So you're telling me there's a chance
I have a delusional friend who is still holding out hope that we win the Big Ten this year. I told him he is delusional and he hit me with the Dumb and Dumber gif.
So, I decided to quantify his delusion. I went to Massey and calculated the odds that we win the Big Ten based on win probabilities. Edit: I didn't feel like calculating for multiple scenarios; I picked the one with the highest probability of happening based on current projections. (So the actual number may be slightly higher. But when you see the final tally you wi--nevermind, don't want to ruin the fun...)
MSU:
- Lose to Northwestern (41%)
- Beat PSU (16%)
- Lose to OSU (82%)
- Lose at least 1/2 to Maryland and Rutgers (9%, and 12%, respectively)
- Finishes with at least 3 Big Ten losses. Head-to-Head doesn't matter.
PSU:
- Lose to OSU (44%)
- Lose to MSU
- Lose at least 1/3 to Rutgers, Nebraska, and Maryland, (1%, 3%, and 4%, respectively)
- Finishes with at least 3 Big Ten losses. Head-to-Head doesn't matter.
OSU:
- Beat PSU
- Lose at least1/2 to Iowa and Illinois (20% and 0%--lol)
- Beat MSU
- Lose to Michigan (32%)
- Finishes with at least 2 Big Ten losses and loses any potential Head-to-Head with us.
UM:
- Beat Rutgers (95%)
- Beat Minnesota (87%)
- Beat Maryland (84%)
- Beat Wisconsin (35%)
- Beat OSU (W)
- Finishes with 2 Big Ten losses and wins possible Head-to-Head against OSU.
---------------------
So, let's multiply all that mess together.
The rough odds for Michigan to win the Big Ten:
0.00062%
His response:
October 27th, 2017 at 1:44 AM ^
October 27th, 2017 at 1:09 PM ^
October 27th, 2017 at 2:21 AM ^
Looking forward to see how Harbaugh and coaches can improve this young team over the next few games. May be we can pull an upset at WI or play a close game against OSU.
October 27th, 2017 at 2:23 AM ^
Totally agree, I just want to see noticeable improvement at this point, instead of regressing. I want to see one of the highest paid coaching staffs be worth their money.
October 27th, 2017 at 7:16 AM ^
October 27th, 2017 at 8:37 AM ^
Every time we buy tickets or make a donation to the AD.
October 27th, 2017 at 9:07 AM ^
know it is usually not directly the fault of the manager, but it is ridiculous the percentage of times that orders are screwed up at drive through window restaurants. I would venture an estimate that my order is wrong 30% of the time, regardless of what place I go to.
October 27th, 2017 at 5:19 PM ^
October 27th, 2017 at 2:21 AM ^
We don't need MSU to lose 4 times lol.
October 27th, 2017 at 2:28 AM ^
that's a mistake.
October 27th, 2017 at 2:44 AM ^
October 27th, 2017 at 2:32 AM ^
Lets Go Blue !!
October 27th, 2017 at 2:44 AM ^
The Punt had a 0.2% chance of happening
October 27th, 2017 at 2:35 AM ^
October 27th, 2017 at 2:42 AM ^
you did
October 27th, 2017 at 2:59 AM ^
Of course there is a mathematical chance, but that reallistically won't happen. Just get me to 2018 when this team will be loaded with seniors and juniors.
October 27th, 2017 at 3:05 AM ^
October 27th, 2017 at 4:49 AM ^
Forget it, Jake.
October 27th, 2017 at 5:52 AM ^
October 27th, 2017 at 6:08 AM ^
October 27th, 2017 at 6:54 AM ^
October 27th, 2017 at 8:52 AM ^
October 27th, 2017 at 8:59 AM ^
You are literally being too literal.
October 27th, 2017 at 7:32 AM ^
OSU losing to Michigan and Iowa
MSU losing to OSU and Northwestern
PSU losing to OSU and MSU
That puts all 4 at 2 losses , not sure how the tie breaker works for that...
October 27th, 2017 at 8:24 AM ^
October 27th, 2017 at 9:19 AM ^
Michigan has no shot in any tiebreaker involving Penn State.
Although, in that scenario, Ohio State wins the Big Ten East. Michigan and PSU both are 1-2 against the tied group, MSU and OSU are 2-1. UM/PSU are elminated and it goes back to head to head between MSU and OSU.
October 27th, 2017 at 7:51 AM ^
October 27th, 2017 at 8:41 AM ^
October 27th, 2017 at 10:09 AM ^
October 27th, 2017 at 9:08 AM ^
That gives me hope.....Kate Upton could leave JV for me!!!!!!!
October 27th, 2017 at 9:35 AM ^
October 27th, 2017 at 9:38 AM ^
October 27th, 2017 at 9:48 AM ^
loss tomorrow and things would actually start to feeling a little Hoke-ish, Circa 2014.
October 27th, 2017 at 9:46 AM ^
I came up with those probabilities in my head without math being involved. Actually these numbers ended up being encouraging.
October 27th, 2017 at 10:06 AM ^
We still have to play the games. And though I'm praying we beat osu through sheer emotion and determination (maybe a little luck), I've watched the previous 7 games. We are not B1G champion material this year. Next year is a different story. Crazier things have happened in college football but not likely.
