The Stoops Paradox
I see a lot of people parroting Stoops’ line about how you can’t use Texas’ head-to-head victory over OU in voting unless you also vote Tech ahead of Texas…but yet OU beat Tech. OMG! There is no solution! I am surprised by how many people seem to buy this argument. It’s an example of specious reasoning called a paradox. Merriam Webster defines “paradox” as:
2 a: a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true b: a self-contradictory statement that at first seems true c: an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises
The argument that Stoops lays out is a great example. Each element is sound. Texas did beat OU. Tech did beat Texas. OU did beat Tech. However, if you buy the proposed premise, then all of these head-to-head results are useless in rating these teams. Captain Kirk could have really stumped that alien computer with this one!
Obviously, that’s stupid. Head to head results are the best data we have for ranking teams. In a playoff, head to head results are all that you use. The unique round robin aspect (thought- would everybody be willing to reject the RRS result if a non-conference opponent were subbed for Tech in this menage a trois?) adds a layer of analysis, but you still need to understand that they mean something.
So, what to do? Stoops proposes throwing them out, and evaluating on the remaining body of work. That is an argument, and lacking another proposal, it is the only one on the table. I think there are better ways to analyze this, though.
I’m not interested in proposing tie-breaking systems. That horse is long out of the stable. I’m interested in ranking teams. I know that the system (polls and computers) does not define what is being ranked- season’s body of work, or hottest team now. Still, the question is- Who has the better team from among these three 11 - 1 teams? Can you use the head to head results? Yes, you can.
Each team has one win and one loss. Ask yourself about each team- if the teams replayed on a neutral field, could you expect a similar result (i.e. did the result seem sound, or a fluke). Obviously, point differential comes into play. Next, ask yourself about each team’s loss- if the teams replayed on a neutral field, would you expect a similar result?
Texas- beat OU by 10 on a neutral field, lost to Tech by 6 on the road
OU- beat Tech by 44 at home, lost at a neutral field to Texas by 10
Tech- beat Texas by 6 at home, lost to OU on the road by 44
The results on the field suggest that in a neutral site round robin, Tech is most likely to go 0 - 2. Who rates higher- Texas or OU? I’m not getting into that. I have my opinion, the Sooners have theirs (wrong), and the voters need to form their own. They just shouldn’t be stupid and intellectually lazy enough to rely on the Stoops Paradox and discard the results.
December 3, 2008 at 3:37 am
One approach is to throw out the worst team in the three way tie and then use head to head to decide between the remaining top two teams. I think this is what the SEC does when they have a 3 way tie.
Tech was obviously the worst since it got blown out by OU and barely won (in the last second) at home against UT. After throwing out Tech, that leaves UT and OU. UT beat OU on a neutral field by two scores so UT wins the tie breaker.
I try not to worry about this too much.
College football is corrupt and obscene in many ways:
* crooked recruiting,
* paying off athletes while they are playing, * letting athletes slide by in school,
* scheduling patsies,
* pretending to be an amateur sport when it is clearly run as a high dollar professional enterprise,
* covering for athletes when they get in trouble,
* huge salaries for coaches,
* mega score boards that are bona-fide environmental hazards
* no playoff system to decide the champion
* anything else that I forgot.
The coaches poll is particularly gross. Let’s face it, college coaches are not ethical paragons. In general, they are about as honest as a politician. Having them evaluate themselves (secretly!) is ludicrous.
December 3, 2008 at 5:42 am
I told my wife the other day that you could paraphrase Stoops’s argument as “I assure you that you can’t logically solve this, so don’t bother trying.”
December 3, 2008 at 5:50 am
I don’t worry about the BCS anymore. We beat them on the field. We outplayed them in all facets that day except maybe at TE, which didn’t exist for us anyway. I know who’s better, who is the more complete football team, who deserves to win the conference, and that sits well with me.
This is a year where we beat all three of our traditional rivals, two of them badly. We have a Heisman caliber QB and the best defense in a conference dominated by offense. This was a great year and a bunch of computers and classless okies can’t change that.
December 3, 2008 at 6:00 am
It’s funny, but the only thing keeping Tech in the 3 way tie, round robin argument, and by default keeping ou in MNC contention, is the fact we have a conference championship game. Precisely because Tech shields any discussion of Texas’ head to head win vs the sooners on a neutral field.
Consider this, if the Big 12 was, say, the PAC 10 or Big 10 or any conference without a conference title game, and the games were completed this weekend, Tech is not even in the conversation in terms of playing in the National Championship game, which means head to head between ou and Texas is the only thing that matters. Voters would also have an extra week to let head to head reality sink in and make the appropriate adjustments.
