In my previous strength of opposition article I incorrectly concluded that there is no strength of opposition effect, this article will attempt to explain the phenomenon. The mistakes in the previous article are not the result of poor statistical evaluation of the data, but rather poor data. I made some mistakes that are documented in the previous article, related to my scripts. I had compared third period of one player to the first period of another (conclude there is no correlation – go figure…).

**Introduction**

Strength of opposition is extremely hard to measure, due to several factors. You must separate offense from defense, because players will be matched to a different type of opposition depending on their strength. Players must then be some how, rated at some given value that evaluates how good a players is (preferably not subjectively), this factor also should not be significantly effected by opposition. One can just look at ice time as a measure of quality (coach is all knowing) and thus work from there, and that is the best way to find out who is played against the “top” lines. To find out if a player’s statistics are skewed by their opposition one needs a rating that looks at quality of the top lines they play against (and second, third and forth lines).

**Lines**

The line of a player is reasonably easy to guess I did a poor approximation predicting line using a linear regression style (more ice time implies better line). Before I go into the analysis I should explain the statistic: Line score basically a number from 0-3 for forwards or 0-2 for defense that rates how much time they are on the ice per game. So 18 minutes of even strength time for a defenseman would make him a 0 for line score, 8 minutes would get you a 2 or so. The exact values don’t have to be perfect because it will just scale it linearly. Forwards spend less time on the ice in general (with a few exceptions) and as such have a different scale. When I look at who each player is playing against I can just take an average of their opponents line scores and approximate the “line of opposition” I do so separately for both forwards and defense (hopefully teams always use a 3 forwards and 2 defense during 5 on 5 situations, otherwise my results are wrong). Once you get the average over a season you can compare players amongst a team (comparing between teams is a little more complicated and I don’t plan on doing it here).

To start me off, I listed two defensemen from every team, who face the top forward lines (interesting how different the score are between divisions: Ovechkin’s and Crosby’s ice time is affecting the results). This list is more here to demonstrate the effectiveness of such tools and demonstrate that the expected results come out. Based on these lists, easy defense opposition, and easy forward opposition, it would appear that coaches have an easier time making defensive style matching than offensive matching (easier to get Ohlund out vs Sakic than Sakic out vs. Brookbank) due to the fact that there are no stars playing against the worst defenseman. And it would appear, that in general the strategy in the NHL is best vs. best (although the small differnces in line scores indicate otherwise). This is likely the result of the fact that you try to get Sakic out as much as you possibly can (required break time then back on ice), whereas Brookbank can go on the ice whenever so you make sure he's out when it wont cost you the game. For interest sake I made the opposite defensive list: defensemen who were protected.

**Strength of Opposition and Statistics**

So now the real question: what does this all mean? In general what we really want to know is how this affects the statistics of players. Would Naslund get more goals per minute if he was played less vs. 4^{th} line opponents (given the same supporting cast)? The answer is most likely yes, but then the question is how many more? The problem with measuring this is that players are so entrenched in their positions it’s hard to look at things in a before and after type setting. One would have to break all players into categories of line (per game/year) and compare how their stats were hurt by playing against tougher opposition, but one would also have to scale out age and developmental issue (injuries). In summary: it’s impossible to figure out the “cost” of being on a different line (from me perspective at least), but I can do something. As I have analyzed before I can look at players in terms of “line shooting percentage” for offense and “expected goals against per hour” for defense. The defensive measure is independent of goaltending and the offensive measure captures many aspects of scoring, while removing the defensive aspects (possession), so good players on bad teams can be measured accurately. Once I know a players “rating” based on the two scales listed above I can look at how “difficult” these lines actually were (some teams have bad top lines), in fact some coaches, I would argue cannot determine talent as there are likely a number of 2^{nd} lines that are more effective than their fellow 1^{st} lines, but I’ll save that discussion for another day. In order to make my comparisons “nice” I converted the above statistics into statistics with an average of 50 and standard deviation of 20, I also made a max of 100 and min of 0, so that players who fell out of the spectrum due to amazing “skills” would not mess with the statistics to extremely (generally extremes are caused by low ice time numbers or error). Once I have both scores I can compare how offensive and defensive their respective opposition is by using the same average techniques mentioned above, however I no longer need to separate defenseman from forwards, because they are on the same scale.

So what was the question again? How does opposition affect a players statistics, more specifically: how does opposition effect expected goals against and line shooting percentage.

**Defenseman:**

Due to the fact that coaches do not appear to match players vs. defenseman, but seem to match players vs. forwards (A regression I did agreed with this theory) I will only compare offensive opposition line scores. If you do a quick regression, using ice time as a weight to scale out errors, you get an interesting relationship: players offensive scores increased with harder oppositions (which may just say top lines score more than third lines and top lines play vs. top lines), however, playing against easier offense resulted in better defensive scores by a factor of 15.7 for every 1 increase in line. Now when you look at the scores, they are a statistic with a standard deviation of around 20, the line scores have a standard deviation of around 0.1, 15.7*0.1 = 1.57 or 8% of 20, so I could conclude inconclusively that player’s defensive scores are 8% the result of opposition.

**Forwards:**

It should be no surprise that forwards have similar results to defenseman, most importantly the line quality, however a forward’s defensive score is even more dependant on opposition than a defenseman (this may be another good indicator of how worthless the minus statistics are). Similar to their defensive scores, forwards saw a marked decrease in scoring when they saw easier opposition (checking lines?), as such I will disregard these results as they provide no useful information on the quality of the forward in question. As for the defensive scores a regression shows a factor 23.1 for forward line score which works out to 2.31 when multiplied by 0.1 (same procedure as above) or 12%, so one can similarly conclude that a forwards defensive results are 12% opposition.

Looking that the regression results, there’s enough error that I can combine the forwards and defensemen into one group, this results in 10% of the variability of the defensive scores coming from opposition (nice number to work with too).

**Conclusion**

Of course the above conclusions are by no means statistically sound, the data in this study has a “tendency” to stay around the average, and team plays a large role as such the data is likely showing less variability as a function of the above variables and “reducing” the score and as such it is likely a larger number (but this is just as guess), however as lower bounds and reasonable starting guesses I will go on to rescale the players scores based on these assumptions. I can rescale the scores to account for these differences, how different are these results? Well it’s not perfect, most players change by one or two points. Meaning my scoring (from 0 to 100) is reasonably accurate even when accounting for opposition. That doesn’t necessarily imply that plus-minus or that “goals for” isn’t related to opposition, it only states that relatively speaking “expected goals against” is not statistically significantly affected by opposition and that interestingly a "lines shooting percentage" decreases with "easier lines".