Thats why I put the percentages as well. Particularly look at the far right column, the trophy multiple. Amongst the haves, the Private schools have a distinct success rate among a the top tier publics, though it's difference is less than that of those publics against anyone else. And once you drop down to the next tier the differences start to wash away altogether. Now how I arrived at sampling 36 and 20 was a little bit more art than science, but over smaller sample groups I am willing to admit advantages aren't gonna be seen pro-rata. The private haves unquestionably are over represented in the haves, but that's still a small piece of the overall pie.
And I probably care more about this question coming as a Naz alum, but, when did they become a have instead of a have not? As their school prestige has risen (accross all facets) other privates have stumbled, many even closing down. The private standard of success (athletically or academically) is as much a story about attrition than anything else. Just think its hilarious that bitter fans will end up treating it as analogous to like ncaa recruitment.
Gosh, there is a lot to respond to since my last post, which was submitted not that long ago. I will try to be more brief here than I was in that last post of mine.
First, many thanks to Snetsrak61 for testing the accuracy of the data coming from Antioch. It was a task I happily avoided, but in some ways was necessary. It removes one possible criticism of the whole analysis.
In response to DrMac210, the proposition that public schools and private schools are equal,
on average, in football strength was not offered by me as a fact. It was offered as a hypothesis to be tested through statistical methodology. If the hypothesis could not be disproved, then there would be no need for a multiplier. It was disproved with a 100% degree of certainty, and therefore a multiplier is justified. The hypothesis also does not suggest every game of the more than 1,200 games contained in the set of outcomes was a 50/50 proposition, only that the mean probability of all the games was 50/50, or very nearly so.
Snetsrak61's review of the data indicates the private schools won 65% of the games since 2001 rather than the 69% figure submitted in the Antioch tweet. This would change the result of the statistical analysis, but not in any meaningful sense. The hypothesis that private-school football teams and public-school football teams are equal in strength would still be disproved. The probability of private schools winning 65% of more than 1,200 games, if the true mean likelihood of winning the games was 50%, is less than one chance in a billion. The reason this last statement remains unchanged from my earlier statement deserves an explanation.
I used a conservative approach in calculating the less than 1 / 1,000,000,000 probability. I began by using a 20-outcome binomial distribution. I did so because that was the largest binomial distribution offered in the statistics book I consulted (Statistics and Probability,
A Basis for Decision Making, Blakeslee & Chinn). Since it was a 20-outcome distribution, the results moved in 5% increments (1/20 = 5%). When evaluating a 69% success rate (winning percentage), I had to choose between 14 wins and 6 losses (70%), and 13 wins and 7 losses (65%). Since 69% is less than 70%, and I didn't want to overstate my case, I used the 65% success rate for my calculations. That success rate is consistent with Snetsrak61's finding that the private schools won at a percentage of 65%, and therefore my earlier calculations and conclusion are still valid.
Ramblinman has found fault, as only he would, with the fact that playoff games were used for the analysis. It is my understanding this discussion was about playoff teams, and assigning those teams to class levels for bracketing purposes. This particular discussion was not about how teams qualify for the playoffs. Consequently, looking only at playoff teams is appropriate.
Snetsrak61 has concluded the private-school football strength tends to be concentrated in about 14 schools. I agree with that. More importantly, the IHSA seems to agree with that. That is why their multiplier rule is waived if a private school has not won three playoff games within a two-year window of time. If that success criterion is not met, the private school is treated in accordance with the same enrollment rules as a public school. The success factor is even more exclusive. That is only applied to private schools if they have played in the championship game both years of a two-year window. Few schools will have the success factor applied to them next year. Sacred Heart-Griffin is the only one that comes to my mind.
Snetsrak61 thinks the success factor should also be applied to public schools. I agree, that has been my opinion for a long time. Sustained success is not achieved solely by private schools. This is one of the few areas where I take issue with the IHSA rules.