South Pender wrote:I get your point. However, using %age as the metric is misleading and is what is causing the confusion and different interpretations we have.
Exactly. That was my main point: the two percentages were presented with the apparent framing that one might expect them to be the same, but there's no
a priori reason to assume this from what was given.
The metrics of the two variables (overall scoring and net offense) differ, and this means that %age increases or decreases are non-comparable. Say that in 2013, mean total points/game/team was 25, and the standard deviation (SD)was 1. And mean net offense/game/team was 300 with a SD of 30. A one-point increase in mean total points is a larger increase than an increase in mean net offense of 20 points (if both variables are cast into comparable units), yet the former is 4% and the latter is 6.66%. To know whether any two figures are consistent, we need to know the metric of the variables (their standard deviations). So the 14% may be equivalent to the 7% (if both were rendered in comparable units) or it might not be.
Yes, if we know how tightly clustered one variable is over many trials while the other is held fixed then this can be useful as you say; it's just that we weren't discussing it in such terms. If the 14 and 7 were the same when expressed in terms of their respective SD's then it would make some sense. But we don't have this information (at least it hasn't been presented so far; maybe it's out there somewhere or in worst case could be determined, laboriously, from the collection of available raw data).
But to answer your question, yes, the data accumulated over the past 50 years does tell us something about how many more points to expect if a certain increase in offensive yardage is recorded. Just not in the %age metric. If the offensive yardage increase is 15%--and that represents a one standard-deviation increase (this latter being the key number)--then I will expect (via simple linear regression) a 2/3SD increase in number of points. Once I know the value of that standard deviation, I can translate that into an expected increase in actual points. And, sure, I could put a .95 CI around it.
Again that was my main point. But I have to admit you've lost me on the 2/3SD, that a one-sigma change in one variable causes a 2/3-sigma change in the other (in same direction of course since it's positive correlation). Where do you get this 2/3 fraction; am I missing something?
Sports can be a peculiar thing. When partaking in fiction, like a book or movie, we adopt a "Willing Suspension of Disbelief" for enjoyment's sake. There's a similar force at work in sports: "Willing Suspension of Rationality". If you doubt this, listen to any conversation between rival team fans. You even see it among fans of the same team. Fans argue over who's the better QB or goalie, and selectively cite stats that support their views while ignoring those that don't.
