The central task of player analysis is to separate out, as much as possible, the abilities of individual players from the effects of their teammates, their competition, and the choices of their coach. As much as possible, we want to know who is helping their team, and who is hurting it, and in what way.
For instance, this chart is for Hampus Lindholm, the minute-leading defender for the Anaheim Ducks in 2018-2019. Isolating individual players from context requires a large body of results to work from; I have made a habit of using two full calendar years of regular season games, which amounts to about 2,500 games of data. In this case, in the subtitle, all games up to and including the games of January 18, 2019 are used. In particular, to get a good idea of how good Lindholm's opponents are, it's important to look beyond just Ducks games.
I run several different regressions to estimate player ability: one for impact on shot rates at 5v5, one for special teams shot rates, and another for shooting ability. The graph shows the outputs of these models for a specific player, as well as some plain (unregressed) measurements of some aspects of their play which I feel are reasonably "individual", that is, penalties drawn and taken and how many of their team's shots a given player takes.
The most important way a skater can affect the results of games is by moving the puck into the offensive zone where they or one of their teammates might score. Therefore, this impact is what gets the most important place in the viz, in the top left. Red areas show where the given player causes shots to be taken at a larger rate than league average, blue areas less. I have also written a detailed explanation of these shot rate maps, which I use often for many purposes. For offence, more shots (red) is good. Lindholm here is a small but definite positive, causing dangerous shots to be taken from the slot. Most of these shots are not taken by him personally.
Similarly, the impact the given player has on their team's defence is shown in the bottom-left. Just as above, red means more shots while blue means fewer, so a good defensive player will be mostly blue, especially in dangerous areas. Here Lindholm shows strongly again, which is especially interesting since he plays on a very weak defensive team and his raw "on-ice" results look very different. You can read a full description of the model from which these results are obtained, but the short version is that I account for teammates, competition, the prevailing score, and the zones of the ice the coach chooses for the player to begin their shifts in.
A similar model for special teams allows me to compute how each individual player contributes to their teams shot rates on the power-play, this is shown in the top-right. This is not as important as 5v5 play, since so many fewer goals are scored at 5v4, and the model operates on fewer minutes of data and somewhat more tenuously follows its assumptions. For all these reasons, I display this data in smaller form, to make it clear that it is less important. Here, pink means more and green means fewer. The number of minutes the skater played on the power-play in the 730 days under consideration is shown also, 234 minutes in Lindholm's case, whose impact is very close to that of an average power-player. Players who played fewer than 100 power-play minutes will not have an estimate here.
The same model which generates power-play ability estimates also outputs penalty-kill estimates, as it must since it takes quality of competition into account. This is displayed in the bottom-right, where again green means fewer and pink means more. Here, Lindholm's impact is strong and helps his team greatly, reducing the frequency with which his opponents shoot from dangerous areas considerably when the Ducks are down a skater.
Finally, I also record some simpler results that do not need a rink to be displayed.