The Mathematically Correct College Football Top 25

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  • InThisMoment
    SBR Wise Guy
    • 09-02-09
    • 615

    #1
    The Mathematically Correct College Football Top 25
    Premise: As we know the polls are largely based on a merit system and pecking order determined by a preseason poll. This is akin to a ladder system where you win and move up, you lose you drop down a random position. These polls remain largely static and while the end result usually results in the correct order, they are by and large flawed.

    Hypothesis: Polls should be FLUID INSTEAD OF STATIC. Meaning they should be BASED ON RESULTS UP TO THAT POINT in the season rather than future projections or biased preseason rankings. All wins and losses are not created equal and need to be accounted for.

    Solution: Given the current BCS parameters, a mathematical formula can be determined to resolve this issue. Criteria should be sorted on a weighted basis with priority for more substantial factors over less substantial factors. Historical data can be used as evidence for this criteria.

    Thus, we derive the equations for proper poll weighting:

    TW= Total wins- C wins
    Zero L> 1 L..., where L stands for loss.
    2 L = Null set.
    C= 0, where C stands for non BCS conference teams (specifically C-USA, MAC, MWC, Sun Belt, WAC, Non-ND independents)*

    RW>HW>RL>HL, this is the essence of the formula where road wins are greater than home wins which are greater than road losses which are greater than home losses. In using this, we can establish a proper hierarchy or mathematically accurate poll.

    *C losses negate 2TW thus having a double loss effect on the data.

    Once again, please note this only measures the PERFORMANCE TO DATE of the teams. We are not in the business of forecasting the future (then again the polls should not be as well) and feel the data will sort itself out over time.

    In the next post I will post the mathematical poll along with the appropriate TW-RW-HW-RL-HL for each team so as to provide some reasoning.

    Comments and questions are welcome but please keep it on topic and with some reasoning.
  • InThisMoment
    SBR Wise Guy
    • 09-02-09
    • 615

    #2
    1. LSU 4-3-1-0-0
    2. Alabama 3-2-1-0-0*
    3. Iowa 3-2-1-0-0
    4. Auburn 3-1-2-0-0
    5. So. Fla. 2-2-0-0-0
    6. Cincy 2-2-0-0-0
    7. Fla. 2-1-1-0-0
    8. Wisconsin 2-1-1-0-0
    9. Kansas 2-0-2-0-0
    10. Missouri 1-0-1-0-0*
    11. Texas 1-0-1-0-0
    12. USC 3-2-1-1-0
    13. Miami-Fla. 3-1-2-1-0
    14. Va. Tech 3-1-2-1-0*
    15. Ga. Tech 3-1-2-1-0
    16.Stanford 3-1-2-1-0
    17. Notre Dame 3-1-2-1-0
    18. TCU 2-2-0-0-0
    19. So. Carolina 2-1-1-1-0
    20. UCLA 2-1-1-1-0
    21.Ohio State 2-1-1-0-1
    22. Penn State 2-1-1-0-1
    23.Oregon 3-0-3-1-0 **
    24. BC 2-0-2-1-0
    25. Michigan 2-0-2-1-0

    *neutral site game counts as away
    **non-BCS (or C) los

    others:
    26. Arizona
    27. Baylor
    28.Rutgers
    29.Boise
    30. Ole Miss
    31.W. Va.
    32. UConn
    33.BYU
    34. Okla. St.
    35. Nebraska
    36. Texas A & M
    Comment
    • InThisMoment
      SBR Wise Guy
      • 09-02-09
      • 615

      #3
      In case this is a bit confusing, let me break it down a little more.

      In essence we have thrown out all games of non-BCS schools (see conferences in original posts). Wins over them have no bearing (while we did take into account losses which count double)

      By doing so, we then isolate the BCS power conferences and give them an equal weighting (not scientifically accurate but for poll and championship game purposes essentially so). By taking this into account we get a clearer picture of relevant data.

      Margin of victory is not taken into account either. A win is a win. The point is to win the game, all of your games, so that is completely irrelevant data when looked at mathematically.

      As you see by weighting this data we get variance from actual poll data. When looked at under close inspection the mathematical formula makes much more sense.
      Comment
      • Fishhead
        SBR Aristocracy
        • 08-11-05
        • 40179

        #4
        So IOWA will be #1 this week after they beat Michigan and LSU and ALABAMA losses?

        KEWL!!!


        Comment
        • InThisMoment
          SBR Wise Guy
          • 09-02-09
          • 615

          #5
          Anomalies:

          -LSU is 1st based on 4 total wins and 3 road wins.

          -Texas is 11th based on 1 total win, and 1 home win and 0 losses.

          -Boise is 29th based on 1 total win, and 1 home win and being a C team.

          -Nebraska is 35th based on 0 total wins and 1 road loss.
          Comment
          • InThisMoment
            SBR Wise Guy
            • 09-02-09
            • 615

            #6
            That is correct, although assuming LSU and 'Bama loses and Auburn wins that would tie Iowa and Auburn mathematically.

            I believe then if Penn State lost, Auburn would jump Iowa as well.

            Bear in mind though that Iowa has played 2 null set games (N. Iowa and Ark. St.) already and they do not have the added championship game of other teams.

            So the likelihood of them not being surpassed in the future hinges largely on them being undefeated and all of them other undefeated teams losing.

            But for now, assuming those two losses that would be absolutely correct given their body of work.

            Obviously we can get into the theoretical debate of the quality of the Big 10. That is neither here nor there for this discussion, however, as we focus on the data. In addition, historically Big 10 teams have NOT been penalized for thier conference affiliation and have equal weighting of other conferences.
            Comment
            • Fishhead
              SBR Aristocracy
              • 08-11-05
              • 40179

              #7
              I would say there is a 55% chance we are looking at a TEX/FLORIDA title game.
              Comment
              • InThisMoment
                SBR Wise Guy
                • 09-02-09
                • 615

                #8
                One other note: This formula actually rewards teams that play other BCS teams versus FCS or non-power conference teams. A win over a BCS school should be worth more than a win over a non-BCS school.
                Comment
                • pavyracer
                  SBR Aristocracy
                  • 04-12-07
                  • 82905

                  #9
                  Why can't we have a system where the games are won on the field and not on paper?
                  Comment
                  • mtneer1212
                    SBR MVP
                    • 06-22-08
                    • 4993

                    #10
                    Any poll which has LSU number 1 and Notre Dame in the top 20 is automatically a non-starter for me. I don't care what algorithm, mathematical formula, or astrological sign you use.
                    Comment
                    • InThisMoment
                      SBR Wise Guy
                      • 09-02-09
                      • 615

                      #11
                      Certainly one could find more egregious examples than these two considering they are not that far from their actual rankings.

                      LSU's ranking is a byproduct of their schedule which is frontloaded with road games as well as backloaded with non-BCS games. Ironically this could actually work to their benefit in the real polls.

                      Given that these things tend to sort themselves out over the season, it is not necessary to take too much stock in everything.

                      However, when you take away bias and emotion and simply look at the data up to this point the picture painted is far more accurate.
                      Comment
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