A message to calm your nerves...using math

Goalscorer9's picture
October 8, 2013 at 7:19p

Hey everyone!

A sentiment that used to be quite obvious seems to have been forgotten here in the buckeye nation as of late.  Going undefeated is hard.

It seems like everyone is very worried about the possibility of the buckeyes going undefeated and being left out of the championship game.  This is a very real possibility, and I completely understand your concerns, but the sentiment has been skewed over the season to the point where some people think it's "unlikely" an undefeated Ohio State team would be selected to go to the national championship game, and even a post saying "almost ZERO" chance today.  It frustrates me when people start using words like "chance" or "probability" which can easily be calculated, and then proceed to spew a baseless opinion, which many times happens to be quite incorrect, so I decided to go the scientific route.

I thought I'd use some probabilities to actually see what the numbers looked like.  It's rather easy to calculate, I'll summarize very briefly: If you assign each game as a probability of a win, you simply multiply all those probabilities together for that team, to find the odds of them going undefeated.  I'll attach my spreadsheet for the numbers I assigned for the 5 teams most are worried about, but here were my findings:

*note: these are obviously a little subjective, as even though the math is objective the percentage for each individual game was something I came up with.  I tried to be as fair as I could.  See the spreadsheet for details.

Alabama has a 28.6% chance of going undefeated (despite having at least a 60% chance of winning each individual game)

Oregon has a 13.3% chance of going undefeated

Clemson has a 13.9% chance of going undefeated

Stanford has a 13.8% chance

Florida State has a 11.58% chance.

Obviously, subtract from 100 and you get the odds of each team losing a game.

If you take Ohio State going undefeated as a given (which you definitely shouldn't, but for the sake of the "if we go undefeated" argument, we will)  There's actually a 40.6% chance that we'd be the ONLY undefeated team (of the six most consider "in the hunt"). 

Even if you are of the crowd that think the SEC automatically gets into the NC game, and we're fighting for the number 2 spot.  There's still a 56.9% chance that Oregon, Clemson, Stanford, and FSU ALL lose a game between now and the end of the season.  That's right, by my projections it's actually more likely than not that all of those teams lose a game.

Are the odds good enough that you should bet your house on it? Absolutely not.  It's very possible OSU gets left out.  But for those of you who are about ready to give up hope, we've got a lot better shot than you think.

I think when many start to panic, is when you look at a team like Oregon or Clemson and see they are favored in every game, and you think that means they are more likely than not to go undefeated.  That's not how probability works.  If you roll a six sided die, most the time it's going to be something other than, say, 6, but if you have to roll the die 8 times, you're likely to get a six somewhere in there.  So even though a team like Oregon will be favored every week from here on out, it's actually far less likely that they finish undefeated than likely.  The 6 is a loss, in this analogy.

If you have a beef with any of the numbers in my spread sheet for individual games, I'd be happy to discuss my reasoning.

I hope this little math break calms your buckeye nerves!

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Seth4Bucks's picture

This is the kind of math they need to be teaching in high school! Music class should be all the OSU songs. Hmm, what else  . . .

dwcbuckeye's picture

Nice job.  Incidentally, what were your game by game probabilities for OSU?

Goalscorer9's picture

Iowa  - 94%  Iowa is playing decent this year, but not great. It's at home coming off a bye.

PSU - 92% Ohio State is the better team, Penn State will give their best effort.

@Purdue -  97% Purdue is very bad.  Still, that field always puts just a hint of fear into me.

@ Illinois - 94% Illinois is improved, but still vastly inferior.  That's another of our least favorite fields and the possibility of scheelhause going off dips my percentage just a bit.

Indiana - 91% could be a shootout, buckeyes should win it fairly easily.

@TTUN - 75% Ohio State is better, but that game is never a gimme when it's up there.

BCG - 68%  I think it will either be a rematch with TTUN or northwestern.  Rematches are always tough to win.

Odds of going undefeated: 36.6%

We have better odds than all the others listed, but it's still not likely we go undfefeated.  Puts things into perspective.....

NoVA Buckeye's picture

I wouldn't rule out Nebraska just yet. Very impressive win in Champaign for the Huskers, against a very good Illinois offense where they held them to just 19 points. As long as Taylor Martinez never plays for the Huskers again, we should meet them in the B1GCCG

The offseason begins when your season ends. Even then there are no days off.

Goalscorer9's picture

certainly could play out that way!  Note sure how much I would change the percentage based on that.

Run_Fido_Run's picture

Good job putting this together.
A question came up yesterday: How to adjust the calculations given that Stanford plays Oregon and FSU plays Clemson? Obviously, there is an auto loss to distribute to either Stanford or Oregon and an auto loss to distribute to either FSU or Clemson. For example, there is a zero percent chance that three+ of those four teams will go undefeated. Do your numbers account for this problem?

Run_Fido_Run's picture

One totally unscientific way I tried to think about this problem was to assume two "survivors" from those four teams and then sort of average out the probability that the survivors would win their other six games. I'm sure there's a much better way to do it, mathematically, but logically it makes some sense to think of these four teams => two survivors.  

Goalscorer9's picture

you definitely could set it up that way.  I would guess the numbers would come out to be about the same.  In fact if you simplify out the equations of the two setups, I'd imagine they cancel out to be the same thing.  I'm not 100% sure though, it's been a few years since I've taken a probability class and I don't really feel like reteaching myself the more complicated set ups at the moment haha

To be truthful I did this in about 20 minutes and didn't want to overcomplicate the set up.

