jschaud
12-04-2006, 06:20 AM
I am a Michigan fan and i feel like we got screwed. I wanted to look closer at the numbers and see what happened so I broke out the calculator. Please do not get into the 'who should go to the title game' nonsense. I just want to see if the math looks correct. Oh, Jim Tressel abstained so i just used his name for the missing voter in the coaches poll.
Here is what we know.
• USC lost giving up 113 possible harris poll votes and 62 possible USA Today votes.
• UF picked up 65 USA votes and UM picked up -1 USA votes
• UF picked up 142 HP votes and UM picked up 18 HP votes
• If you multiple 113 HP voters by 47 (the combined points for second and third) they do not equal the points totaled by UM and UF, thus one team was voted worse than third.
• We lost one voter in each poll from the subsequent weeks.
So here is the math.
T = Tressel’s vote
X = votes either gained or lost based on perspective
USC = votes gained from USC loss
USC = 62 as both teams move up 1 spot and gain 1 point as such
USA Today Equation---------
Michigan side of equation
-1 = 62 – T – X
Florida side of equation
+65 = 62 –T + X
*(-1) = *(-1)
-65 = -62 + T - X
substitution from equations
-66 = -2*X
X = 33
33 net voters that had UM ranked higher than UF the previous week changed their mind.
Harris Poll Equation-------------
Y = missing voter
X = votes gained or lost bases on perspective
USC = votes gained from USC loss
USC = 113 as both teams move up 1 spot and gain 1 point
Michigan side of equation
+18 = 113 – Y – X
Florida side of equation
+142 = 113 – Y + X
*(-1) = *(-1)
Substitution
-124 = 2X
X = 61
61 net voters that had UM ranked higher than UF the previous week changed their mind.
So, 33 of 62 USA voters moved Florida ahead of UM and 61 of 114 HP voters moved UF ahead of UM.
Based on the separation in the final poll of .0101 and the tie in the computer polls, we can solve for how many voters could have changed their mind and UM still would have been in the title game.
X = net point change in USA today poll
Y = net point change in Harris poll
Z = 0 as the teams were even in the computer polls
.0102 = 1/3*(X/1550) + 1/3*(Y/2825) + z
Now, since any vote that UM picks up is one that Florida loses, the margin is half as great. Additionally, if the Harris poll people were accountable, Florida should not have ever been given a first place vote, so we adjust for that.
No first place vote and removal of computer poll for simplification
.00985 = 1/3*(X/1550) + 1/3*(Y/2825)
Halving of margin to account for UM gain and UF loss with each vote
.004923 = 1/3*(X/1550) + 1/3*(Y/2825)
Simplified by multiplying by 3 on both sides
.01477 = X/1550 + Y/2825
solve for lowest common denominator to simplify equation
.01477 = 113*X/113*1550 + 62*Y/62*2825
.01477 = 113*X/175150 + 62*Y/175150
2586.795 = 113*X + 62*Y
so if 23 of the 33 USA voters that changed their mind didn’t we have UM in the title game OR if 42 of the 61 voters that changed their mind didn’t we have UM in the title game. If 34.4% of the voters that decided to move UF ahead of UM would have kept Michigan in the spot above them, UM would be in the title game. The difference in the national championship berth? 11 writers and 21 pollsters.
2 Scenarios
The difference needed to put Michigan in the title game in the coaches poll.
.0101 = 1/3 * (X/1550) -------simplified-
X = 46.965 points
So UM needed a net gain of 47 points on Florida to go to the title game. That is Lloyd Carr and one other friendly coach dropping Florida from 3rd to out of the poll and moving UM from 2 to 1 in the polls. Boom, 48 net points.
How about the Harris poll. Some jackass made UF number 1 and most likely put UM in fourth or worse.
.0101 = 1/3 * (X/2825) -------------------
X = 85.5975 = ~86
That means 4 of 114 voters could have been bought to leave Florida completely out of the polls, we all know the amount of money involved in college football, it wouldn’t even be that hard to do.
Here is what we know.
• USC lost giving up 113 possible harris poll votes and 62 possible USA Today votes.
• UF picked up 65 USA votes and UM picked up -1 USA votes
• UF picked up 142 HP votes and UM picked up 18 HP votes
• If you multiple 113 HP voters by 47 (the combined points for second and third) they do not equal the points totaled by UM and UF, thus one team was voted worse than third.
• We lost one voter in each poll from the subsequent weeks.
So here is the math.
T = Tressel’s vote
X = votes either gained or lost based on perspective
USC = votes gained from USC loss
USC = 62 as both teams move up 1 spot and gain 1 point as such
USA Today Equation---------
Michigan side of equation
-1 = 62 – T – X
Florida side of equation
+65 = 62 –T + X
*(-1) = *(-1)
-65 = -62 + T - X
substitution from equations
-66 = -2*X
X = 33
33 net voters that had UM ranked higher than UF the previous week changed their mind.
Harris Poll Equation-------------
Y = missing voter
X = votes gained or lost bases on perspective
USC = votes gained from USC loss
USC = 113 as both teams move up 1 spot and gain 1 point
Michigan side of equation
+18 = 113 – Y – X
Florida side of equation
+142 = 113 – Y + X
*(-1) = *(-1)
Substitution
-124 = 2X
X = 61
61 net voters that had UM ranked higher than UF the previous week changed their mind.
So, 33 of 62 USA voters moved Florida ahead of UM and 61 of 114 HP voters moved UF ahead of UM.
Based on the separation in the final poll of .0101 and the tie in the computer polls, we can solve for how many voters could have changed their mind and UM still would have been in the title game.
X = net point change in USA today poll
Y = net point change in Harris poll
Z = 0 as the teams were even in the computer polls
.0102 = 1/3*(X/1550) + 1/3*(Y/2825) + z
Now, since any vote that UM picks up is one that Florida loses, the margin is half as great. Additionally, if the Harris poll people were accountable, Florida should not have ever been given a first place vote, so we adjust for that.
No first place vote and removal of computer poll for simplification
.00985 = 1/3*(X/1550) + 1/3*(Y/2825)
Halving of margin to account for UM gain and UF loss with each vote
.004923 = 1/3*(X/1550) + 1/3*(Y/2825)
Simplified by multiplying by 3 on both sides
.01477 = X/1550 + Y/2825
solve for lowest common denominator to simplify equation
.01477 = 113*X/113*1550 + 62*Y/62*2825
.01477 = 113*X/175150 + 62*Y/175150
2586.795 = 113*X + 62*Y
so if 23 of the 33 USA voters that changed their mind didn’t we have UM in the title game OR if 42 of the 61 voters that changed their mind didn’t we have UM in the title game. If 34.4% of the voters that decided to move UF ahead of UM would have kept Michigan in the spot above them, UM would be in the title game. The difference in the national championship berth? 11 writers and 21 pollsters.
2 Scenarios
The difference needed to put Michigan in the title game in the coaches poll.
.0101 = 1/3 * (X/1550) -------simplified-
X = 46.965 points
So UM needed a net gain of 47 points on Florida to go to the title game. That is Lloyd Carr and one other friendly coach dropping Florida from 3rd to out of the poll and moving UM from 2 to 1 in the polls. Boom, 48 net points.
How about the Harris poll. Some jackass made UF number 1 and most likely put UM in fourth or worse.
.0101 = 1/3 * (X/2825) -------------------
X = 85.5975 = ~86
That means 4 of 114 voters could have been bought to leave Florida completely out of the polls, we all know the amount of money involved in college football, it wouldn’t even be that hard to do.