After all, only about 35% of league play occurs with the score tied. And of that 35%, one-fifth consists of special teams play. Taken together, that means that time played at even strength with the score tied represents less than 30% of a typical NHL game.
Indeed, if we examine the relationship between a team's even strength shot ratio with the score tied and it's overall goal ratio for every season since the lockout, we find an average correlation of 0.556, meaning that even strength shot ratio only accounts for roughly 30% of the variance in outscoring with respect to a single NHL season.
However, because goals in the modern-day NHL are relatively rare events, a substantial proportion of the team-to-team variation in seasonal goal ratio can be attributed to luck. For example, random variation accounted for 47, 35, and 41 percent of team variation in goal ratio in 2007-08, 2009-10 and 2009-10, respectively.
In a hypothetical season with a sufficiently long schedule, that random variation would eventually disappear, leaving each team with a goal ratio commensurate with its abilities. What each team's goal ratio might look like in such a scenario can be approximated by taking its seasonal statistics - namely, shot ratio, shooting percentage and save percentage - and adjusting them to account for the extent to which each one is affected by random variation.* For both shooting and save percentage, the adjustment is significant as luck accounts for a majority of the variation in respect of both over the course of a single season, as indicated in the table below.
For shot ratio, however, the adjustment is less severe as the impact of randomness is comparatively smaller. Consequently, as the sample size increases, so too does the correlation between shot ratio and goal ratio.
If this exercise is performed for each post-lockout season, one is able to determine the relationship between true goal ratio and even strength shot ratio with the score tied. The results:**
Therefore, in an imaginary league in which luck is a complete non-factor, EV shot ratio with the score tied would account for roughly 65% of the variance in outscoring. In other words, even though the two variables may not be strongly correlated over the course of a single season, a team's EV shot ratio with the score tied serves as a reasonably good indicator of how it can be expected to perform over the long run. This is especially true for the three most recent seasons, in which EV shot ratio accounts for 75% of the variation in outscoring ability. It seems that as the level of parity between teams has increased, even strength shooting has become even more important.
Finally, the remaining 35% of outscoring variance indicates that there are other sustainable components of team success. Apportioning the remaining proportion of the variance between these components gives us an idea of their relative importance.
As special teams ability and EV tied shot ratio are correlated variables, residual special teams skill refers to the proportion of special teams skill that cannot be accounted for by EV tied shot ratio. Residual specials teams skill accounts for about 49% of the remaining variance.
Similarly, residual EV shot ratio refers to the proportion of even strength outshooting that cannot be predicted by EV shot ratio. This accounts for 7% of the remaining variance.
The rest of the remaining variance is explained by even strength shooting, even strength save percentage and residual variance. Residual variance is the amount of variance left over after subtracting the sum of the other four components from 1. It results from the fact that the four components are not uncorrelated, independent variables.
* even strength and special teams statistics were, of course, treated separately for this part of the analysis
**There is an alternative calculation that can be applied as a check on the correctness of these values. As the seasonal reliability of both goal ratio and EV tied shot ratio is imperfect, it is necessary to upwardly adjust the observed correlations between the two variables in order to ascertain their 'true' relationship - that is, the correlation that would result if each variable was perfectly reliable.
The adjustment involves dividing the observed correlation by the square root of the product of each variable's reliability co-efficient. In other words
r adjusted = r observed/ SQRT( reliability EV tied shot ratio* reliability goal ratio )
The application of the above formula involves determining the reliability co-efficients for each variable, which can be calculated as follows:
reliability = 1- [(1- split half reliability)/SQRT(2)]The average adjusted correlation is 0.81, which is comparable to the average adjusted correlation obtained through the first method (0.804). It should be noted that this second method is likely to slightly overestimate the true correlation, given that the two variables are not truly independent.
EDIT: Accidentally used Fenwick ratio instead of Shot ratio when determining observed correlations for 2007-08, 2008-09 and 2009-10. Table and accompanying discussion has been edited accordingly.
EDIT 2: In re-thinking the method used in the alternative calculation, it occurred to me that the better way to adjust the observed correlations would be to calculate all three input values at the half-season level.
There's no sense in using the split-half reliabilities in order to estimate the full reason reliabilities for EV shot ratio and goal ratio when the split-half reliabilities can be used themselves, given that the split-half correlation between EV shot ratio and goal ratio is readily ascertained.
This approach produced the following results.*
* the half-season values were calculated through randomly selecting 40 games, randomly selecting another 40 games without replacement, and determining the correlation between the relevant variables across the data sets. This was repeated 1000 times, with the average values used.