Have Nazem Kadri’s Embellishments Finally Caught Up To Him?

We all have that one player who we would hate if it were not for the fact that they play for our favourite team. Players like these are usually classified as “pests” and are notorious for aggravating the other team. They do this to draw penalties, which improves their teams’ chances of scoring and, ultimately, winning. Although they draw plenty of penalties and take few themselves, the most annoying part of their game is that they can also score often and make plays. As a Leafs fan, the player who best fits this description for me is Nazem Kadri. While his offensive talent is obvious by both the eye test and the numbers, Kadri has often been labelled an embellisher and is not exactly a gentleman on the ice. But when he plays by the rules, he is a highly effective skilled agitator who is loved by Leafs fans and despised by everyone else.

This season, however, Nazem Kadri seems like a much different player. Kadri had the best offensive season of his career this season, scoring 61 points in 82 games, despite losing a core component of his game: his ability to draw penalties. Indeed, the whistles seem to have gone silent for him this year. This was especially clear in the early stages of this season, when Kadri could not draw a penalty if his life depended on it. Now that the regular season has ended, I decided to dig into the numbers to see if the statistics support what we see on the ice. Is Nazem Kadri drawing less penalties this year than in the past, or is the eye test deceiving us?

In order to answer this, we need to know how frequently he was able to draw penalties in previous seasons and compare it to how often he did so this year. The graph below shows his penalties drawn per 60 minutes in all situations throughout his entire career (according to data from corsica.hockey):

Screenshot 2017-04-10 12.04.44.png

Kadri did not get much ice time in the beginning of his career so the results for the 2010-11 and 2011-12 seasons should be taken with a grain of salt (and are coloured lightly as a result). Once he earned a regular spot in the Leafs lineup, Kadri frequently enabled the Leafs to go on the powerplay, drawing 2.738 penalties per 60 minutes in the lockout shortened season. While that year was a career high for him in this area, we can clearly see that this season is likely a career low due to sample size issues in 2011-12. For every 60 minutes of ice time Kadri played, he drew nearly one less penalty this year compared to last year. That is a significant drop for any player in a large sample of ice time, and is especially noticeable for a forward who plays a shutdown role against the opponents top forward lines. The data confirms the eye test when we approach it from this angle.

The sudden decline in Kadri’s ability to draw penalties tells us that our eyes have not deceived us this season, but it does not tell us how costly it has been to the Leafs. By framing this drop in terms of goals, we will learn how it has effected the Leafs as a team. This can be achieved using a component of a statistic called “Goals Above Replacement” (or GAR for short) by @DTMAboutHeart. While you can read a more detailed explanation of it here, the basic idea is to quantify the value of a player in terms of how many goals their play is worth. A player provides value to his team if he is worth more goals than what you would expect from a replacement level player (i.e. an AHL caliber player). One component of a players GAR measures how many goals he is worth solely from his ability to draw penalties; at the risk of sounding redundant, I’d like to clarify that if a replacement level player was given playing time in the NHL, we would expect his penalty drawing ability alone to be worth 0 goals above replacement. The graph below displays the value of Kadri’s ability to draw penalties, expressed in terms of GAR per 60 minutes:

Screenshot 2017-04-11 11.13.37.png

The peaks and valleys of this graph look identical to the previous one, except Kadri’s 2011-12 season is missing from GAR (and this graph) due to an insufficient sample size of TOI. Nazem Kadri’s penalty drawing abilities have always been positive and have therefore never hurt his team. Last season, Kadri’s penalty drawing ability was worth ~0.35 goals above replacement level every 60 minutes of ice time, which dropped to ~0.08 per 60 minutes this season. In total, his penalty drawing ability plunged from 7.44 GAR last year to 1.80 GAR this year, costing him 5.64 goals above replacement. That dramatic drop in value is too large to be explained away by bad luck alone. Drawing penalties was obviously a significant aspect of Kadri’s game and the referees have taken that away from him this season. Both the data and the eye test tell us that the referees have caught on to his embellishment tactics and are consequently reluctant to give him the benefit of the doubt.

