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An All About the Jersey Hockey Stat Primer: Shooting and Save Percentages and PDO.

Continuing the series of primers about hockey stats, this post focuses on shooting percentage, save percentage, and PDO. This also includes the Law of Large Numbers, the Gambler’s Fallacy, and plenty of Kyle Palmieri.

New Jersey Devils v Detroit Red Wings
The Pride of Montvale, New Jersey scored on 16.1% of his shots last season. What can that tell us? A bit more than you may think.
Photo by Gregory Shamus/Getty Images

Last week, I posted a primer about Corsi. What it means, what it can tell us about our favorite players and teams, what people have learned from its development, and even its drawbacks. Essentially, it describes what happens on the ice for a team or a player. It speaks to how well the team is playing or how well the team plays with that player. It is about the process. It is not about the results, though. Games are not won by Corsi. They are won by goals. You want your players to score goals and your goaltender to prevent them. This second post will go over three stats related to that: Shooting percentage, save percentage, and PDO.

Let us begin with the first two.

Shooting and Save Percentages: What are they?

A shooting percentage is the number of goals scored over the number of shots on net. This can be calculated for a player or a team. This is usually labeled as S% of Sh%.

A save percentage is the number of saves made over the number of shots on net against. Again, this can be calculated for a player or a team. This is usually labeled as Sv% or Save%.

These percentages can be presented in two ways. The most common way is specific to the player or the team. For an example, let us look to the Pride of Montvale, New Jersey as Kyle Palmieri led the Devils in goalscoring last season. Per, his shooting percentage last season was approximately 16.1%. This is calculated from his 25 goals out of 155 shots on net. Rounded to one decimal point, that results in 16.1%.

The not-as-common way is similar to how Corsi is utilized: an on-ice shooting percentage. That would show what the team’s shooting percentage was when a player was on the ice. According to Natural Stat Trick in all situations, the Devils’ shooting percentage was 10.76% when Palmieri was on the ice. The Devils scored 71 goals out of 660 shots on net. Rounded to two decimal places, that results in 10.76%.

Notice that they are two very different percentages. Even though the process is the same - goals over shots on net - what they represent provides a different look at things. The on-ice percentage is especially notable as it was the fourth highest on the Devils and yet considerably lower than Palmieri’s own shooting percentage. This is because of the other Devils on the ice were taking shots. They were not as successful as they scored 46 out of 505 shots for a team non-Palmieri shooting percentage of 9.1%. Not everyone is shooting from the same places Palmieri is shooting, not everyone has Palmieri’s apparent talent, and not everyone got the same bounces as Palmieri. Hence, it is quite different from Palmieri’s own shooting percentage.

The same representation applies to save percentages. A goaltender’s primary job is to stop the puck. This should be a good stat to represent how well they have done at it. Per, Mackenzie Blackwood stopped 1,328 shots out of 1,452 against. This means he had a save percentage of approximately 91.5%. This was the best out of all of the goaltenders who suited up for the Devils last season. It is the main reason why Blackwood is seen as the Devils’ best goaltender.

It does not make much sense to look at the on-ice save percentage for a goaltender since they are on the ice all of the time they have to make a save. So let us go back to Palmieri. Palmieri’s on-ice save percentage was approximately 90.8% last season per Natural Stat Trick in all situations. When he was on the ice, the Devils allowed 522 shots and 48 goals. That meant the Devils goaltenders made 474 saves when Palmieri was on the ice, which results in that save percentage rounded up to 90.8%.

Palmieri’s on-ice save percentage ranked 14th out of all Devils skaters last season so several other Devils have had better and worse on-ice save percentages than Palmieri. How could that be? There are possible reasons for that too. As Palmieri was on the Devils’ first line, he often played against the other team’s better forwards - which meant the goalies were facing the other team’s better forwards. It could also be a function of Palmieri’s own teammates not being particularly great at helping their goaltender. It could also be a function of just bad fortune. It’s not like Blackwood, Schneider, Senn, or Domingue actually decided to make fewer saves than other Devils when #21 was on the ice.

In both cases of on-ice percentages, I referred to fortune as a factor. Is there a way to measure that? Not exactly but there’s a stat that does a decent enough job of filling in that particular blank.

What is PDO?

