Welcome back everyone. This is the 4th article in this introduction to Hockey-Analytics/Hockey-Advanced-Statistics. In case you missed the first couple of articles in this series, you can find them as follows:

Part 1: - What is the field of Hockey Analytics and Why Might You be Interested?
Part 2.1: - The Importance of Context Part 1 - Time on Ice
Part 2.2: - The Importance of Context Part 2 - Evaluating the Difficulty of Certain TOI through QUALCOMP and Zone-Starts

So in the last post in this series we discussed what makes certain ice time "harder," in that the circumstances (the opponents faced, where you start your faceoffs) make it harder to put up positive numbers.

But there's of course another important part of the context of ice time that needs to be taken into account - the quality of one's teammates.

If a player plays alongside quality teammates, then obviously he's going to have an easier time putting up positive numbers. If a player plays alongside terrible teammates, then he's going to have a harder time doing so. Thus to discern a player's true value, and his true contributions to the team, we must account not only for the competition that player faces, but the support he has from the other teammates who are on the ice with him. Once again this should be fairly obvious.

Fortunately, we have measures that can account for this to a good extent (better than we can account for quality of competition, in fact).

Unlike Quality of Competition, there actually are two main statistical metrics which can be used to eliminate the influence of teammates on a player's numbers. Thus, using these statistics, we can get an estimate of a player's actual value by separating his contributions from his teammates.

These two statistical measures are as follows:

WOWY - With or Without You:

If you were a coach, with unlimited practice time to use with your players, how would you attempt to evaluate the contributions of each individual player as part of individual lines or setups? One such method would be quite simple: you'd try out that player with 4 other players (and a goalie) on the ice, and then try those same 4 other players with a player whose value you've already discovered. The difference in performance (+/-, shot differential, etc.) is the difference in valuation between those two players on that line.

In other words, you'd test out a line of player WITH PlayerX and compare how that same line of players WITHOUT PlayerX (and with some scrub as the 5th player instead).

Now we. the fans, don't control the players who play on the ice, and don't get to see practices (generally). So we can't do such easy experiments. But despite that, we can still use the play on the ice to do a similar analysis on specific players. These analyses are called "With or Without You" analyses, or WOWY for short.

If you're a frequent visitor to LighthouseHockey, you may have seen one of BenHasna's great uses of the WOWY technique to evaluate a player (in those links, Frans Nielsen and Nino Niedereiter). Essentially, you can show how a player in question is the one causing a group of players working together to succeed (Frans, in the Ben Hasna piece) or how another player's success may only be coming due to the hands of another guy (BenHasna's piece on Nino).

WOWY analyses are terrific and are really the best method for judging a player's worth, without having to deal with the issue of teammates (Note of course that you still have the issue of quality of competition to deal with). However, they're kind of time-consuming to do. More importantly, there's no particular website which will easily spit out a WOWY analysis for you in seconds flat, you have to do it somewhat manually.

Which for most of you, makes this technique kind of pointless. But fortunately, a similar concept has been invented, which does much the same thing as WOWY, but is easily available for anyone to use or look up.

RELATIVE STATISTICS: Relative +/- (Rating) and Relative Corsi (Corsi Rel)

Relative Statistics are the answer here. What these statistics do are simple: They compare the value of a player with him on the ice to him off the ice (regardless of other players involved). Unlike pure WOWY analyses, these do not attempt to compare how a specific 4 other players do with or without the player in question, but simply compares the performance of the team as a whole with the player on and off the ice.

The most basic Relative Statistic is known as Relative +/-: Relative +/- works really simply. You take the +/- of a player while he's on the ice per 60 minutes and subtracts from it the +/- per 60 of the team when that player is OFF the ice.

So for example, lets look at John Tavares, who was -16 this year overall, for a +/- of -0.66 per 60 minutes while he was on the ice. However, when Tavares was off the ice, the team's +/- was -0.62 per 60 minutes. Thus his relative +/- was simply -0.04, meaning the team would be outscored by 0.04 more goals per 60 minutes with him on the ice than with him off the ice. That's not terrific (obviously), but it's far better than his -16 +/- makes him look (it essentially marks him as a player whose +/- should've been -1 rather than -16).

Here are the top 6 forwards in Relative +/- on the Islanders last year, minimum 38 games played (38 rather than 40 so Kyle Okposo qualifies):
1. Michael Grabner +1.12
2. Kyle Okposo +1.10
3. Frans Nielsen +1.04
4. P.A. Parenteau +0.50
5. Matt Moulson +0.18
6. John Tavares -0.04

This list shouldn't surprise anyone here: The FN-GO line was the Isles best line by far overall, while the Tavares line was #2. Now how about D-Men?
1. Jack Hillen +0.62
2. Andrew Macdonald +0.36
3. Radek Martinek +0.20
4. Travis Hamonic +0.11

Wait, Jack Hillen? Can that truly be right?

Well it's here we run into the problem with using Relative +/-: the measure relies upon +/- (obviously), which is a flawed statistic due to the fact that well, there aren't many goals in 60 minutes of hockey, or even a whole season. Thus we have a smaller sample size, which can result in some odd results. In other words, the sample size of goals is so small that we may get one player as better than others simply due to luck of the draw, such as because he played in front of a ridiculously hot goalie when others did not.