Run_Fido_Run's picture

I don't blame you at all. For some silly reason, I got curious about this problem and was hoping to hear how to deal with it, in theory of course, because I don't want to do the work myself, either. Like you, I enjoy spitting out some back-of-the-envelope numbers, but please don't ask me to crack one of my old text books.

Goalscorer9's picture

I believe my numbers account for that.  The biggest error in my set up is that it has oregon and stanford plying in the P12CG and Clemson and FSU each playing in the ACCCG, which obviously wouldn't happen.  But I set it up as the odds of each team individually going undefeated, and then found the overall picture based on those numbers.

The fact that I gave each P12 and each ACC .5 odds in the games they play each other, if you take the .5 times the 2 teams in the game that gives the expectation of 1 loss.  So I believe that is included in the way I calculated things.

If I were trying to find the odds of all 5 teams winning out, I think I would have to adjust my set up, as that would obviously be impossible.

Run_Fido_Run's picture

I'm not sure about that - is there a math whiz in the house? From what I can tell, your calculations for each individual team are just fine - keeping in mind, as you noted, that we have to make the game-by-game probability guesses. The tricky part, I think, is when we start to gage the odds of 1, 2, or 3, etc. undefeated teams from those independently-arrived numbers. From what I can tell, your numbers do not show that there's a zero percent probability that 3 of those 4 will go undefeated, and then so working backward from that problem, I wonder if the calculations for 2, 1, or 0 undefeated teams is also off just a bit?  

Goalscorer9's picture

correct.  It doesn't account for that.  In fact, off the top of my head I don't know how to calculate what are the odds of 1 of those 5 teams going undefeated.  I tried for about 2 minutes (I think it involves chaining together a few "given that" set ups) and decided my main point could be made without doing all of that work haha

Goalscorer9's picture

I think my equation for all 5 losing, and my equation for all 4 losing (excluding alabama) should be pretty close, but the set up for 4/5 losing is a lot more tricky.

I think I still have my old probability profs e-mail, and he gets excited about solving this type of stuff.  Maybe I'll send him a message tomorrow if I get the time.  I took the class my first quarter of grad school (which was over 2 years ago) so I don't remember all the details haha

d5k's picture

Oregon and Stanford going undefeated are mutually exclusive events so the probability of either of them going undefeated is the sum of the probabilities of each one going undefeated.  
Let O = Oregon going undefeated, S = Stanford undefeated, etc. for the ACC and P12.
P (2 teams going undefeated from ACC & P12) = (P(S) + P(O))* (P(C) + P(FS))
The multiplication is allowed since ACC and P12 games are independent events.
Ends up being 27.1% chance of undefeated P12 team, 25.5% chance of undefeated ACC team, and the 28.6% chance of undefeated Alabama.  Probability of all 3 happening (product of the 3 above) becomes 1.97%.  Probability of 2 happening (sum of the product of the 3 combinations of 2) is 21.9%.
Probability of P12 or ACC champ being undefeated would be 52.6% (sum of all 4).  Probability of exactly 1 of the 2 is 52.6 - 6.9 = 45.7% since you have to subtract the probability of both events occurring.
The 40.6% should be 38.9% (chance none of them go undefeated) and the 57 should be 54.3 (chance neither P12 or ACC champ goes undefeated).  You just didn't account for the fact that someone has to win the game between S and O, C and FSU.

Run_Fido_Run's picture

Thanks! And roughly 22 percent seems about right. Perhaps the more likely scenario that would keep an undefeated Ohio State out is an undefeated ACC or P12 team + one loss SEC champ. 

RhTN's picture

I thought it said meth... I'll walk backwards slowly...

Alpo's picture

I don't think meth calms nerves very well!!!  ;)

TMac's picture

I knew history said more than two undefeated teams are unlikely (but certainly possible) - Thanks for the math to back that up. 

ONE Not Done!

Alpo's picture

Good work here, thanks for doing the Math so I didn't have to. Hopefully this will calm some folks down, but probably not

unholy bucknut's picture

This is cool what you did here, but it's still just your opinion fused together by a cute little math problem. It's no basis for anything but i'm picking up what you're putting down. Good work I like it. +1 for sheer creativity.

Goalscorer9's picture

yeah it's still highly subjective, but I think it is at least put together in a way that is more grounded in reality than just saying "no way oregon loses from here on out" or something similar

unholy bucknut's picture

It is  for sure and I enjoyed it good post brother.

gobucks96's picture

but what if it snows?!  Calculate that!
Seriously, nice work..

Earle's picture

Interesting analysis, but using math does not calm my nerves.

"It was my understanding that there would be no math"

Have you tried Not Your Father's Root Beer?  It tastes just like the real thing, but it packs a punch (5.9%ABV).  It's a little sweet for me though.  Two is my limit.

twalsh's picture

I like it, now time to have a drink to calm me down!
Go Bucks!!

Geraffi's picture

Great work.  You can't argue with math, because, if you do, you will lose!
Here's another really basic math fact that should help to illustrate your point that it's rare and difficult to go undefeated.
In 123 seasons, Ohio State has had exactly 6 (SIX) undefeated seasons.
123-6=117 seasons in which the Buckeyes have lost at least one game.
Basically one undefeated in every 20.5 seasons.
It's not crazy.  It's math!

FitzBuck's picture

It would appear your post has a lot of numbers.  
(All kidding aside this is what all of the "chicken littles" needed.)

Fitzbuck | Toledo - Ohio's right armpit | "A troll by any other name is still a troll".

Indy_Buck87's picture

Some smart dudes at Stanford actually developed a statistical model to calculate the probability of a team winning a game: http://www.stanford.edu/class/stats50/handouts/stern.pdf

I know of only two things that are infinite, space and human stupidity.....and I'm not sure about space". Albert Einstein.