GO BLUE!!
October 27th, 2017 at 10:29 AM ^
I love the stats and percentages but im setting my sights low and hoping for a 4 way tie.
October 27th, 2017 at 10:40 AM ^
don't lose to msu coming off a bye and we would still be involved.
October 27th, 2017 at 11:38 AM ^
October 27th, 2017 at 1:25 PM ^
this is pretty bad analysis.
For example, by your numbers there is only a 0.27% that PSU loses the necessary 3 games to fall behind us. But you have chosen only the most likely path to PSU going 2-3 in the last 5. In fact, there are many ways for PSU to go 2-3 in the last 5. There are also many (well, 5) ways for PSU to go 1-4 in the last 5. It is also possible for PSU to go 0-5 in their last 5.
Because you are undercounting by many, your projections are probably off by a factor of 3 or 4. As a quick example, I ran PSU through a million seasons using your win% numbers, and PSU finishes 2-3 or below on 0.81% of the simulations. That means PSU is actually 3x more likely than you think to lose 3 or more games.
Of course none of this matters, because 3*(very close to 0) = very close to 0.
Just thought I should mention it because it looks like you are trying to do a serious analysis, but your final result is actually way off.
The best way to do uncertainty analysis with many independent random variables is to do a Monte-Carlo type simulation. Instead of finding the *correct theoretical* answer. Just simulate the season N times and find out how often Michigan finishes in first place. The central limit theorem ensures that our approximate solution to that question given N simulations should be arbitrarily close to the *true theoretical* answer depending on our choice of large enough N.
October 27th, 2017 at 1:29 PM ^
October 27th, 2017 at 1:34 PM ^
I know that, but you must also know that your scenario is not the *only* path for Michigan to end up on top.
My example is only illustrative. I am pointing out that by not counting less likely scenarios, you are missing the total probability of a certain outcome by a significant margin.
So yeah, if PSU beats MSU it's a different equation, I agree. The thing is, you have to add all those pathways together to get the true number.
Anyway, you are of course right that the likelihood of a Michigan B1G championship is astronomically low. I just wanted to join the nerd party.
EDIT: Oh! I did miss the edit at the bottom. Does "joint probabilities" mean that you did add up the other pathways I am mentioning? Oops. Well done, then, and a fine day to you sir.
October 27th, 2017 at 1:38 PM ^
October 27th, 2017 at 1:47 PM ^
I'm not sure I am convinced you've handled it correctly, still. Because there are many games left, there are very few (if any) games that *need* to have a certain outcome. I haven't looked, but it seems like it should even be possible for Michigan to lose a game, and have everyone else lose 2-3 more, and have a massive tie for 6-3. Of course this scenario will be exceedingly rare, but I doubt that you've counted it in your outcomes.
You apparently have given this a fair amount of thought, so if there is a single game that *must* go a certain way, I would like to hear it. It just doesn't seem neccessary that you should "fix" any single game yet.
October 27th, 2017 at 2:20 PM ^
and Michigan automatically loses the head-to-head tie-breaker.
And no, I still didn't account for all the scenarios, it is true. I ignored scenarios like the following:
Penn State beats OSU and MSU, then loses to Rutgers, Nebraska, and Maryland.
- If Penn State beats OSU and MSU, then the odds of them losing any of the following games goes down even further from the already extremely low odds they are now.
- The odds of them losing all three of those with the current win probabilities is below the rounding error.
So no, I didn't do all of the scenarios, but I don't think it changes it by a significant factor.
October 27th, 2017 at 2:26 PM ^
of the cases. And to be clear, my original comment was based on the pre-edit numbers. After that, we were just nitpicking about whether you had convered 100% of the cases. It seems like there should be some sort of crazy way to get involved in a 3 way tie with, like, rutgers and OSU and win that tiebreaker based on head to head. But obviously, cases like this are barely moving the needle at all.
October 27th, 2017 at 2:46 PM ^
is the Michigan Difference.
October 27th, 2017 at 1:36 PM ^
October 27th, 2017 at 1:53 PM ^
October 28th, 2017 at 4:39 PM ^
check out response below
October 28th, 2017 at 4:37 PM ^
I wouldn't agree that OP's analysis is "pretty bad". It doesn't cover all the scenarios (as you note) but the prob's for those events are an order of magnitude smaller. OP is multiplying the prob's for some events that are not independent ... so the calculations would be off a little bit there. But I doubt the correct number is an order of magnitude different from what the OP has.
Now about your comments (repeated below):
"The best way to do uncertainty analysis with many independent random variables is to do a Monte-Carlo type simulation."
This is not uncertainty analysis ... it is about calculating the probability of an event. Monte Carlo is used to "estimate" such probabilities when the event of interest is complex But in this case, it is more complicated to set up the Monte Carlo and count the proportion of "successes" ... it is easier to compute the probability exactly.
"The central limit theorem ensures that our approximate solution to that question given N simulations should be arbitrarily close to the *true theoretical* answer depending on our choice of large enough N."
It is the "Law of Large Numbers" (LLN) ... not central limit theorm. The CLT tells you that the distribution, suitably normalized, goes to a normal distribution -- it is a more delicate results than the LLN and gives you standard errors around your estimate from Monte Carlo.