So…not only did the sooners need their conference to have a championship game to get in the national championship picture in this scenario, but they also needed the conference to have the most inane conference championship tie breaking rules to get in the conference championship game and then have any shot at a national championship.
The fact that you have to use these huge leaps of logic and circumstantial gymnastics to get the sooners into the big game should tell folks all they need to know about who actually deserves to go.
December 3, 2008 at 6:35 am
This reminds me of the PBS pre-school game “One of these things is not like the other.” Which of the three teams doesn’t fit with the other two. That team is clearly Tech. They got blown out in Norman after an extra week to prepare and heal up. Texas and OU lost close, competitive games. Tech played nobodies outside the conference and also struggled with teams (Baylor, aggy, Nebraska) that Texas and OU dominated. The fact that Tech doesn’t belong with OU and Texas is reflected in the BCS (they are 7th) as well as the human polls (8th).
December 3, 2008 at 6:50 am
The three-way paradox argument does work — but only if each of the three teams has a credible claim to “win” the tie. Suppose Tech played a comparable schedule to Texas and OU such that S-O-S was roughly comparable (as it is with Texas and OU). Suppose Tech lost to OU in heartbreaking fashion. Suppose Texas beat OU at home, rather than on a neutral field. THEN, all three teams would have arguments and Stoops would have a point that you have to “throw out” the head-to-head results.
What’s ironic is that NO ONE — not even Tech — argues that Tech deserves to win the tie. Leach admitted that by suggesting using graduation rates to break the tie. That’s an admission that they have no argument.
Should it really matter in deciding whether Texas or OU wins that Tech managed to beat Nebraska in OT? If they’d lost that game, then there is absolutely no debate because they’d be “out” of the discussion. But they’re out of the discussion anyway.
Oh well, no point in more useless anguish. Lets hope we can somehow finagle a meaningful bowl game against the Ala-Florida loser. I’m not optimistic.
December 3, 2008 at 6:50 am
I would expect that for a human, ranking team A above team B means that our human expects team A to beat team B in a game. That isn’t what most humans do though.
Most people, even here on BC, put Alabama at number 1 while expecting a lower ranked Florida to beat them. “They have shown blah blah blah and have earned the number one spot until someone beats them.”
Considering Texas and Oklahoma, I personally would rank Texas higher using either standard. The second “what you have proven on the field so far” criterion is obviously UT’s. The first criterion, based on expectations of performance in a head to head match up (or 10 or 100) is a more divisive question. I know longhorn fans that would predict an ou victory (or 6 or 51), but I’d still expect UT’s offense to outperform OU’s defense to a greater degree than oklahoma’s offense would the texas D.
Tech doesn’t warrant deep thought in either of the criteria. I wouldn’t expect them to beat texas or oklahoma and their body of work doesn’t match up either.
There is one criterion that i didn’t mention yet, and it’s the one that is now universally derided and loathed. It’s also the one that the general media discussion gave to ou. An awkward crown of laurels hewn from Style Points has been lain upon the sooner head. It has been noted before: style points are for goddamned ice skaters, not motherfucking football teams. If those shitbags getting paid to orally defecate all game long say style points next year i’ll hit the mute button on the sumbitch starting in october.
December 3, 2008 at 7:06 am
Standing ovation.
December 3, 2008 at 9:45 am
First of all let me say that I think you guys deserve to be in the conference championship game.
However, I find it highly ironic that Texas fan is complaining about the Big 12 conference when everything from eligibility rules to the television contract to revenue split to location of the conference headquarters to future direction of CCG location has been slanted in Texas’s favor by the league, and slanted dramatically. And I suspect, had Texas wanted the Big 12 to adopt the tiebreaking procedures that exist in the other conferences and suggested this prior to this season, it’s highly likely the rules would be different, allowing Texas to be crowned the South Champion.
Secondly, while I agree that the head to head win over OU should settle the tie, and the SEC/ACC conference tiebreaking procedures are superior, I can’t say that I’m overwhelmingly offended by the selection of OU as the South Champion. Tech certainly would be in the conversation if it wasn’t for the obscene beatdown that OU put on them. If Tech had lost by one score or less to OU at OU, they would have just as good of an argument as either OU or Texas. In effect by taking Tech completely out of the picture because of the beatdown that OU layed on them, you are effectively penalizing OU for their superior performance against Tech.