For additional context, it is also useful to look at the penalty drawing rates of his linemates as well to see if it is effecting them too. We want to know how often Kadri’s linemates drew penalties in previous seasons and then compare those rates to this season. To measure this, I simply found out how often the Leafs drew penalties when Kadri was on the ice and then subtracted the penalties that were drawn by Kadri. The following graph contains data from corsica.hockey and displays how often Kadri’s linemates drew penalties with him on the ice:

Screenshot 2017-04-10 12.15.40.png

The top line shows how often the Leafs drew penalties when Kadri was on the ice, while the bottom line illustrates the rate at which Kadri’s linemates drew penalties. The top line tells us that the Leafs are drawing penalties less often with Kadri on the ice than they have in the last two seasons. Earlier in this post, we learned that Kadri himself is drawing penalties less often than before and now we can see that his entire team is suffering because of it (whenever he is on the ice). Despite this, the slight uptick in the bottom line shows that Kadri’s linemates are actually drawing penalties more frequently than last season. However, an increase of 0.367 penalties drawn per 60 minutes is not very much especially given the variability of Kadri’s own rates throughout his career. The penalty drawing rates of Kadri’s linemates suggest that Kadri’s inability to draw penalties at a high frequency this season is an issue that is isolated to him alone.

While this is an interesting way to explore Kadri’s penalty drawing rates, no method is perfect and we must be aware of the flaws of our analyses. When we analyze the penalty drawing rates for Kadri’s linemates, for example, we are not accounting for the fact that Kadri does not play with the same four skaters every shift of every season and that players may vary in their capability to draw penalties. It is therefore possible that the slight uptick in the rate of penalties drawn by Kadri’s linemates can be explained away by the possibility that one of those linemates this season is also good at drawing penalties. Nevertheless, all three approaches we have seen thus far have painted a clear picture that matches what many fans have noticed throughout this season. 

By analyzing Kadri’s penalty drawing abilities from different perspectives, we have observed that the data passes the eye test. Kadri is drawing less penalties than ever before while the penalty drawing rates of his linemates have remained virtually unchanged since last season — a signal that this issue has not become a problem for his linemates too. He personally drew 0.926 less penalties per 60 minutes compared to last season, decreasing his value in this area by 5.64 goals above replacement. Although this particular drop is not as large as the one from 2012-13 to 2013-14, this one is more noticeable because it is recent and examples of blatant non-calls against Kadri from this season come to mind easier than examples from three years ago. This is confirmed by the data, which reveals that the value of his penalty drawing abilities is at an all-time low. It makes sense, then, that many fans including myself have noticed so many non-calls against Kadri this season in particular. Altogether, the data and the eye test both paint the same picture of silent whistles (belonging to the referees) and loud complaints from Leafs fans. While Kadri still plays like a skilled agitator, he is less effective in that regard without his ability to send his team to the powerplay. Hockey fans who cheer for other teams and dislike Kadri for his embellishments should rejoice if this trend continues, but Leafs fans should hope that the whistles don’t stay silent for long.


Quantifying Gretzky’s “Office” in The Modern NHL

If you start learning about Wayne Gretzky’s iconic hockey career, you will eventually hear about something called “the office.” The area behind the net was dubbed “the office” because it was where Gretzky wreaked havoc on opposing defenders and preyed on helpless goalies. By taking the puck behind the net, Gretzky forced the opposition to pay attention to him while turning their backs to his four other teammates. His spectacular play in “the office” is one of the reasons he tallied so many assists throughout his career. While teams have gradually adapted their defensive systems and tactics to control this area of the ice, the advantages of playing the puck behind the net in the offensive zone still exist. Courtesy of Ryan Stimson and the Passing Project, we can now analyze data from the 2015-16 season to see which forwards succeed by playing below the icing line.

Quantifying play within this area may seem complicated at first, but we can make it easier for ourselves by simplifying things as much as possible. While Gretzky’s “Office” was only the section of ice behind the net, we’ll expand our version of this space to include the entire area below the icing line.  We can be certain that every shot assist from below the icing line has two characteristics:

  • A player located below the icing line makes a pass to a teammate.

  • The recipient of the pass shoots the puck.

These two characteristics can now be quantified using the data released in the article linked above. Analyzing the data will tell us how often players make passes from “the office” (and elsewhere below the icing line) that lead to shots. We will also be able to see which players receive these passes and take the subsequent shots most frequently. Although we probably won’t find anyone as dominant as we’d expect Gretzky to have been, it is fun to look at the data nonetheless.

