the more that’s true.
You might postulate that Marion Gaborik, to take your example, will ALWAYS have a higher PDO than everyone else, but it’s not outside the normal range. Gaborik has had a 5v5 PDO of 103.1, 99.6, 102.5, and 103.4 between 2010-11 and 2012-13. His 5v5 on-ice shooting percentages have been 9.84, 7.14, 9.79, and 9.55, which are (mostly) above league average but certainly not 12%. His personal shooting percentages aren’t that high, either, in the 5-8% range. http://www.stats.hockeyanalysis.com/showplayer.php?pid=306
So, yes, Gaborik can be expected to sustain an above average PDO, but that’s 103, not 116. If he’s seeing 108 or above, that’s highly unlikely to continue for a full season as long as he plays most of the season (50 games or more).
Whatever the strength of his linemates and his personal shooting prowess, that skill doesn’t drive his PDO or his on-ice shooting percentages beyond the normal range. If he were shooting 12%, it would be abnormal and not likely to keep going, since very few players do that long term. This isn’t a hypothetical based on what I think ought to happen. These are the actual numbers.
Bergeron is an interesting study. He’s an extraordinary player playing on an extraordinary team. He’s probably one of the reasons the Bruins do maintain a high PDO year in and year out. Nonetheless, his on-ice save percentages generally are within .005 of Tuukka Rask’s 5v5 save percentages, sometimes higher, sometimes lower. His PDOs still end up between 102.0 and 103.4. http://www.stats.hockeyanalysis.com/showplayer.php?pid=572
That’s well within the normal range for players. At the high end, true, but he’s a high end player. If, however, he starts putting up a 94.2 (which he’s at right now), you’d expect that to come up. Again, these are not what I think Bergeron ought to be putting up because he’s an extraordinary defensive player. These are the numbers he actually experienced.
PDO might work better for players than for teams because it is, again, a way to compare the difference between a sample and a larger population, and players have smaller samples than teams. Thus, outliers are going to have stronger effects on a player’s sample than a team. In fact, that’s why team PDO ends up in a narrower range than player PDO over the course of a season.
And, once more, this isn’t about “performance.” It’s about results. When combined with other information, it helps to tell if results are matching performance. It doesn’t tell how good or bad a player’s actually performing.
PS. Never assume on-ice sv% to be constant. It never is and it never will be.
PDO for individuals can be used too…
This article is great. The only problem is still leaves a bit of mystery of how PDO is actually used. A good example of how a team would make changes based on PDO numbers would be really helpful.
Since you used Forsberg as an example, what does Nashville do now? Does Laviolette decide to play him some more because he’s hot? Or does he decide to start to shelter him since we all believe he will regress? I know you mentioned that it’s an overall team performance thing and not an individual player metric, but it’s hard to not try and use it in that manner – especially in cases like this.
Thanks for the kind words, Derek.
For myself, I don’t think a team ought to use PDO on its own to make any decisions. It has to be used in conjunction with performance measures and good old eye test analysis. So to use Forsberg again, he’s got a very good Fenwick rate (54.9%), playing with guys who are basically winning possession battles (52.8% Teammate FF), and against opponents who are slightly less likely to stop him doing what he wants (49.7% Opp FF). He’s getting 55% zone starts. In usage terms, he’s offensively optimized. I don’t think there’s much more Laviolette can do to help him out. http://www.stats.hockeyanalysis.com/showplayer.php?pid=1776
What PDO should tell Laviolette is to focus as much as possible on the process in his case. When things start to cool off for him in terms of points or goals against, if the process is still good, don’t necessarily change things. As long as the process is still good, the long-term performance will come around. Patience.
If the underlying numbers aren’t good, though, and he gets cold, do something to change the process. That’s when you might want to shelter an offensive guy more or give them better zone starts. But it’s also when you go back to basics in practice & video and try to see what’s happening and what can be done about it.
PDO’s also a warning to GMs not to buy high on players who appear to have “turned a corner” or sell low on guys who’ve “lost a step,” IF their underlying performance is still where it’s supposed to be. Shooting percentage variation is probably at the root of a lot of bad contracts and bad trades.
All that said, a lot of coaches believe in the “hot hand” effect, although the evidence that it actually exists is spotty at best. I don’t know if Laviolette is one of those guys, so I have no way to predict how he’ll approach things. He may play him more until he cools off. He may stay the course. I don’t know.
I’m not sure why you keep using the “randomness” of a coin flip as a comparison. Nothing about PDO is random at all. Also, when you assume that “The greater the distance from 100, the more likely there will be a change. If it’s low, it will go up. If it’s high, it will go down. This is called regression to the mean, and the NHL (or any hockey league), the mean is exactly 100. Always. By definition. Every shot in the league is either a goal or a save. There aren’t any shots in the league that are not goals or saves. Thus league save percentage plus league shooting percentage is always and invariably 100. The average, then, is mathematically defined,” you have to realize the period in which your numbers can be accumulated. In business, where analytics originate, that period is every quarter and fiscal year. In the article you admit that regression might take more games than there are in a season. This negates PDO entirely as a usable statistic in the NHL. All we heard all season long was how Anaheim was going to regress, but they never did. Why can’t the analytics community see the higher PDO teams as simply better teams? PDO shouldn’t even be looked at over the course of a season because there are zero carry over variables game to game. Different opponents, different strategies, even different lineups, all can change a teams PDO game to game. PDO is only useful to determine singe game performances, but by the time data is compiled, the game is over and we know who won. Its useless for anything but making an educated guess, which only gives you slightly less of a chance at being wrong with a prediction. PDO simply doesn’t work as you claim.
Again. Not an assumption. Not an educated guess. A fact. It works this way every year all the time. It’s a fact. Look it up.
PDO is not a measure of who is a better team. It is a measure of the difference between a sample and a population. And regardless of the time elapsed from shot one on day one, the league average is always 100. The time period is irrelevant to league average because every single shot on goal is either a save or a goal whether there is one shot or 10000.
I’m not sure what part of “not everyone gets to 100” is confusing you, but I’ll restate that. Not everyone gets to 100 every season. Some teams do maintain higher PDOs year after year. Some teams have high PDOs one year and not the next. Some teams maintain low PDOs. They are still within 3 points of the mean. Every season. Every single time.
And the fact that there are different opponents/strategies/personnel throughout the season is what makes one team’s sample come closer and closer to the population. That’s what is meant by adding data. No team’s sample will ever reach the size of all shots in the league because they cannot play every game in a league. Thus the sample will never = the population. Some teams will have samples that more closely resemble the whole population than other samples do.
Anaheim did regress. Their season-ending PDO was 101.9. Their playoff PDO was 100.5. Not 104, which it was for a while. Regression =/= losing. It means that small-sample results are sometimes not representative of full-season results.
People claimed Anaheim would start losing because their PDO was higher than their possession and scoring chance measures could account for. Guess what? They did start losing, and their losses coincided with a dip in their PDO. That’s not the fault of PDO. PDO isn’t the cause of losing. It’s a measure of whether one team’s sample is far from or close to the population as a whole.