December 3, 2008 at 9:54 am
I agree with the premise of your post, TaylorT. Really, even though Tech has the same record as Texas and OU, the weakness of their OOC and in-conference schedule, coupled with the way they lost to OU, should take them out of the equation. Had they played as tough a schedule as Texas, the Raiders would have lost more than one game. Thus, what you’re really trying to do is tie-break between OU and Texas. In that case, there’s a clear way to do it, and it’s the head-to-head.
Unfortunately, the pollsters aren’t that rational, and the computers aren’t concerned with tie-breakers (they apparently look at overall results). This isn’t the team with a head-to-head loss has been crowned MNC over the head-to-head victor with an identical record. Remember 1993? Florida State lost to ND, who then lost to Boston College on a last-second field goal. Both teams won their bowl game (although FSU barely won), and the polls picked FSU as national champ. In that case, though, there was no 3-way paradox to confuse the issue.
December 3, 2008 at 10:26 am
These types of blatant injustices usually find a way of righting themselves or working themselves out. I would not be the lease bit surprised if OU slipped in Kansas City, nor would I be surprised if Florida topped ‘Bama in a 10-7 grudge match that leaves voters underwhelmed and thus throwing UT to Miami.
Personally, I prefer the later because I would love the opportunity to beat OU twice in one year on a neutral field.
Nevertheless, I will bet that something happens to right the wrong.
December 3, 2008 at 10:27 am
“…least bit surprised…”
December 3, 2008 at 10:53 am
Zizzy- unless you consider Florida mudholing OU as righting the wrong, I’m afraid you will be wrong.
December 3, 2008 at 10:53 am
Trips, I have to disagree with CCG hiding the dispute. Without a CCG, there might be a two-week gap, but the B12 still would have to pick a champion among its three best teams, all of whom remain 7-1 in the league, and still tied under those criteria that ended up with the BCS vote.
What the extra week probably would have done is draw Stoops into the discussion.
December 3, 2008 at 11:23 am
The real distraction was the Big 12 tiebreaker.
The BCS voters are not supposed to pick who should go the big championship game, they are supposed to rank the best teams in the country. Its a coincidence that the Big 12 chooses to use those rankings to break their tie. As such, there was no more a tie between the three in the big 12 south than there was between every team in the nation that was tied with one loss.
The question is not: how do we break the tie amongst these three; its who are the best 2 teams in the country?
So no need to “break” the tie. You end up with OU and Texas clearly jockeying for position with Tech out of the picture. How do you rank those two: one of them beat the other on a neutral field by ten points.
The fact that the BCS would ultimately be used to break the Big 12 tie is what confused the voters.
December 3, 2008 at 6:50 pm
can you imagine how crazy the game in dallas will be next year if somehow ou wins the bcs title and we take the ap? discounting the danger to my sac, this is what i want to happen.
December 3, 2008 at 8:11 pm
well, I seriously doubt that will happen…
but if it did, we’d be the champions without an asterisk.
December 3, 2008 at 8:38 pm
I’m all for Mike Gundy’s solution. Throw the North/South divisions out the window and let the two highest ranked teams play for the title. Does Missouri really deserve to have a shot at the conference championship? NO. They would be no better than 5th in the South having lost at home to Oklahoma State.
“In effect by taking Tech completely out of the picture because of the beatdown that OU layed on them, you are effectively penalizing OU for their superior performance against Tech.”
I’m curious to see one of the Barkers address this point. Because the entire UT head to head argument relies on OU’s massacre of Tech to eliminate Tech. If OU loses to Oklahoma State, then its the Red Raiders on their way to Lubbock regardless of the BCS rankings that would’ve rightfully listed Texas as the better team.
December 4, 2008 at 4:31 am
“Because the entire UT head to head argument relies on OU’s massacre of Tech to eliminate Tech.”
no it doesn’t. baylor, nebraska, their non-conference schedule, the tech ceiling, their ranking in every ranking system.
December 4, 2008 at 5:54 am
No, I gave an example of an argument that UT or OU could use in the original post, and OU gets credit for blasting Tech.
It seems to me that there is an argument Stoops could have used that doesn’t rely on throwing away the head-to-head results. He could have said that yes, Texas beat OU in October, but Tech beat Texas. Granted, it was in Lubbock, but that game (this could be Stoops talking) showed those teams were comparable at that time, and that OU blasting Tech shows how much OU has improved since then. He didn’t resort to that argument (its weakness is that it requires you to make a subjective assessment when there is contrary objective evidence) overtly because he didn’t have to. His paradox argument, where you throw the games out, worked well enough with voters who aren’t very good at reasoning. I wrote this post because I’m so tired of people throwing it out there, folding their arms, and saying, “sic is est, Jack”.