Lets begin by determining which forwards are the best at being sources of danger when they have the puck below the icing line. The metric that quantifies this is called Behind-the-Net Shot Assists per 60 minutes, or BtNSA/60 for short. In other words, a Behind-the-Net Shot Assist is any pass that originated below the icing line and led to a shot. We are looking at a sample of 282 forwards who played at least 300 minutes at 5v5 during the 2015-16 regular season games that have been tracked. Here is the top 15:

Screenshot 2017-03-06 15.03.22.png

The first thing I noticed is how good Henrik Sedin is. His 3.201 BtNSA/60 dwarfs the black line which shows the average of 0.972 BtNSA/60. When he has the puck behind the net, he assists on shots more than three times as often as the average forward in this sample. That is very, very good.

Sidney Crosby also shows up here, as does Joe Thornton. Fresh off recording his 1000th career assist a few nights ago, Thornton is considered one of the best playmakers in the league. Their ability to create offence in this way is merely one reason why they are both elite players.

While a Behind-the-Net Shot Assist is awarded to a player who completes this type of  pass, the next step is to see which players were frequently on the receiving end of these passes. But first, a bit of clarification. Since not all passes lead to shots, the following distinction is crucial: behind-the-net passes that lead directly to shots are different than behind-the-net passes that do not. The latter is not a Behind-the-Net Shot Assist because a shot was not taken after the pass was completed. Because we want to know who is taking these shots most often, we should not assume that these shooters are also the most frequent recipients of behind-the-net passes. It is important to know what the data is telling us before we analyze it.

Here is the leaderboard using the same sample as before, but this time we are measuring forwards by how often they shot the puck after receiving a behind-the-net pass:

Screenshot 2017-03-07 13.05.57.png

Nino Niederreiter shows up first here, taking a shot following a behind-the-net pass more than once every 30 minutes (2.159 times every 60 minutes) at 5v5; the average is 0.830 iBtN Shots/60. Niederreiter’s result is interesting itself, but more importantly, I believe, is that the previous leaderboard revealed that he is also one of the best passers from below the icing line. If you look at the first leaderboard again, you will see that Niederreiter shows up third overall, with 2.491 Behind-the-Net Shot Assists every 60 minutes at 5v5. This suggests that Niederreiter might have a subtle talent that is overlooked by the traditional hockey statistics. Further analysis of Niederreiter’s play below the icing line should be conducted to determine how and why he is so successful in both of these categories.

While Henrik Sedin led the way in terms of Behind-the-Net Shot Assists, his twin brother, Daniel, was the 6th most frequent shooter following a pass from below the icing line. I found this to be quite fascinating because their chemistry is undoubted by traditionalists and the analytics crowd alike, and this is yet another lens through which we can view it. Henrik is responsible for digging the puck out from below the icing line and then passing it in front, where Daniel is waiting to receive the pass and to shoot the puck towards the net. Playing below the icing line is one of the ways the Sedin twins create their magic.

Altogether, we can graph each player’s results in both metrics to visualize where their results rank in both areas.

Screenshot 2017-03-08 12.01.06.png

The x-axis measures the first metric in this post: Behind-the-Net Shot Assists. Players who appear to the right of the vertical green box are the best passers from below the icing line. Along the y-axis, you will find the most frequent shooters following a behind-the-net pass. The forwards who appear in the second leaderboard shown in this post are the ones who appear towards the top of this graph. The boundaries of both green boxes represent one standard deviation above/below the mean (i.e. the gray line) for their respective metrics. In the top right, you can find the players who are most involved in passing from behind the net and shooting the puck following these passes.

Two linemates on the Washington Capitals – Niklas Backstrom and Alex Ovechkin – are another interesting case study here. They spend most of their 5v5 ice time together, yet they appear on opposite ends of the graph. We can see that Backstrom is found in the bottom right, meaning he records Behind-the-Net Shot Assists quite frequently but is rarely the shooter, while Ovechkin is found in the upper left, indicating that he is the shooter more often than the passer. This passes (no pun intended) the eye-test because everyone knows that Ovechkin loves to shoot and is very good at it, too. Like the Sedins, I’d presume that Backstrom and Ovechkin work together to generate offence from below the icing line. Perhaps this is one reason why Ovechkin is arguably the best goal scorer of this era.

If you would like to see how the players on your favourite team perform in these metrics, you can do so here.

The ability to generate offence from behind the net has clear strategic advantages for teams who seek to be as offensively dynamic as possible. While entering the offensive zone with control of the puck is the best way to generate shots, teams with players like Nino Niederreiter or the Sedin twins in their lineup will probably create more shots following a dump and chase than teams without them. Sure, dump-ins are inferior to controlled entries, but players who can generate offence from “the office” or elsewhere below the icing line minimize the gap between both options.

