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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 right-skewed 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

Mean

716.1293

Standard Error

15.4058

Median

676.5

Mode

605

Standard Deviation

165.9255

Sample Variance

27531.28

Kurtosis

1.391443

Skewness

1.21985

 

 

Division 1 Schools that have made Final Four

Mean

761.4444

Standard Error

38.9226

Median

747

Mode

#N/A

Standard Deviation

165.1346

Sample Variance

27269.44

Kurtosis

0.112654

Skewness

0.800306

 

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 non-public 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 non-public 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 non-public 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 non-publics, 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 r-squared value is very low, so enrollment does not explain much with regard to computer points. Compare this to the .135 r-squared score when one adds information about the public or non-public 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):

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