The other day, I wrote about how, in any particular season, the sum of a team's shooting and save percentage is correlated with how much time that team spent playing with the lead, and how this relationship is, in turn, related to shot differential.
The purpose of this post is to elaborate upon that.
Firstly, the issue of causation. While it goes without saying that correlation does not imply causation, I think it's reasonable to assume that there some sort of causal relationship here.
I think that the arrow of causation is bi-directional. For one, a team that is lucky or good with the percentages when the score is tied will, on average, tend to play with the lead more. In this sense, having a good team PDO number causes a team to play more with the lead.
On the other hand, however, I think that playing with lead is, in and of itself, beneficial to shooting and save percentage. I'm basing this assumption on the fact that shot ratios are subject to the leading/trailing effect. I suspect that there's some sort of trade off involved whereby the leading team's advantage in shot ratio is met with a corresponding disadvantage in the percentages.
Thus, good percentages leads to playing with the lead more, which in turn begets good percentages.
Secondly, my prediction is that playing with the lead accounts for the fact that the spread in even strength shooting percentage is somewhat larger than what would be predicated by chance alone.
Here is what has demonstrated thus far:
The distribution of team EV S% when the score is tied is entirely random.
There are no 'real effects' with respect to EV S% when the score is tied. That is to say, it has no sustain.
Some of the variation in overall EV S% at the team level is non-random. That is to say, there is more variation than what would be predicted from chance alone.
This being the case, the logical implication is that the playing to score effect is one of - perhaps the only - non-random contributions to EV S%.
As a preliminary test for this hypothesis, I looked at the relationship between [minutes played with the lead - minutes played trailing] and various even strength variables for the 2008-09 season. The results are contained below:
While the results are not unequivocally supportive, I think it tends to accord with my theory.
The teams that do better with the percentages when the score is tied at EV tend to play more with the lead overall - that's not unexpected. Moreover, and perhaps more importantly, teams that did better with the percentages at EV when the score wasn't tied tended to play more with the lead as well.
Of course, I'll refrain from saying anything with confidence until further analysis is performed.