I often see people look to break down a player’s minutes by difficulty. Recently, I had an idea on how we can use a RAPM model to show that. RAPM models are basically just big linear regressors that favor coefficients closer to zero. By adding up the factors we’re interested in and smoothing the results, we can see how players performed at different difficulty levels.
There’s been plenty of talk of how Moritz Seider was thrown to the wolves this year, so he seems a pretty natural example to showcase this.
The Model
Before we get to Mo, we should probably go over some model specifics.
For this project, we’re looking at only 5-on-5 play from the 2023/24 regular season. There are no priors included in the RAPM model, so everyone starts from scratch.
The target variable is expected goals. Specifically, we’re using the Venn-ABERS calibrated expected goal model I wrote about previously, simply because it’s what I had readily at hand. This will end up bringing us into the expected xG realm, but we’ll manage.
In addition to each offensive and defensive player on the ice, the RAPM model includes terms for:
- Period
- Score state
- Zone start (including on-the-fly and PP residual)
- Home or away
- Whether or not teams were playing on the second half of a back-to-back
Additionally, there’s an interaction term for period and score state. For the sake of consistency in our nomenclature, the combination of these terms will be referred to as quality of situation (QoS).
I should probably also mention that I was lazy in how I incorporated the zone starts and finding the end of a powerplay. Feel free to completely disregard all findings as a result of these oversights. I won’t mind.
It may be worth pointing out that something no RAPM model adequately accounts for is what you may call chemistry. For example, Zach Hyman likely puts up better numbers because he regularly plays with Connor McDavid than he would if he was paired with Sam Carrick. That isn’t because Hyman would be playing any worse with Carrick, it’s that his skillset doesn’t complement Carrick the same way it does McDavid.
This is part of the reason these types of models aren’t the most predictive year-over-year. Put a player in a different situation, alongside different teammates, and you can see very different results. Something to keep in mind as we look at Seider.
The All Tomato
All right, we’ll start by looking at Seider’s overall numbers and then break things down by offense and defense.
I chose to grab the top 64 defensepeople (including Seider) in total ice time this past season. They should give us a rough approximation of what can be expected from a top pairing dman.
Let’s first check out how difficult Seider’s minutes were. I’m quite fond of the swarmplots Evolving-Hockey uses for these kinds of things, so we’ll go ahead and borrow that.
The higher numbers are easier minutes, lower are more difficult. Seider’s situational usage wasn’t bad, but he had the toughest matchups with some of the weaker teammates. However, it’s important to note the different scales used on the y-axis. We can get an idea of the importance of each of these by putting them on the same scale.
I had to switch to a violin plot or the QoC would be a straight line of dots (also why I didn’t just use an equal scale on the first plot).
This provides a nice example of the common (and over-reductive) suggestion that QoC doesn’t really matter. In smaller sample sizes, it obviously matters. Just as it’s easier for Hyman to play with McDavid than Carrick, it’s more difficult for opponents to play against 97 than 39. But, in the regular season, for each game you have to play McDavid, you get one against San Jose. As a result, over the course of the year, things tend to even out.
Anyway, let’s go ahead and see how this affected Seider’s numbers.
He had some of the toughest minutes, but he also wasn’t exactly helping the cause. He ended up ranked 62nd of the 64 defenders in total RAPM.
Now, let’s break it down by difficulty at the stint level. We can compare the results of each stint to how difficult it was expected to be, average that up, and smooth it out. We’ll start by comparing his icetime to the average of the 64 D.
On all these types of plots, the left side will be the more difficult minutes. Seider was clearly getting a rougher go than our typical top pair D.
Let’s compare Seider to a couple high end D: the Norris favourite (Quinn Hughes) and the RAPM favourite (Evan Bouchard). We can look at how far above or below average their typical minutes were. I’m also going to truncate the x-axis to get rid of the extremes that rarely come up.
Tough sledding for Seider, easy street for Bouchard, somewhere in between for Hughes.
Next, let’s see how well their xG results compared to average based on how difficult the minutes were.
You could be forgiven for thinking this plot makes Hughes out to have the best results (he was actually 4th in RAPM). He seems to be doing the best in the most difficult minutes as well as the easiest. However, as we saw, the majority of minutes come from the middle part of the plot. The middle also happens to be where Bouchard crushed it this year. That, along with his consistently above average results elsewhere, is what put him on top.
Seider, on the other hand, is pretty much the opposite of Bouchard. He has some interesting symmetry going on, but he seems to hit his low point in the most common minutes with not much to offset it.
The Offensive Seider
Moving beyond the overall game, we can do much the same thing, but focus on a single side of the puck. We’ll start by getting offensive.
I’m not going to bother with the violin plots again, but bear in mind the differing scales. The QoS is so low because the most common score state (tie game) is also the least offensive score state. The offensive and defensive side of it basically cancels out, but it shows up as a pretty strong negative when they’re split up.
Also, do try to locate the Ekholm-Bouchard pairing on the QoT chart.
Anyway, looks pretty clear that the toughest competition isn’t made up of the best defensive players. But Seider’s still on the low side for offensive expectations.
And, like his overall game, his numbers sag below the already low expectation. He’s only 9th worst of the 64 in offense, though.
Breaking it down and smoothing it out, we get minutes that look like this.
The dotted line is a typical xG rate. Bouchard gets a lot more of the easier offensive minutes, probably because the forwards he plays with most are some of the easiest to play with. Hughes doesn’t stray too far from 0. Seider mainly sees his minutes decrease as things get easier.
As for their results in those minutes.
Pretty similar to the overall chart. Though it’s kind of curious that, as things get easier, Seider does worse relative the average top pair D.
In Mo’s Defense
Finally, let’s see how Mo does at preventing offense. Keep in mind that, on defense, you want low xG, not high.
Seider was finding his way into easier situations than almost anyone, but he also had the weakest teammates and the most difficult opponents.
The combination resulted in only the 7th most difficult defensive minutes. And, once again, Seider didn’t improve his team’s results in those minutes.
As far as the type of minutes seen, Bouchard and Hughes are both pretty much hugging the equator. Seider has a clear drop on the easier side and peaks well past an average shift’s xG.
The xG results show Hughes as outperforming a typical top pair D most as the minutes get more difficult. Bouchard’s doing pretty well all along, but does have a bit of a drop on the more difficult side. Seider’s struggling pretty much all the way across.
Wrap Up
This might seem like an indictment of Seider’s play, but he just happened to be a convenient example. He’s a young player who got put in a tough situation and saw his numbers take a dip. It happens and hopefully we’ll see him rebound next season.
What I really wanted to show is how a fairly common model we already use can be extended to produce a little finer detail than is typically provided. We could go even further with this, though we’d probably hit diminishing returns pretty quick.
The Bucketless 