Calling all Mathematicians

[Dr. D]

With the release of the first FHSAA Power Rankings coming soon, I am hoping there is someone out there who has been trying to gain some insight into the super-duper, top-secret, never-to-be-revealed MaxPreps/CalPreps/FHSAA Power Rankings formula.  I have done some high school mathematics and linear regression, and my conclusion is that these Rankings are weighted approximately 60% to a team's overall record, and approximately 40% to strength of schedule.  Meaning a team seeking a higher seed would be better off with a higher winning percentage and an average schedule, as opposed to a lower winning percentage and a more difficult schedule.  Information that might be useful to coaches when setting up a schedule, but which seems to be guarded with the security of nuclear codes.  Anyway, if there are any mathematical geniuses out there, it would be interesting to hear your observations.  Thanks.

[DarterBlue2]

2 hours ago, Dr. D said:

With the release of the first FHSAA Power Rankings coming soon, I am hoping there is someone out there who has been trying to gain some insight into the super-duper, top-secret, never-to-be-revealed MaxPreps/CalPreps/FHSAA Power Rankings formula.  I have done some high school mathematics and linear regression, and my conclusion is that these Rankings are weighted approximately 60% to a team's overall record, and approximately 40% to strength of schedule.  Meaning a team seeking a higher seed would be better off with a higher winning percentage and an average schedule, as opposed to a lower winning percentage and a more difficult schedule.  Information that might be useful to coaches when setting up a schedule, but which seems to be guarded with the security of nuclear codes.  Anyway, if there are any mathematical geniuses out there, it would be interesting to hear your observations.  Thanks.

Given the secrecy of the rankings, the best one can do is once they come out, take a statistically representative sample of ranked teams and attempt, using different methodologies, to replicate their rankings under different assumptions. While it's almost certain that an exact fit will not be obtained, one should be able to come up with a method that fits, more or less, the rankings made by the authorities within a 95% level of confidence. 

Given the overall secrecy of the methodology, to my way of thinking, it's imperative that staffs try and replicate them. This is the only way you can reasonably determine that your school was treated fairly. For aside from district champs which get an automatic birth, and, to a lesser degree, district runner ups with say a 9-1 record against good competition with their only loss being to the district champ, it will be almost impossible to determine whether your team was properly excluded/included in the playoffs or not. Further, the question of where you rank if included is also open when the rules and or methodology are not transparent. Thus, if you end up being ranked 8th in your region when you should have been 5, it will greatly impact your early opponent and could also affect home/away status.  

[nolebull813]

It’s pretty straightforward. Garbage in, garbage out. 

[Perspective]

Has anyone from the FHSAA every offered up an explanation as to why the formula is secret?  Why can't/shouldn't there be transparency? 

[Perspective]

On a related note, is MaxPreps formula disclosed?  I noticed that in the MaxPreps national rankings, they have Miami Central ranked 4th and Chaminade-Madonna ranked 5th.  Yet in the MaxPreps state rankings, they've got C-M 2nd and Central 3rd.   Can anyone explain this?

[PinellasFB]

I'm a mathematician (masters in applied mathematics) and until the formula is revealed, it can be anything.  A true power index is typically a weighted formula that heavily leans on last years results for the early rankings but these weights effectively go to zero as the season nears the end and there are enough teams that have played each other to have statistical relevance for the current year.  Probably the single biggest measure of power is margin of victory/loss so the FHSAA has really gimped the formula by removing this from the calculation, thus becoming full "elo chess" ranking.  Elo chess ranking works for chess players because there are thousands and thousands of matches where the binary win or loss result becomes statistically relevant.  This does not work well for football because of how few games a season has.  From my observation of last year, a tough district/region is over-rewarded whereas a powerful team from a weak region is severely penalized.  In the end, the most powerful teams generally made the final four so most of the complaint is leaving out deserving teams and taking too many teams from a single district.

[Dr. D]

2 hours ago, Perspective said:

Has anyone from the FHSAA every offered up an explanation as to why the formula is secret?  Why can't/shouldn't there be transparency? 

The RPI system used by the FHSAA prior to the current system offered transparency and reproducibility.  One could even calculate "what if" scenarios to see the potential impact of future outcomes.  When the FHSAA tweaked the percentage weighting of the 3 variables (team's record, opponents' records, opponents' opponents' records), it was openly publicized.  I would suspect that the FHSAA's financial/legal relationship with MaxPreps precludes the public release of their algorithm.    

[Perspective]

2 hours ago, Dr. D said:

The RPI system used by the FHSAA prior to the current system offered transparency and reproducibility.  One could even calculate "what if" scenarios to see the potential impact of future outcomes.  When the FHSAA tweaked the percentage weighting of the 3 variables (team's record, opponents' records, opponents' opponents' records), it was openly publicized.  I would suspect that the FHSAA's financial/legal relationship with MaxPreps precludes the public release of their algorithm.    

It would be interesting to see if the FHSAA raised that "defense" in response to a public records request.  

[Jambun82]

14 hours ago, PinellasFB said:

I'm a mathematician (masters in applied mathematics) and until the formula is revealed, it can be anything.  A true power index is typically a weighted formula that heavily leans on last years results for the early rankings but these weights effectively go to zero as the season nears the end and there are enough teams that have played each other to have statistical relevance for the current year.  Probably the single biggest measure of power is margin of victory/loss so the FHSAA has really gimped the formula by removing this from the calculation, thus becoming full "elo chess" ranking.  Elo chess ranking works for chess players because there are thousands and thousands of matches where the binary win or loss result becomes statistically relevant.  This does not work well for football because of how few games a season has.  From my observation of last year, a tough district/region is over-rewarded whereas a powerful team from a weak region is severely penalized.  In the end, the most powerful teams generally made the final four so most of the complaint is leaving out deserving teams and taking too many teams from a single district.