The sum of an on-ice save percentage and on-ice shooting percentage is known as PDO. Depending on how the site lists the percentages, you may see this sum around 1 or 100. It is not meant to be an actual percentage. Do not worry about the lack of unit with PDO; the value itself and meaning of PDO is what is important.

PDO does not actually stand for anything. PDO is the name of a commenter from Vic Ferrari’s (Tim Barnes’) blog, Irreverent Oiler Fans. PDO came up with the suggestion to combine the two stats based on an observation that the Edmonton Oilers would give up on players who had low combined percentages and sign players who had high ones - only for them to crash down to earth. Tim started to track that and it turned out that over time, a player’s or a team’s PDO would regress to their true value. Other bloggers in the scene ran with that such as Tyler Dellow (who works for New Jersey), Gabe “Hawerchuk” Desjardens (founder of Behind the Net, consulted for franchises in the past), the late Tore “JLikens” Purdy. Gabe in particular was very supportive of the PDO concept.

Generally, the true PDO value for a team or a player is around one (or one hundred). So if you see a team or a player with a PDO that is well above one, then they could have had good fortune in their game. To put it another way, they’ve got the benefit of the bounces. Likewise, if you see a team or a player with a PDO that is well below one, then they have had some poorer fortune. Maybe the goaltenders have been cold. Maybe their finishing has been off. Maybe they have been doing a lot of good things, but to put it in that same other way, they are not getting the bounces.

I do want to emphasize that exceptionally good players and teams may actually have a true value higher than one. The Tampa Bay Lightning, for example, have had a PDO over 102 in each of the last three seasons (102.1, 103.8, 102.2). Tampa Bay was one of the best teams of the last three seasons. Repeated high values in shooting and save percentages is not a total coincidence. Similarly, exceptionally bad players and teams may have a true value below one. The 2019-20 Detroit Red Wings may not be as bad as a 960 PDO suggests strongly that they were deeply unfortunate last season. They are also deeply without a lot of talent, so they were not likely to end up around one if that same squad could play hundreds of games together. They were a truly terrible team.

Let us apply this to Palmieri’s 2019-20 season. When Palmieri was on the ice for the Devils, the team’s shooting percentage was 10.76% and the team’s save percentage was 90.8%. This sums up to 101.56. While this value is not a percentage, it is above 100 and it does suggest that Palmieri had favorable percentages on the ice over the 65 games he played in 2019-20. To put it another way, he had good luck over the whole of last season.

However, it was not always the case in 2019-20 for Palmieri. Percentages and PDO absolutely does change over the course of time. And it takes time for these values to converge on whatever the true value may be.

How Much Time Does it Take for Percentages and PDO to Converge?

We do not know.

Seriously, we do not know.

While we know that PDO as well as shooting and save percentages will tend to converge towards whatever their true value is supposed to be, there is no set number of shots or minutes or games or days where that will be met. It may take 10 to 12 games. It may take more than 82 games - meaning that a team riding high (or low) by one or both percentages may be able to maintain it for a season. Back in 2011, Desjardens posted a graph showing that future PDO regresses to around 87% from where it started as shots for and against go from 1,000. It ended up around that mark at 3,000 shots. (For perspective’s sake, the last 82 game season by the Devils saw 5,082 shots taken for and against them.) I would disagree with Desjardens now that shooting percentage or talent does not matter. I would agree that is not a major factor; something JFresh recently wrote about in full detail in his newsletter about PDO. (Aside: I would not blame you if you read that instead of this, but hey you’re already this far in.) But, the point remains: if you start especially hot or cold, then do not expect it to last.

There is actually a part of probability theory that explains this. It is called The Law of Large Numbers. If you run an experiment over and over, eventually the average of your results will start to converge to an expected value. The easiest example to demonstrate this is to flip a coin. Assuming it is a fair coin, we know that you have a 50% chance of it coming up heads. That’s the expected value. If you flip it one time, then you may or may not get one head. If you flip it three more times, you may not necessarily get two heads and two tails. If you flip it ten more times, you may not necessarily get five heads and five tails. But if you keep going, you will increasingly get to a point where 50% of your results will be heads and each individual flip will not make much of a difference to the overall result. The concept is that with a “large enough number of experiments,” you will reach the expected the value.

