The Mathematical breakdown of likelihood of Bama/OSU in title game

Background:

The coaches poll, Harris poll and Computers each count for 1/3 of a team's BCS ranking.

Coaches poll:

Bama: .9485

OSU: .9268

The coaches poll was released earlier today was not kind to the Cowboys. With 59 total voters, Bama totaled a 32 point edge. While we don't know for certain how this broke down, this result is equivalent to 14 coaches voting the Cowboys 2nd and Bama 3rd (23.7%), 44 voting for Bama 2nd and (nt)OSU 3rd (74.6%) and one voting for Bama 2nd and OSU 4th (1.7%).

This was a significantly worse result for the Cowboys than what they got in the AP  where Alabama garnered a 16 point edge with a total of 60 voters. 

Computers:

Given that both the Coaches and AP polls broke for Alabama, the Cowboys' hopes seem to hinge on getting help from the computers. There are 6 computer rankings. The highest and lowest result for each team gets dropped. Last week 4 of the 6 computers put Alabama at 2nd and OSU 3rd and the remaining 2 put Oklahoma State 2nd and Alabama 3rd.

If these results hold or the Cowboys are only able to flip one computer, their chance at a title game is functionally zero.

If they flip two computers this will be the computer score

OSU: .95

Bama: .93

This would nearly wipe out Bama's edge gained from the Coaches poll, but OSU would still need to top Bama by a slim margin in the Harris poll to get a title shot. Given the results from the Coaches and AP polls, this seems unlikely, though not impossible.

If they flip 3 or 4 computers this will be the computer score:

OSU: .96

Bama: .92

The remainder of this analysis will deal with this possibility.

UPDATE: 2 computer rankings (Sagarin and Wolfe) have been released they both have Bama 2nd. This means OSU flipping 3 or 4 computers is no longer a possibility. OSU will have to at minimum gain 5 points on Alabama in the Harris poll to go to the BCS. This means they will need to top Bama on 52.18% of Harris poll ballots assuming neither team is ranked beneath 3rd.

Harris Poll

Assuming OSU flips 3 or all 4 computers, Bama would have to make up a .0183 edge in the Harris poll. (The difference in computer score and coaches score)

The Harris Poll has 115 voters. For Bama to overtake OSU they would need to be placed 53 spots above the Cowboys in the aggregate. Assuming all voters put Bama and OSU in some comination of 2nd and 3rd Bama would need 84 of the 115 voters (73%) to rank them 2nd.

For perspective, if the Harris poll comes out with similar results to the coaches poll Bama will top OSU by ,0034 points. If it comes out with similar results the AP the Cowboys will overtake Bama by .0063.

Conclusions

• If the Cowboys can't flip a computer, or only flip one they are doomed.
• If they flip 2 it is still highly unlikely they get to the National Championship
• If the Cowboys flip 3 or 4, Bama will need at least 73% of Harris poll voters to rank them 2nd, assuming all voters rank Bama and OSU at least 3rd.
• For the non mathematically inclined: If the Cowboys flip 3 or 4 computers and the Harris voters rank the teams as the coaches did it's rematch time. If the Harris voters rank the teams like the AP did T Boone will be very happy.

Updated Conclusions

• If Richard Billingsly (computer) keeps Bama at 2 they are definitely in.
• If Billingsly switches OSU and Bama OSU must gain 5 points on Bama in the Harris poll. This means they would need 52.18% of Harris voters to put them above Bama assuming neither team gets ranked below 3rd. Given the results of the coaches and AP poll this seems unlikely.
• The Tide will likely roll to a rematch.