Monday, December 2, 2013

Conference USA's Tiebreaking Travesty

A letter to the Conference USA office:

By Chris McComas

Good morning,

I just wanted to drop you gentleman a line regarding the formula you used to determine home-field advantage for the CUSA title game this weekend. First off, I don't expect the game location to be switched, or anything like that, but wanted to address a few points to hopefully prevent such an error by the conference in the future.

First off, my name is Christopher McComas. I am a Marshall alumnus and fan. Many years ago I computed my own "power ratings" similar to those used in the BCS equation. At one point I actually had a couple phone conversations with Roy Kramer of the SEC and Tom Mickle of the ACC, who were at the time the top two in the BCS, about the possibility of including my ratings in the BCS formula. Ultimately my ratings weren't added, but I had a wonderful opportunity to talk with some gentlemen whom I respected greatly.

The BCS formula is designed so that the human element, Coaches Poll and Harris Interactive Poll, carries more weight than the computer element, two-thirds for the human element to one-third for the computer element. This tweak was made in 2004 so it would make it next to impossible for the top-ranked team in the polls to not end up ranked first or second in the BCS after the 2003-2004 season ended with a split national championship.

All that said, let's move on to CUSA's tie-breaker for home-field advantage. We can skip down to Step No. 3: "If still tied, team with highest BCS ranking." Since Marshall received votes in both of the human polls the BCS, there was enough data to determine a rating for each team based on the formula the BCS uses for all other teams.

Rice would have ended up with 0.0 for the Harris Poll, 0.0 for the Coaches Poll, and 0.0 for the computer ratings. Marshall would have ended up with 0.0038 (10/2625) for the Harris Poll, 0.0084 (13/1550) for the Coaches Poll, and 0.0 for the computer ratings. There was no need to change the formula, since there was enough data to determine each team’s BCS rating based on the original BCS formula, and thus determine which of the two had a higher "BCS Ranking," which would have settled Step No. 3 of your tie-breaking procedure.

Marshall would have had a BCS rating of:

0.0041 = (0.0084 + 0.0038 + 0.0) / 3

Rice would've had a BCS rating of:

0.0000 = (0.0 + 0.0 + 0.0) / 3

(According to the complete BCS standings published at BCS Guru, Marshall is No. 33 while Rice is unranked.)

I'm not sure why you as a conference felt that the computers must be included, the BCS doesn't include computer ratings when a team is outside the Top 25 of a computer rating. You can look at Fresno State this week as an example, as it received 0.0 as its computer component because it was not ranked in the Top 25 in ANY of the six computer components.

You might wonder why the BCS would exclude computer ratings outside the Top 25 in their official calculations, but it's pretty simple. The voters in both of the human elements are limited to voting for 25 teams, which creates a 25-point scale, i.e. 25 points for first, 24 for second, etc all the way down to 1 point for twenty-fifth. In the official BCS calculations, the computers carry the same scale, 25 for first, etc. This keeps the three elements evenly weighted, so that the computers don't outweigh the polls.

When CUSA made the decision to rank Rice and Marshall’s computer ratings and base it on ALL 125 teams in FBS this year, you created a 125 scale that you used only for the computer. This decision essentially gave the computers 5 times the value/weight as the human polls.

The human polls as I mentioned are only on a 25-team scale, so Marshall finished 29th out of 36 in the Coaches Poll and 31st out of 36 in the Harris Poll, it doesn’t see them as the 29th and 31st best team out of 125, only out of the 36 teams that received votes this week. The polls don't recognize or count for the other FBS teams not getting a single vote. It sees Marshall near the bottom of the 36 teams getting votes and awards them accordingly.

If you would've weighted the human polls on a 125 scale, then Marshall's 13 points in the Coaches Poll would've been worth 1,313 and its 10 points in the Harris Poll would've been worth 1,010. I got this by doing a 125 scale, 125 for 1st, 124 for 2nd, etc. Recalculating the BCS equation to determine the ratings for the Coaches Poll element would've been 62 x 125 (62 voters, 125 max points for the new "perfect score" or "max score") or 7,750. You would divide Marshall's 1,313 by the 7,750 to come up with 0.1694 instead of the 0.0084. To calculate the new Harris Poll score it would've been 105 x 125 (105 voters, 125 max points for the max score) or 13,125. To get Marshall's new score divide the 1,010 its earned by the 13,125 and you get 0.0770.

Using Marshall's. 0.1694 and 0.077 along with the 0.55 the conference gave the Herd for their computer element, their new BCS ranking would be 0.2655, or more than the 0.2093 you calculated for Rice.

(Conference USA's official release, with modified formula explained)

The fair way to have done it would've been to just ask the BCS to compute out the ratings until Marshall or Rice showed up in the rankings, as I noted above there was enough data that one of them was going to have an official BCS rating greater than zero, using the BCS' traditional formula.

If that option wasn't good enough for you, you could've used your method, but taken steps to ensure that the three components all received fair weight and one of the components wasn't drastically overvalued. As it stands, you completely bungled the process and penalized a team for your office's ineptitude in math.

Thanks for your time,

Chris McComas


Anonymous said...

I don't follow CUSA football at all (I'm a Cal fan) but agree that CUSA got this one wrong.

The strongest argument is that the BCS ranking formula does award 0 points for computer rankings beyond 25th, as is the case for Fresno State which Mr. McComas pointed out.

But it could also be argued that the computer rankings are dropped beyond 25 only for the purposes of ranking the top 25 teams. For ranking beyond 25, it's not particularly wrong, or even necessary, to extend the computer rankings.

Where CUSA screwed up, is not disclosing ahead of time what is the tie breaking formula for the case where both teams are outside top 25.

I would like to point out one thing though: even if we cut down the computer weight by 5 times (as Mr. McComas believes the computer weight is 5 times what it should be), Rice would still win the tiebreaker.

Rice: 0 + 0 + 0.628/5 = 0.1256
Marshall: 0.0038 + 0.0084 + 0.55/5 = 0.1222

McComas's 0.2655 calculation makes little sense because you can't extend the human polls to a 125-team scale and award 0 points for would-be rankings from 26 to 125.

Anonymous said...

Marshall should have stayed in the Mid-American Conference where they essentially bought home-field advantage for the first several MAC championship games.