The challenge in hockey is that we do not exactly know what the expected value is or when enough “experiments” take place. Even if we expect a shooting or save percentage to improve, the player, the coaching staff, and management may not have luxury to wait it until it works itself out. If it ends up taking 1,000, 2,000, or 3,000 shots for cold streaks to heat up, then a team could be done for that season already. The player, the coach, or management may not have a job anymore if they are just waiting for improvement. Likewise, a team that starts hot should be enjoyed, but expecting the success to be sustained at that level can lead to real disappointments in the face of higher expectations. That also does not bode well for the player, the coach, or management. We know from the Law of Large Numbers that the percentages and PDO will converge to a true value at some point. Whether that is measured in games or shots is beside the point. We do not know how much “large enough” will be or whether the true value is enough to have the team get the goals and saves needed to be a winning team.

This leads to a concept that I have fallen to many times: The Gambler’s Fallacy. The fallacy is to think that bad streak will necessarily balance itself out given past results in a short period. If I flip a coin three times and it comes up tails each time, then I may think that the next coin flip will be heads. After all, a coin has two sides - surely, there must be a head coming up. It is very, very unlikely to get four tails in a row flipping a coin. And that is the fallacy. Over a large number of experiments, that is true. For the next single experiment, that is not necessarily true. I could still get tails. It may be very, very unlikely to have four straight coin flips to come up tails, but it is not impossible. Again, we do not know how long is long enough for regression to set in. But expecting, demanding, and hoping it starts with the next event is a fallacy.

Let’s apply these concepts to the Devils. Specifically, to the Pride of Montvale, New Jersey.

Let’s Go Back to Palmieri

We know he scored 16.1% of his shots on net over the season. We know the team’s shooting percentage when Palmieri was on the ice 10.76%. This does not mean he scored at a consistent rate. Look at his game log and you will see stretches of scoring and not scoring. In October 2019, Palmieri scored six goals in ten games out of 30 shots. His shooting percentage was 20%. However, in November, Palmieri scored 3 goals in 15 games out of 27 shots with an eight-game goalless streak. His shooting percentage fell to 15.8%. In December, Palmieri scored 6 in 14 games with 38 shots on net and had a three-game goal streak in the middle. His shooting percentage held steady at 15.8%. Over his own season, his shooting percentage started to fluctuate less and less even with cold and hot streaks thrown in there. While we may not have reached whatever the “true value” should have been for Palmieri, there were changes over the 65 games Palmieri played last season compared to where he was after the first, second, and third months. If we lived in a world where we could keep the 2019-20 Devils playing for hundreds (thousands?) of games, then we would likely know what it is. But we do not, so we have to deal with what we have.

Likewise, Palmieri’s PDO also changed. The Devils’ goaltenders were rough in October. The Devils with Palmieri on the ice scored on 13.16% of their shots. That is higher than Palmieri’s on-ice shooting percentage at the end of 2019-20, Yet, Palmieri’s PDO at that time was a very low 97.5 since his on-ice save percentage was a woeful 84.38%. We know Cory Schneider was bad last season. You may have forgot that Blackwood started 2019-20 poorly too. Does this mean Palmieri himself was at fault? Not necessarily. We would have to go to the videotape to see if Palmieri was at fault for the 10 goals against out of 64 shots. Yet, Palmieri’s main job is not to stop pucks. That is the goaltender’s responsibility.

The good news is that the goaltending did improve over time. While Palmieri’s teammates changed and finished a lower percentage of their shots, Blackwood rebounded in a big way and the few appearances from Senn and Domingue did not totally kneecap the on-ice save percentage. As a result, after 65 games, Palmieri’s PDO improved to a much more favorable 101.75. That is a big change from a PDO of 97.5 after the first month of the season, which shows Palmieri suffered quite a bit of bad fortune. Again, we do not know if Palmieri’s PDO of 101.75 was bound to go back or go up over further time. We do know that time did lead to a more favorable value compared to where it was back on November 1.

This all matters because PDO and the percentages do represent results to degree. Results help shape how we view a player and what we expect of them. This is especially important for management. Remember that PDO came up with this suggestion because Edmonton kept buying players who were especially fortunate and, for lack of a better term, came down to Earth. One of the early decisions of Tom Fitzgerald has to make is whether to offer a contract extension to Palmieri, assuming he is interested in one. While we do not know his interest, we know Palmieri is coming off a season with a high shooting percentage of 16.1% - the highest in a single season in his career - and a PDO above 100. It would be a bit foolish to give him a contract that expects the 29-year old winger to continue firing pucks in at that rate and have great on-ice percentages, which will be driven the goalies - players Palmieri does not control. There are other factors in determining if Palmieri should be extended and for how much, but these should not be ignored.