Although I don’t suggest that coaches should preach the dump and chase, I assume that this strategy might be less risky if conducted with players who excel at generating offence below the icing line. In the future, we will eventually be able to pair this data with zone entry data to determine if this impact actually exists. Assuming that the impact is noticeable, I highly doubt that it will turn out to be a preferable option to controlled entries. At best, it is most likely the best option for an inferior strategy.

Of course, all of this theory assumes that playing below the icing line is a skill that can be repeated year after year. In other words, is a player’s BtNSA/60 a repeatable skill? From  the post linked at the beginning of this article, we know that BtNSA/60 is one of two components within a metric called Danger Zone Shot Assists. Compared to G60 (i.e. current scoring rate), Danger Zone Shot Assists per 60 minutes is a metric that is not only more repeatable, but is also a better predictor of future scoring than a players current scoring rate itself. A players Danger Zone Shot Assist rate is calculated by adding his Behind-the-Net Shot Assist rate with his Royal Road Shot Assist rate (i.e. how often he completes passes which travel across the slot prior to a shot being taken). While BtNSA/60 itself might not be an improvement upon existing metrics, it is definitely a core component of a statistic that improves our ability to predict a players future scoring rate.

Predicting future scoring is very difficult, especially in an era where goals are scarce and defences thrive. The data from the Passing Project is one resource that can help us discover new ways to repeatedly create offence — a mission that is now more important than ever before. The data shows us how players like Niederreiter and Backstrom break down these modern defensive systems by posing offensive threats whenever they have the puck below the icing line. Passing from this area is an avenue for success in the low-scoring environment that is today’s NHL. But for Gretzky, it was just another day at “the office.”

Hello Anchoring Bias, My Old Friend: How Anchors Impact Player Evaluation

Pierre McGuire once offered the following analysis of a top prospect at an NHL Entry Draft: “Toronto wins big here. This is huge for the Toronto Maple Leafs and their organization going forward. This is the start of their rebuild, and you couldn’t build it on better shoulders than [Player X’s].”

Without any context, it may seem obvious who McGuire is talking about here: Auston Matthews. Indeed, McGuire is certainly implying that whichever player he is discussing is bound to become the Leafs saviour someday. It should not surprise you to learn that this quote was said during the first round of an NHL Draft, rather than a later round. After all, describing a player in such a manner is normally reserved for generational talents; these kinds of players do not fall very far in the draft, if at all. When analysts describe players in this light, casual fans expect nothing less than greatness, especially in Toronto.

So would it surprise you if Pierre McGuire is describing a player not named Auston Matthews? Here is some additional information to consider: McGuire is talking about a player selected in the top 5, but not first overall. The mystery player is not Auston Matthews (1st in 2016), nor is it William Nylander (8th in 2014). Perhaps he is describing Mitch Marner — the Leafs 4th overall pick in 2015? While I don’t blame you for being convinced that Marner is the correct answer, this is still false.

The final clue is that Player X is a defenceman who was drafted 5th overall by Toronto. Unfortunately, Morgan Rielly (5th overall in 2012) is not the correct answer either. It should be clear by now that there is something wrong with McGuire’s analysis of the player. From the quote alone, though, it is implied that we should expect greatness from this player. But in hindsight, without even knowing the player yet, we know that this is not what the player turned out to be. Not at all.

As the Leafs management team walked up to the podium to draft Player X, McGuire continued his analysis by saying: “When you can get a player like Luke Schenn, you just go crazy as a scout. This is a franchise player.”

(If you don’t believe me, see for yourself by watching Schenn get drafted).

Yes, Player X is indeed Luke Schenn — the 5th overall pick at the 2008 NHL Entry Draft. It is fine if you are surprised; what you feel right now is only a tiny amount of the surprise felt by Leafs fans upon realizing that Luke Schenn is actually a much worse version of the player many analysts like McGuire proclaimed he would to become. In reality, he never lived up to the unrealistic expectations that were set for him. The praise bestowed upon Schenn was not only preached by McGuire, though. To the best of my memory, many other analysts were wrong about Luke Schenn at the time, so it is unfair to single out McGuire for this mistake. Neveretheless, many of us fans still find it difficult to view Schenn as the player he is, because in our minds, he will always be the superstar who never was.