December 4, 2008 at 6:48 am
NateHeupel-
The three way tie scenario is easy to address.
It’s simply about who played where?? Tech’s win was at home. OU’s win was at home. Texas’ win was at a neutral site.
Location of losses. Texas lost on the road close. Tech lost on the road big. OU lost at a neutral site by 10, scoring 14 of their 35 points over the last 40 minutes of play.
It’s as simple as that! If you can’t take Tech out of the equation, then you can’t take LOCATION out either. That, my friend, is why Texas would win the argument any way you look at it.
December 4, 2008 at 6:58 am
“In effect by taking Tech completely out of the picture because of the beatdown that OU layed on them, you are effectively penalizing OU for their superior performance against Tech.”
I’ve seen some Sooners offer the NFL tiebreaker system as a model for a new B12 tiebreaker. I don’t see a ton of difference between them, but one thing I do know, having followed NFL tiebreakers for several years:
When any step eliminates one team from a three-way tie, the tiebreaker immediately reverts to the two-way steps… the first of which is head to head.
[Once upon a time, I needed to contact the NFL office about the tiebreakers, and learned that this is done so suddenly that the step that culls a team is not even completed -- that is, they don't order the remaining teams under that step, to pick a winner, and be finished. They go back to the top of the appropriate list.]
The OU argument is that a team must be selected *only* from among the three. With no other losses by which to differentiate, the selection at least for some voters came down to an individual decision as to which team was “playing better.” (I actually don’t mind this — if I were voting, I would try to evaluate the season as a whole. But, I’d also be free to eliminate any team I chose, for whatever reason.)
But the NFL does it like the OB wants to look at it. They try to peel off pretenders and make it as simple as possible under the rules. The simplest of those, of course, is head to head.
And, as far as penalizing OU, it was the same voters who didn’t exactly roll over regarding head to head between Texas and OU (given the margins in the polls between UT and OU) who dropped Tech to the lower half of the top 10. (Remember, the computers still like Tech a lot.) The voters didn’t penalize OU for steamrolling Tech. They penalized *Tech.* It’s only a “penalty” to the Sooners if OU can’t win the argument without Tech.
December 4, 2008 at 9:02 am
Again, I think on balance Texas deserves the South Championship.
However, I do think a close OU win over Tech would mean Tech is not eliminated from the conversation. If OU beat Tech in a similar fashion to how Tech beat Texas then they would be substantially close to OU and Texas in the polls. And no I don’t think there’s some Grand Canyon sized gap between the OOC strength of Tech and Texas. And no I don’t think the Sooners had a murderers row in front of them either. All 3 teams had 4 easy wins for a legitimate top 10 team and all 3 teams got 4 wins. And don’t start with effing TCU and Cincinnati. Please. Those should be penciled in as “W”s for any team pretending to lay claim to the Big 12 championship. The first of the three of those teams to get up on their high horse about OOC schedule strength needs to get bitchslapped right back off.
As far as the suggestion of letting the top 2 teams play for the conference championship, there are a number of problems with this. Foremost, it would require a change in NCAA rules, not just Big 12 rules, because the whole reason we have these conference title games is because the SEC was smart enough to exploit an NCAA loophole that allowed far flung conferences with 12 teams to split into 2 divisions and play a CCG with each division champions - a rule that I believe existed for 1-aa teams, not initially inserted for major college football.
Secondly, I’d like to understand how much you guys would like that rule being applied in 2007 when both Missouri and Kansas sat 7-1 with the best league records entering the CCG and no south team would have qualified under a “take the top 2″ approach. Understanding that these teams just played a neutral site game the week before. That might have been considered a much worse result than what we are facing this year. So I don’t want to hear any bitching about the setup of the division champions playing unless you are prepared to make the claim that problems associated with applying that approach in 2007 wouldn’t have exceeded the benefits in 2008.
So no I don’t feel in the least bit sorry for any of the 3 teams. OU got lucky but lost so they deserved their division championship to have an asterisk. The conference almost rubber stamps everything Texas wants anyway so they should have had them rubber stamp changes to the tie breaking procedures before the season if they thought they were so much better. And Tech got owned in Norman so they aren’t even part of the equation in my mind. All 3 teams played pussy OOC’s. So all 3 deserve to have the result put up to a coin flip which you are basically doing with the absurdity of the BCS poll.
December 4, 2008 at 10:22 am
For the record, I had nothing to do with it.
December 4, 2008 at 1:03 pm
Don’t blame me. I voted Palin.