We can solve that problem by using Relative Corsi instead of Relative +/-. Relative Corsi is calculated the same basic way as Relative +/-, but using Corsi (Shot Differential) instead of +/- (goal differential). Since there are far more shots per game than goals, this gives us a much larger, and more satisfactory sample size. I'll get into corsi in its own post in the coming weeks, but for now, lets look at the top Isles by Relative Corsi:

FORWARDS:
1. Kyle Okposo +20.2
2. Michael Grabner +13.5
3. Frans Nielsen +13.5
4. P.A. Parenteau +10.3
5. John Tavares +9.1
6. Matt Moulson +8.8

Once again, no surprises here, though the Tavares line suddenly is all in positive numbers, with JT ahead of MMM.

DEFENSEMEN:
1. Travis Hamonic +7.5
2. Andrew Macdonald +1.2
3. Jack Hillen -1.8
4. Bruno Gervais -5.7
5. Radek Martinek -6.1

Well the top 2 is far better here, with the #1 D-line, and Rookie Travis Hamonic rising to the top. Curiously, Jack Hillen is still pretty nice here, and perhaps his value has been underrated defensively. If you're curious btw why Bruno is ranked above Martinek here, remember that he faced much weaker opposition than any of the rest of this top 5.

Now here's the best part. Both of these relative statistics are easily available on BehindtheNet.ca for you to peruse. Relative +/- is listed there as RATING, while Relative Corsi is listed there as Corsi Rel. They're both terrific statistics, so please check them out - they provide a great evaluation of player worth by taking out a good deal of the impact of his teammates.

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But Relative Metrics DO have an issue: if a player constantly plays with the same group of players (say there's one line-trio that's together for the entire year), the metrics will basically simply tell you the value of a particular line, rather than any specific player. You can see that above, the top 6 in both Relative Measures are simply the top two line trios.

For this reason, Relative Metrics are obviously better for Defensemen (As they'll only ever share one partner). But even then, obviously this is a flaw. So to properly value players, we need to have a metric which evaluates the actual quality of teammates. For that we have the QUALCOMP series of metrics:

QUALTEAM METRICS: QUALTEAM, Corsi QUALTEAM, Relative Corsi QUALTEAM:

QUALTEAM measures are based on the same concept as QUALCOMP, which was talked about in Part 2.2. Essentially, these measures each measure the quality of the teammates on the ice as the same time as each player, weighted* by the time those teammates actually spend on the ice with that player.

*MATH NOTE (Feel Free to Ignore this if you want, just accept that it works): So if Player A has linemates PlayerB and PlayerC on the ice with him 100% of the time, and Defensemen PlayerD, PlayerE, PlayerF, and PlayerG on the ice with him 50% of the time each, his QUALTEAM value will be the Average Value of these players weighted as follows: (1*PlayerB+1*PlayerC+.5*PlayerD+.5*PlayerE+.5*PlayerF+.5*PlayerG)/4.

These three measures only differ in what statistic they use to value the teammates of each specific player. QUALTEAM uses Relative +/- (per 60), Corsi QUALTEAM uses Corsi (per 60), and Relative Corsi QUALTEAM uses Relative Corsi (per 60).

Incidentally, I prefer Corsi QUALTEAM over the other two measures, because it's not using a Relative Statistic. When you're comparing players on different teams, you want to know how good that player's teammates ARE, not how good that player's teammates are compared to his own team. So for example, if you looked at Relative Corsi QUALTEAM or QUALTEAM for Logan Couture and Michael Grabner, Grabner looks to have stronger teammate support than Couture.

But that's obviously ridiculous: No offense to FN or KO, but well Grabner has had far worse teammates (generally defensemen are the cause here btw) than Couture, a player on a far better team. But what's happening here is that the relative metrics note that Grabner is on the Isles best overall line trio, while Couture is on the 2nd line. But we don't really want to know that when we're comparing them!

Corsi QUALTEAM fixes this problem because it doesn't use a relative metric. So here, Grabner had a Corsi QUALTEAM of roughly -5.7, while Couture had a Corsi QUALTEAM of roughly +8.8. This makes sense; clearly Couture had greater support for him from his teammates, which means we should have expected him to put up better numbers than Grabner (if all other things were the same).

Thus I would stick to Corsi QUALTEAM (known on behindthenet as Corsi QoT) for now.

All three measures of QUALTEAM all can be found on behindthenet.ca (http://www.behindthenet.ca//nhl_statistics.php?s=29&f1=2010_s&f2=5v5&f5=NYI&c=0+1+3+5+7+8+10+13+12+15+16+29+30+45+46+63#mf=t)

QUALTEAM is simply listed on behindthenet as "QUALTEAM."
Corsi QUALTEAM is listed as "Corsi QoT."
Relative Corsi QUALTEAM is listed as "Corsi Rel QoT."

Conclusion:

QUALTEAM metrics are, like QUALCOMP metrics, not really as helpful as we like, because we don't really know how much more or less we should expect from a player's numbers due to better or worse teammate support. But they provide us with more context for explaining what happened on the ice to cause the player to put up certain numbers, and are invaluable in comparing the value of two different players.

Relative Metrics, such as Relative +/- and Relative Corsi, are also invaluable in stripping out the team's effect on a player's numbers, and unlike QUALTEAM/QUALCOMP, actually provides us with a number we can use to evaluate players with - these metrics account for context, but don't TELL US the context. It thus gives us a bigger picture of what is going on. I'll talk about these a little more as we go on with this series, as they are very important.

Anyhow, next time I'll talk shortly about the concept of the Replacement Player, and then we can move on from context measures to measures that actually measure player performance.