Naturally, the next logical step is to determine where everyone went wrong with Schenn. How and why do our expectations for some players get so out of hand? In Luke Schenn’s case, and many others like it, his status as a top 5 pick in the NHL draft attached to him like a parasite. For most NHL players, however, their reputations are not adversely affected by their draft position to the same extent as Schenn’s. But that does not mean it has no effect whatsoever. In general, a players draft position is likely to be mentioned whenever they are traded, signed as a free agent, or even discussed in conversation. As fans, we use their draft position as a reference point to begin formulating our opinions of the player. This is especially the case for younger players with little to no NHL experience. Despite the fact that players cannot control where they are drafted or the amount of hype surrounding them, our first impressions of a player significantly influence our judgements of their performance.

If our opinions of players are completely rational, we would never use a players draft position as a reference point to judge them. But as hockey fans, we know this is not the case. In Daniel Kahneman’s book, Thinking Fast and Slow, he explains how we allow our first impressions to lead us astray:

“The phenomenon we were studying is so common and so important in the everyday world that you should know its name: it is an anchoring effect. It occurs when people consider a particular value for an unknown quantity before estimating that quantity. What happens is one of the most reliable and robust results of experimental psychology: the estimates stay close to the number that people considered—hence the image of an anchor… If you consider how much you should pay for a house, you will be influenced by the asking price. The same house will appear more valuable if its listing price is high than if it is low, even if you are determined to resist the influence of this number… Any number that you are asked to consider as a possible solution to an estimation problem will induce an anchoring effect.

By using a players draft position to evaluate their potential, we are surrendering ourselves to the anchoring effect. The value that we consider is the players draft position, while the outcome we want to estimate is the future performance of that player. This presents a problem because we already know a player has zero control over their draft position, yet we use that value to estimate their future performance.

Like many problems, they often teach us important lessons. The lesson we can learn from anchoring bias is that an individual piece of information has the power to influence all of our subsequent analysis. Luke Schenn’s draft position suggested that he would become a franchise cornerstone, and the hype surrounding him at the draft validated that expectation. To this day, many fans still blame him for not becoming that type of player. You probably understand that first impressions are easy to form and difficult, if not impossible, to eradicate. The main takeaway here is that our estimations are led astray when we fail to ignore anchors.

Judging a player using irrelevant information like his draft position is no more useful than trying to determine the cost of a house for sale by its listing price. We assume, and oftentimes rightly so, that the value we are told to consider is one that the experts believe is correct. When a house is for sale, it is logical to assume that the asking price is the true value of the house, but it is definitely possible that this number is totally wrong. This is why we need to conduct proper research before we decide on the correct price. The same is true for hockey players: after Schenn was drafted, for example, all subsequent evaluations of his potential were anchored by the expectation that accompanies a 5th overall pick rather than his true talent level. It was easy to get fooled by the anchor because all of the praise surrounding him justified our impulse to refer to his draft position. Both factors collaborated to induce unrealistic expectations for him.

As it turns out, his true talent is closer to being a bottom pairing defender than what you should expect from a 5th overall draft choice. He still provides some value, but he is nowhere near as valuable as a superstar. This does not mean that he belongs in the AHL, but we often speak of him as if the opposite is true. The anchoring effect therefore minimizes our ability to acknowledge Schenn’s value.

In order to ignore anchors, we must be able to identify them to begin with. This is simply another way of saying that if we want to evaluate players more accurately, we must separate the signal from the noise. A players context-neutral production is the signal, and his draft position is the noise. Mistaking the latter for the former is what convinces analysts like Pierre McGuire that Luke Schenn is destined for greatness. By teaching ourselves how to recognize and avoid anchors in our everyday lives, we can provide more objective analyses.

Another manifestation of the anchoring effect is hidden within this article itself. Before I revealed that Pierre McGuire was describing Luke Schenn, you were expecting Player X to be a superstar. There is no indication in the opening paragraph that Pierre McGuire was not describing Auston Matthews. Due to this, your expectations were anchored on the expectation that Player X was either Auston Matthews or a similar Leafs player. Once I revealed the true identity of Player X, your thoughts on both Luke Schenn and McGuire’s analysis were heavily influenced by that anchor. While the hidden anchor within this article is a quote rather than a number, it still induces the same effect. In this case, our expectations are based on a certain “value”  — Auston Matthews is much more valuable than Luke Schenn — and we are surprised when that expectation is not met. The lesson this teaches us is that although anchors are sometimes useful, they are also capable of misleading us.