(By the way, it is even trickier for Blackwood since he has only faced 2,100 shots over two seasons and he is 23. Good luck, Mr. Fitzgerald.)

Situations Matter Too

So far, I have focused on Palmieri (and a little bit of Blackwood). All of this has focused on a player so far. What about the team? What about the New Jersey Devils?

The Devils, as a whole, had a team shooting percentage of 8.73% and a team save percentage of 90.08% in all situations according to Natural Stat Trick last season. That yielded a PDO of 98.8% - which suggests they were a bit unfortunate. However, we know that Blackwood did rebound in a big way from his start to the 2019-20 season and helped bring that save percentage up. We also know the Devils traded away Taylor Hall and Blake Coleman, among other players, that would likely hurt a team’s shooting percentage as they were significant forwards on the squad. The true value may be a bit higher but this may be closer to the truth than I may want to admit.

However, there is a key phrase to consider: all situations. The reality is that the game situation does impact these percentages and, by extension, PDO. Let us look at the ranges of shooting and save percentages for the whole league in 2019-20 broken down by situation from Natural Stat Trick:

Shooting percentages

  • All Situations: 7.38% to 11.17%
  • 5-on-5 Only: 6.11% to 9.71%
  • Power Plays: 10% to 20.27%
  • Penalty Kills: 4.35% to 18.99%

Save percentages

  • All Situations: 88.63% to 92.06%
  • 5-on-5 Only: 90.12% to 93.38%
  • Power Plays: 83.08% to 98.51%
  • Penalty Kills: 83.45% to 90.61%

You can see that the ranges vary differently by the situation. 5-on-5 hockey is the most common situation in hockey and as such, the range is the tightest. There is not as much variation among the teams since every team will play thousands of minutes in 5-on-5 in a season. Additionally, a 5-on-5 situation does not inherently favor one side or the other like a power play or a penalty kill does. As expected, power plays are meant to be offensive and teams are more successful at finishing their shots. Save percentages for a team on a power play is all over the place since penalty killing teams are not likely to get a lot of shots since they are on defense and if they do, it is usually on a scoring chance. That also explains the very wide range in shooting percentage among PK teams whereas the save percentage, while still pretty wide, is not as extreme in its differences.

What this means is that you may want to consider filtering out situations as needed when you look at percentages. Similar to Corsi, 5-on-5 situations takes out the inherently offensive or defensive nature of special teams and speaks more to what a team does in general. The right thing to do is to look up the percentages for the whole league so you have an idea of whether the Devils’ shooting or save percentage is actually good compared with their peers.

This also applies for players. While power plays absolutely matter for an offensive player like Palmieri, looking at his 5-on-5 shooting percentage may be more helpful to determine his expectations for the future and whether he was especially fortunate or not in this past season. Palmieri’s 5-on-5 shooting percentage was 12.75%, which is more in line with his past seasons and may be more likely to repeat. While a goaltender typically needs to be your best penalty killer, Blackwood’s save percentage in 5-on-5 situations may be more reliable in establishing his quality as a goalie. Blackwood’s 5-on-5 save percentage was 92.6%, which is excellent. PDO is a nice rule of thumb in that you do not need to do that, but looking at 5-on-5 PDO may be more useful in determining if someone or some team is especially fortunate or not without mixing in special teams that can skew results one way or another.

The Drawback & Your Turn

One of the drawbacks with shooting percentage, save percentage, and PDO is the lack of context about the shots. Where the shot is taken, how it is taken, and such does not matter. This is a drawback shared by Corsi and Fenwick, too. Intuitively, we know that a shot from the slot is a better shot to take than a shot from the blueline. The good news is that we have data to support that and track that. In the third post of this series, I will go over two stats that go into that: scoring chances and expected goals.

In the meantime, I would like to know what you think and what you have learned about shooting percentages, save percentages, and PDO. I know a lot is to be digested, especially the probability theory information. However, even these simple looking stats have led to a lot of discussion and changes in how we view players and teams - as well as the management of teams themselves. Please provide any further questions about these stats in the comments. Thank you for reading.