Do the largest Division 1 schools have a stranglehold on the state football playoff system?
The OHSAA recently announced a plan for a new classification system, the goal of which is to protect the smallest schools in Division 1 from being effectively precluded from performing well in the state playoff system. The argument is that since the range of enrollment numbers in Division 1 is so great (could theoretically be infinite), the smallest schools in that division are at a greater disadvantage than the smallest schools in other divisions.
Of course, this plan could negatively affect a number of schools, including those schools which are now at the higher end of the scale for enrollment for their respective division since they would possibly be bumped into another division by realignment. However, the loudest complainers are probably those in Division VI. That division would, by design, have more schools than the other divisions, thereby increasing the difficulty for any Division VI team to win a regional or state championship.
I decided to look at the participants in the state final four since 1998 to get an idea if it really is almost impossible for a small Division 1 school to be successful in the current playoff situation. Below are histograms and statistics that help begin that study:
Distribution for all Division 1 Schools:
As can easily be seen, the division is made up largely of schools that are closer to the minimum enrollment requirement. This would be known as a rightskewed distribution. A small number of the very largest schools make up the right side of this distribution. To the OHSAA's defense, they probably looked at this distribution and decided there was a natural break that would allow them to make a new division of the "Super D1s."
But what about the results of the tournaments. I plotted those schools that have had at least one appearance in the Division 1 final four since 1998:
Distribution of Division 1 Schools that appeared in Final Four:
Since the population size is much smaller, the distribution is a bit more jagged. However, it does seem to follow roughly the same distribution as the entire Division 1 population as a whole. What's more important is that there certainly does not appear to be an absolute domination of the tournaments by the very largest schools. This would indicate that the OHSAA's planned realignment is not actually necessary.
But let's look at the numbers themselves. Below are the important statistics regarding enrollment for both populations:
All Division 1 Schools

Division 1 Schools that have made Final Four

These numbers show a bit more difference than the histograms suggested. The mean and median enrollments are higher for those schools that have made the final four. It is interesting to note that skewness has actually lessened among the final four participants. That could be for a number of reasons, including but not limited to: 1) The largest schools are not doing well in the playoffs, so the right tail of the distribution is absent (this seems to be shown in the histograms) or 2) the smallest schools are not doing well in the playoffs (this seems to be supported by the above tables which show an elevated median for final four participants).
I wanted to look specifically at the schools
that have made the final four since 1998. I know that this is also a hot topic,
but it is interesting to note the number of nonpublic schools in this list:
CITYSCHOOL 
BOYS 
CINCINNATI ST XAVIER 
1111 
CLEVELAND ST IGNATIUS 
1085 
CINCINNATI COLERAIN 
927 
HUBER HEIGHTS WAYNE 
916 
CINCINNATI ELDER 
833 
CANTON CANTON MC KINLEY 
819 
HILLIARD HILLIARD DAVIDSON 
770 
FINDLAY FINDLAY 
768 
COLUMBUS UPPER ARLINGTON 
756 
CLEVELAND GLENVILLE ACADEMIC CAMPUS 
738 
LAKEWOOD ST EDWARD 
703 
SOLON SOLON 
679 
WARREN WARREN G HARDING 
651 
MASSILLON PERRY 
645 
TOLEDO ST JOHN'S JESUIT 
605 
LEBANON LEBANON 
602 
COLUMBUS WORTHINGTON KILBOURNE 
586 
MASSILLON WASHINGTON 
584 
Seeing this list of schools reminded me of another study I did about a year ago. It studied whether nonpublic schools outperformed public schools using Harbin points as the indicator of performance. That study was done when it was rumored that the OHSAA was considering a multiplier for nonpublic schools which would possibly put them in a higher division. Click here to see that study in full. Generally, I found that there was some outperformance by the nonpublics, but more important to this study is the fact that in Division 1, the pts per student decreased as enrollment increased. Below is a scatterplot and regression that shows this relationship:
However, this is a marginal rate, it doesn't mean that the largest schools aren't gaining something from each additional student.
The following shows the relationship between number of students and computer points, not the marginal gain.
It shows that there is a general trend upward in computer points with growing enrollments. However, the rsquared value is very low, so enrollment does not explain much with regard to computer points. Compare this to the .135 rsquared score when one adds information about the public or nonpublic status of the school and it can be seen that pure enrollment numbers do not make for a dominant football team alone.
My Conclusions (reasonable minds may certainly differ):
The distribution differences between all Division 1 schools and those that have made the final four are not large and probably do not warrant a realignment for playoff purposes
The statistical differences between those two pools, though more compelling, are still not sufficiently different to warrant a realignment for playoff purposes.
Looking at the schools that would likely be impacted by the realignment, it seems the OHSAA may have more than enrollment equity in mind. If the realignment goes through, St. Xavier, St. Ignatius, Elder, and St. Edward would be aligned in the new Division. The only current D1 nonpublic that has qualified for the final four since 1998 that wouldn't have the enrollment to go to the larger division would be Toledo St. John's Jesuit. This would go a long way to silence those that call for differential treatment for publics and nonpublics.
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