Although anchors influence our estimations, it is possible to move our estimations away from the anchor to a certain extent. Many of you likely experienced an adjustment of some sort as I slowly revealed the identity of Player X. Adjusting away from an anchor is also accounted for in Kahneman’s description of the anchoring effect, but he adds that “the adjustment typically ends prematurely, because people stop when they are no longer certain that they should move farther.” As I revealed more information, you became increasingly uncomfortable having Auston Matthews as your answer. You gradually adjusted your guess away from Auston Matthews and towards Morgan Rielly. By the time I revealed the final clue — Player X is a defenceman who was drafted by Toronto 5th overall — you would not have been surprised if I had said that Player X was Morgan Rielly. Sure, Rielly doesn’t exactly fit McGuire’s description of Player X, but he is still a major part of the current Leafs core.

Regardless of how well you adjusted from Matthews to Rielly, however, you were almost certainly surprised when you realized the true identity of Player X. This happened because you were unable to entirely ignore the anchor. You were expecting a superstar, and I gave you a bottom pairing defenceman. In this way, you can now see how all subsequent analysis is influenced by your first impressions.

In general, this is also how many hockey fans evaluate NHL players: we are anchored on where they are drafted, and we adjust our opinions of them as their careers progress. This is especially true around the trade deadline  — a time when many potential trades are being discussed by fans and analysts alike. In particular, the Leafs are still searching for a number one defenceman. Those who don’t believe that the Leafs need one will point a finger towards Morgan Rielly and say “he was drafted 5th overall in 2012 and is currently playing on the top-pair — he is our number 1 defenceman!” While you know that Rielly is definitely better than Luke Schenn, you also might believe that Rielly has not shown that he can succeed on the top pair just yet. That does not mean that Rielly is bad, it simply means that his maximum potential might only be as a top 4 defenceman, not a top 2. Morgan Rielly still provides value, but you know not to justify your impulse to call him a superstar by referring to his status as a former 5th overall pick. Less knowledgeable fans will be influenced by the anchor, but you won’t. You know better by now.

Finding Elite Defence Pairings Using Z-Scores

The NHL Awards Show is meant to be an entertaining experience for fans, but it is impossible to satisfy everyone.  Last year, many people were outraged that Drew Doughty was named the NHL’s best defenceman after a season in which the numbers suggested that he was slightly worse than Jake Muzzin, his own defence partner. In a sense, this outcome represents a fundamental divide amongst hockey fans with respect to how we evaluate defencemen. Traditionalists argue that Doughty was the best defenceman in the league that season and therefore deserved to win the Norris trophy. Those who value objective statistics, however, believe that Doughty was probably not the best defenceman on his own team, let alone the best in the entire league. Despite these differences in opinion, one fact that both sides can agree on is that Doughty-Muzzin is an elite defence pairing.

For the L.A. Kings and their fans, the “Doughty versus Muzzin” argument matters less than the “Doughty AND Muzzin” argument; if there was an award for the NHL’s best defence pairing, Doughty and Muzzin would likely be in the conversation every year. While the Norris trophy attempts to identify the best defenceman in the league, I will now try to quantify the output of elite defence pairings. By the end of this post, you will have a better idea of how to spot an elite defence pairing by looking at their statistics.

We’ll define a defence pairing as two defensemen who have played together for at least 500 minutes at even-strength since the 2013-14 season. Since I downloaded the data from corsica.hockey during the All-Star break, this sample does not include data from games played after January 27, 2017. In order to figure out how elite defence pairings perform, the first thing we need to do is determine what separates an elite pairing from a good pairing.

Defining Elite – An Important Analogy:

The first step we need to take is to determine what separates an elite pairing from a good pairing. In order to explain my methodology, we’ll use an analogy from school.

Imagine that you are in school and your teacher is returning your test grades. The teacher gives you two numbers: your mark (84%) and the class average (80%). Immediately, you know that you are 4% above average. This is certainly good because it tells you that you did better than most of your classmates. What it doesn’t tell you is how much better you did. You know that you’re mark is somewhere amongst the students who scored above average on the test, but you do not know your specific location amongst them. Is your mark exceptional, or are you barely above average? If you want to answer this, you need to ask your teacher for one more piece of information: the standard deviation. Using this third number along with the two numbers from before allows you to calculate your z-score. If you are already familiar with z-scores, you can skip the next section.

