Fascinating that you don't see the irony of such a post, particularly after posting
I mean, the irony is so thick that it's dripping off the freaking internet.
The FACT is that your ASSERTION was a poor one that clearly wasn't thought out. Your RESPONSE to an easy REBUTTAL was to then make a FACT claim that's completely without the necessary CONTEXT.
And, yeah, my measure really helps the case for the traditional set up.
Excuse me? Maybe I'm not communicating clearly.
If 88% of the teams use the traditional set up, then one would "expect" 88% of the Super Bowls to be won by those teams, assuming complete independence (more on this later). Depending on the timeframe used, we're actually seeing 65% to 78%.
Similarly, 12% of the teams use my proposed methodology. Depending on the timeframe used, we're seeing them win 22% to 35% of the Superbowls compared to the "expected" 12% (about 2 to 3 times more often).
Now, I'm using the "expected" in quotes because we know independence isn't the case. There's some anti-selection in place - meaning that in theory, only the best-of-the-best coaches currently have the final say. Therefore, one should actually expect their results to be better than "expected" under the independence assumption. Indeed, that is what we are seeing here.
If we were seeing the final-say coaches have a winning percentage less than or in the neighborhood of the "expected" value, then we could possibly conclude that the current system is better (if we agree it's an accurate metric). But thst's not what we're seeing. That said, we can't conclude anything further than that because of the anti-selection issues. We would need to either use some other measurement thst could be appropriate, or wait for a world where the percentage of coaches with final say is closer to 50% to measure using this statistic.
My contention is that the coach having final say is a better system, but there are very limited examples of it in real life so it's just speculation on my part. I would obviously need to prove it, but it's hard to prove something that isn't really seen in real life. Nevertheless, the limited existing data does not do anything to prove my contention incorrect. I could very well be incorrect and the current system is the most effective, but nothing posted so far has done so. But I do want to make it perfectly clear that my hypothesis is just speculation based on my narrative - but so are all new ideas - and that I would need to see more data appear to effectively prove or disprove it.