Algebra is completely worthless, correct? 

[Cat_Scratch2]

Have to say that some of the rankings really make no sense. You have no wins and a similar strength of schedule ranked over a team that has no losses and a higher SOS.  I think Jam was poking fun at the FHSAA cause they clearly are not using pure numbers... It may be that they are using the human factor as another variable.

[PinellasFB]

5 hours ago, Jambun82 said:

Algebra is completely worthless, correct? 

Not sure what you mean here lol?  Is it worthless in evaluating this formula?  If it's statistical based, then yes algebra is not enough to understand the formula. 

[PinellasFB]

38 minutes ago, Cat_Scratch2 said:

Have to say that some of the rankings really make no sense. You have no wins and a similar strength of schedule ranked over a team that has no losses and a higher SOS.  I think Jam was poking fun at the FHSAA cause they clearly are not using pure numbers... It may be that they are using the human factor as another variable.

This is a big hint of what I mentioned earlier that early season rankings are weighted heavily upon last years results, with these weights eventually going to zero when this year's results become statistically significant.  This suggests a statistical power measurement to me.  By statistics based, I mean using statistical (stochastic) processes, not football team stats... just in case anyone was confused.

[Jambun82]

3 hours ago, PinellasFB said:

Not sure what you mean here lol?  Is it worthless in evaluating this formula?  If it's statistical based, then yes algebra is not enough to understand the formula. 

Algebra is completely worthless, correct? 

[PinellasFB]

4 minutes ago, Jambun82 said:

Algebra is completely worthless, correct? 

Of course it is.  You really need calculus, differential equations and statistics to model anything in the real world.

[DarterBlue2]

11 minutes ago, PinellasFB said:

Of course it is.  You really need calculus, differential equations and statistics to model anything in the real world.

But without mastering Algebraic techniques first, you cannot go on to calculus, differential equations, statistical methods, multivariate regression, mathematical induction, and the like successfully. It's the same with Trig, you need Trig to successfully master calculus. 

[Jambun82]

52 minutes ago, PinellasFB said:

Of course it is.  You really need calculus, differential equations and statistics to model anything in the real world.

Thank you for the clarification. 

[PinellasFB]

2 hours ago, DarterBlue2 said:

But without mastering Algebraic techniques first, you cannot go on to calculus, differential equations, statistical methods, multivariate regression, mathematical induction, and the like successfully. It's the same with Trig, you need Trig to successfully master calculus. 

Heh I thought he was just trolling.  I guess not?  

[Nulli Secundus]

3 hours ago, DarterBlue2 said:

But without mastering Algebraic techniques first, you cannot go on to calculus, differential equations, statistical methods, multivariate regression, mathematical induction, and the like successfully. It's the same with Trig, you need Trig to successfully master calculus. 

Child's play!  The class I remember math majors flunking was Discrete Structures (aka Discrete Math), lol.  

[DarterBlue2]

40 minutes ago, PinellasFB said:

Heh I thought he was just trolling.  I guess not?  

I don't think @Jambun82 trolls. To me he's just a strange individual. I must confess, I really don't know how to read him, but would not want him to be part of the crew officiating an Apopka game. 

[PinellasFB]

45 minutes ago, Nulli Secundus said:

Child's play!  The class I remember math majors flunking was Discrete Structures (aka Discrete Math), lol.  

Matrix math can be very hard but it's not the class I remember math majors failing.  Real Analysis was BY FAR the hardest math class I've ever dealt with and I've pretty much taken the gauntlet of them.  For example, real analysis is where you have to prove 1+1=2 and it was a two page painful proof.  You can no longer assume everything you've ever assumed was true, including that numbers are real.  It's bizarre and painful.

[THAT S--T WAS FUNNY]

1 hour ago, DarterBlue2 said:

I don't think @Jambun82 trolls. To me he's just a strange individual. I must confess, I really don't know how to read him, but would not want him to be part of the crew officiating an Apopka game. 

My thoughts exactly. The kids deserve better. 

[Jambun82]

9 hours ago, DarterBlue2 said:

I don't think @Jambun82 trolls. To me he's just a strange individual. I must confess, I really don't know how to read him, but would not want him to be part of the crew officiating an Apopka game. 

I have been to Apopka High School once. It is a very nice school, not like West Orange, but then again that is the gold standard for schools in Orange County. I look forward to  going back one day. Thank you for the very nice compliments DarterBlue2, and will you admit that Algebra is completely worthless? 

[Jambun82]

7 hours ago, THAT S--T WAS FUNNY said:

My thoughts exactly. The kids deserve better. 

What do kids deserve better?

[anonimis]

http://calpreps.com/ratings.htm

I remember calpreps being used by MaxPreps, but I could be wrong.

Casella and Berger's Statistical Inference is about as far as my math/stats knowledge goes.  As a coach, I wouldn't want to have to coach in a system where you are forced to win run up scores because winning by 42 instead of 63 may hurt your rating.  Did the FHSAA ever say there was a cap on margin of victory?

[Dr. D]

In the words of the FHSAA, "The score of a game does not affect the FHSAA Power Ranking" (i.e. margin of victory is not included in the algorithm).  At the January 2023 meeting of the FHSAA Athletic Directors Advisory Committee, the following proposal from the Football Advisory Committee was endorsed.  I believe it would have to be approved a second time by the FAC and ADAC to be enacted, and it could be modified along the way.  But there is hope that margin of victory will become a factor, up to a point.