Calculating and Interpreting Z-Scores:

Your z-score is the answer to the question: how many standard deviations above the class average is my mark on the test? I prefer using z-scores to interpret my test results whenever possible because they are easily to calculate and simple to interpret. In fact, you are already halfway there! You already know that your mark is 4% above average because you subtracted your mark from the average. If you divide that number by the standard deviation, you have successfully calculated your z-score.

Your z-score will be a positive number if your mark is above average or a negative number if it is below average. If your z-score is 1, your mark on the test is 1 standard deviation above the class average. A z-score of -1 means that your mark is 1 standard deviation below average. Assuming we’re dealing with a normal distribution of test marks, 68% of your classmates will have z-scores somewhere between -1 and 1. The remaining 32% are either below -1 or above 1. Since we’re determining whether your test score is exceptional or merely good, we need to know if your z-score is above 1 or somewhere between 0 and 1.

If the standard deviation is 5, your z-score is 0.8 (since 4/5 = 0.8) which tells you that you are 0.8 standard deviations above the mean. That is good, but not great. But if the standard deviation was actually 3, your z-score would be 1.33 (since 4/3 = 1.33) which means that your mark is 1.33 standard deviations above the mean — a very good score! Ultimately, z-scores help us distinguish between exceptional and unexceptional results.

How can z-scores help us define “elite”?

Similarly to how we can use z-scores to interpret a mark on a test, we can also use them to interpret the results of a certain defence pairing in a specific statistic. Since there are a variety of statistics that can be used to evaluate defence, we will look at each statistic one-by-one. In any given statistic, I will define elite as any result that translates to a z-score of 1 or greater. In general, this will translate to the results that fall into the 84th percentile or greater*. If we want to determine if Doughty-Muzzin are elite shot suppressors, for example, we need to know the z-score of their on-ice CA60 (shots against per 60 minutes). Their CA60 of 44.87 is 1.83 standard deviations better than the CA60 of an average defence pairing, so they are elite shot suppressors.

*Why the 84th percentile? Recall from the previous section that 32% of all results will have z-scores that are either less than -1 or greater than 1. If these two subsets of the sample account for 32% of the entire sample, then each individual subset accounts for 32/2 = 16% of the sample. Since we’re concerned with the best (i.e. elite) results, we’re looking at the results with the highest z-scores and highest percentiles. 100 is the highest possible percentile, so 100 – 16 = 84, hence the 84th percentile or greater.

We now have sufficient information to be able to answer the following question: what do the statistics of an elite defence pairing look like? In the chart below, you can see for yourself, with explanations to follow.

Screenshot 2017-02-08 16.12.21.png

The first column of this chart is titled “Average of Elite Pairings” because it is the average result of all pairings whose z-scores were at least 1. While the first column gives us a general idea of what should be considered an elite result in each statistic, the second column, “Cut-off,” is the worst result in the sample which was considered elite. In other words, the “Cut-off” is the worst result in the sample that translates to a z-score greater than or equal to 1. Aside from z-scores, the third column is another way to translate where a cut-off ranks amongst the sample population. For example, in order for a defence pairing to be considered elite at suppressing scoring chances, they need to have a SCA60 of 6.47 (or lower) which translates to the 83rd percentile (or better) and a z-score greater than or equal to 1.04. Altogether, the chart above is a useful reference for evaluating the performance of above-average defence pairings.


We’ve seen how z-scores can be a useful tool for distinguishing between elite and above-average results. The most obvious way that we can use them to judge defence pairings is by comparing the performance to other pairings using z-scores. I have done this with Doughty-Muzzin in the chart below:

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When Doughty and Muzzin are on the ice together, they are elite shot suppressors and are above-average at preventing scoring chances and in expected goals. None of this is surprising.

Another way to incorporate z-scores into our evaluations is to make a leaderboard for pairings in a certain statistic using z-scores as a cut-off rather than arbitrarily doing a “top 10” or “top 15.” I made this viz so you can see all defence pairings who are elite in CA60. You can also use the z-CA60 filter to view all of the worst pairings in CA60 as well, by setting it to show everyone with a z-score of less than 1. (A few Leafs pairings will show up here, by the way). 

Concluding Thoughts:

Altogether, the days leading up to the NHL Awards are often filled with debates surrounding certain trophies. Last year, it was Drew Doughty at the centre of the traditionalist versus analytics debate. Despite the divergent opinions on this topic, his play with Muzzin is certainly deserving of more recognition. Although there are no NHL awards for elite defence pairings, you can use z-scores for the results of individual players as well. So regardless of which player(s) will be involved in the debates this year, you now have another tool in your repertoire to objectively separate elite performance from above-average performance. 

