In today's thread there was a conversation about whether or not FO% was really that important to a team's success. Knowing that FO% has an effect on scoring chances, zone finishes, etc, I was definitely curious. So I threw together some graphs comparing FO% to various team stats.
Based on the distribution, the relationship is loose, but based on the trend-lines a definite relationship does exist - and in every instance it points in the direct one would expect.
I was personally most curious about the relationship of FO% and Team Corsi since Corsi is a large sample size and reduces some of the noise (ex: SV% effect on GF/G and GA/G). So that one is at the end.
First off, FO% vs Team Record (Pts) for this past year.

Same data based on the past 3 seasons (as are most of the graphs).







I realized the data would probably be more telling (and maybe I'd get a tighter dispersement) if instead of charting FO% against GF/G and GA/G or ShotsFor/G and ShotAgainst/G separately, if I charted FO% against the ratios of each, so here those are below. The next two graphs were indeed much more conclusive in establishing the relationships.
FO% vs GForAgainst% (GF / (GF+GA))

If you want to be an elite team, FO% appears to be important. 12 of the 13 top teams in Goal Differential % had an above average Team FO%.
FO% vs ShotsForAgainst% (SF / (SF + SA))

And here is the graph for FO% vs Corsi. I didn't have this year's Team Corsi ratings, so I used last year's. As you can see, the dispersement is relatively tight. I assume that if I used the data from 3 seasons it would tighten up even more.
Note: the title of the horizontal axis should read "Team Corsi."
So in conclusion, yes there is a relationship between team FO% and how a team fares in other important aspects of the game which lead to scoring and overall record.
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