Well, that is interesting.
Must confess that I've never pulled back the curtain to this extent on push rates, as I was working with a set from someone with more expertise in the particular field than I. And they have been a quick and useful tool for what I was doing, as compared to other alternative methods available to me with the resources at hand for ranking relative mathematical advantage on contest plays.
If I understand these correctly, a push rate measures the percentage of time a game lined at a particular number, such as the favorite laying 3, will fall exactly on that number for a push. I believe that about 14 to 15% of all NFL game results (
i.e., the margin of victory) -- regardless of the spread set on a game by the market -- fall on the 3. In contrast, about roughly 9% of games lined at -3 in the past have ended with the favorite winning by 3. And I assume that the push rate is in reference to a consensus market closing number for games, as lines of course move during the week and further may vary at different properties at the close.
So, when I see push-rate charts with perhaps close but varying percentage values, my most natural assumption would be that those varying values would be due to the push-rate analyses having been (a) conducted over different periods of time and/or possibly lengths of time; and/or (b) different consensus closing numbers having been used.
(It thus would be nice when folks publish a push rate chart to note the period of time covered and the consensus closing number source relied upon, as many often do. The 2011 threads where we did the analysis of SuperContest stale line moves no longer are available online on VFV, so I can't go back now and see what Donnie may have said about the underlying basis for the push rates that he was using.)
But it is new information to me that people are making what I would call subjective judgements -- a/k/a logic -- in assigning push rates.
The empiricist in me would feel more comfortable with push rates based on actual experience -- how the numbers actually fall over time -- rather than upon assumptions about what will happen and how the numbers likely will fall over time.
For example, the third graphic on the site below would suggest that -- perhaps counterintuitively -- the rule changes did not reduce the incidence of games overall falling on the 3 and the 7 in the first three years of the rule change:
https://www.actionnetwork.com/how-t...-tips-odds-rule-changes-margin-victory-spread
As I've demonstrated -- empirically -- multiple times on posting boards, including here, I let my math skills atrophy while going down an instead wordsmith track in college and law school. But I did take logic and advanced logic as a philosophy major. And, to me, presumed logic can be a subjective and slippery beast.
For example, as NFL games start to come down to the wire, the trailing team has a strong incentive if and as they score late to get the scoring differential back to a margin of, e.g., 3 or 7. In practice over time, that tendency may to a large extent counteract an otherwise logical assumption that the rule changes would negatively impact the number of times that games will end on margins of victory of 3 or 7.
Time, as they say, will tell. But if I'm going to use purportedly mathematical values sometimes carried out up to multiple decimal places, my druthers would be that those highly specific multiple-decimal-place values reflect what "the math" actually has shown, not what someone subjectively thinks it will show.