Where Does Auston Matthews’ Offence Rank Amongst The NHL’s Best Scorers?

Unless you’ve been living under a rock since October or not following hockey, you’ve heard that Auston Matthews is having an incredible rookie season. Within the first 47 games of his career, the 19-year-old is now representing the Toronto Maple Leafs at the NHL All Star game in Los Angeles. This brief break in the NHL schedule provides us with an opportunity to take a step back from his game-to-game accomplishments, and take a look at how his production this season ranks amongst some of his fellow All Stars. To do this, I have picked three players who most people would consider to be some of the best, if not THE best, players in world. I’ll introduce each players Offensive Production Chart, and then I’ll bring in Matthews’ chart at the end. My goal is to determine if Matthews’ production thus far is comparable to the league’s top offensive threats. 

Connor McDavid:

We’ll start with the player who the Leafs could have drafted, if not for one stubborn lottery ball: Connor McDavid. Although the Leafs won the draft lottery that gave them Auston Matthews, it was incredibly difficult to lose the opportunity to see a lifelong Leafs fan save the franchise. Here’s how McDavid has produced at 5v5 in his first season as Oiler’s captain:

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The categories on the chart on pretty self-explanatory. After his rookie season was cut short due to injury, McDavid made up for lost time this year by collecting more points in all situations (59) than any other player in the league before the All Star break. In fact, his 42 assists alone would tie him with Joe Pavelski and Mikael Granlund for 20th overall in league scoring. His remarkable ability to generate goals for his teammates is also exemplified by his primary assist rate at 5v5 — he has earned primary assists more often than every forward with at least 400 TOI except Nino Niederreiter. His 5v5 production alone may not scream “best player in the NHL” right now, but all indicators suggest that he could be there very soon. 

Sidney Crosby:

If there is a human being who is better at hockey than Connor McDavid right now, his name is Sidney Crosby. Fresh off a Stanley Cup victory last June, the Penguins captain has gathered 4 less points than McDavid, albeit in 9 less games. Here is how Crosby has produced at 5v5 so far this season:

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Sidney Crosby is approaching the end of his prime, but he’s certainly not slowing down. The only “blemish” on his offensive production in 2016-17, if you could call it that, is the rate at which he shoots the puck at 5v5. His iCF60 of 14.58 ranks 59th out of the 293 forwards in this sample. However, that is still 1st line caliber when you realize that there are 90 top line forwards in the league (30 teams in the league and 3 forwards on each top line). Sidney Crosby is still the best player on the planet.

Alex Ovechkin:

Since bursting onto the scene in 2005-06 by scoring 52 goals and 106 points as a rookie, Alex Ovechkin has been lauded as the best goal scorer in the entire league. Eleven years later, here is how “The Great Eight” has produced so far this season:

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The least surprising components of this chart are his shooting and scoring rates; everyone knows he shoots very often and scores a lot, and his numbers prove it. The number that caught my eye is his primary assist rate. Not only is Ovechkin the NHL’s most dangerous scoring threat, but he is one of the best playmakers as well (this season, at least). Perhaps the Capitals captain deserves more praise than he currently receives.

Auston Matthews:

After analyzing the current production of the NHL’s three brightest stars, let’s turn our attention to a fourth. This is how Auston Matthews has produced on offence in his rookie season:

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When it comes to scoring goals, Auston Matthews doesn’t need the man-advantage to dominate the league. His scoring rate is second only to Michael Grabner’s 1.76 goals per 60 minutes, with Crosby’s 1.71 not too far behind. Matthews is first in expected scoring and scoring chances. The frequency at which he earns primary points, shots, and shots on goal are all in the top 8 or better. Not bad for a teenager.

The only “weakness” in his offensive game is his playmaking ability. While his primary assist rate is barely above average, that is expected for someone who plays with Zach Hyman and Connor Brown. He might not shine like McDavid does in this area, but his scoring capabilities more than make up for it.

Despite all of this, I believe that it is still too early to declare Auston Matthews as the best player in the world, strictly in terms of offensive production. He might not put up over 100 points as a rookie like Crosby and Ovechkin did over a decade ago, nor is he as flashy as McDavid. But if his current production is any indication, he could definitely be in that conversation for years to come.