Adv. Stats Win Probabilities Rehash, Week 11 Results

Submitted by Ecky Pting on

So, here’s the latest Total Wins Probabilities for U-M, Sparty, OSU and PSU too (since they do have a slim chance to advance), updated with the Week 11 results. You may have already seen Drew Hallett’s post on Maize’N’Brew, which pretty much stole the thunder here. It just goes to show that once all the crazier scenarios get eliminated, things simplify a great deal. Hallett compared numbers between S&P+ and Massey, making some reference to a log5 analysis that was “invented” by Bill James, but really uses a formula found in any introductory Stats text that covers Poisson binomial distributions. Whatever – as long as Bill James isn’t submitting a doctoral thesis or filing a patent, it’s inconsequential. Getting down from the soapbox and on with the Diary, it’s now necessary to at least differentiate a bit here. Since I’ve been charting FPI statistics in the other Fancy-Stats Schedule Rundown Diary, I’ll show both S&P+ and FPI-based Total Wins probability distributions in the embiggable charts below:

B1GE Football Total Wins PDF, 2015 wk. 11

B1GE Football Total Wins PDF, FPI-based 2015 wk. 11

The S&P+ and FPI win probabilities for each team's remaining games that inform the charts above are shown in the table below, along with the wins expectation values:

Michigan
Michigan State
Ohio State
Penn State
Opp
S&P+
FPI
Opp
S&P+
FPI
Opp
S&P+
FPI
Opp
S&P+
FPI
@PSU
66%
63.0%
@OSU
20%
20.9%
MSU
80%
79.1%
U-M
34%
37.0%
OSU
55%
37.9%
PSU
60%
76.4%
@U-M
45%
62.1%
@MSU
40%
23.6%
Wins:
9.2
9.0
 
9.8
10.0
 
11.3
11.4
 
7.7
7.6

Mr. Obvious: “Penn State? Really?!”

Mr. Smarty-pants: “Does the Pope wear Gucci slippers?"

Here are a few things to take away from the charts:

  • Using S&P+, U-M remains the most likely to win out by the slimmest of margins (now 36.3% compared to 37.0% last week), followed by OSU (36.0% vs. 20.5% last week) and then PSU at 13.6%. Sparty is the least likely to win out at 12.0%, up from 10.1% last week.
  • Using FPI, OSU is the most likely to win out at a whopping 49.1%, followed by U-M at 23.9%, MSU at 16.0%, and PSU at 8.7%.
  • Using both S&P+ and FPI, U-M’s and Sparty’s, two most expected totals are 9 and 10 wins. OSU’s are 11 and 12 wins; and PSU, 7 and 8 wins.
  • Using S&P+, the most expected result for all four teams is one more loss.
  • Using FPI, the most expected result for OSU is to win out; for U-M and MSU, one more loss; and for PSU, to lose out.

As you know by now if you've read this Diary before, given all of this win probability data, it's possible to investigate how things might play out for the remainder of the season, or rather, how likely it is that a particular sequence of events would actually transpire. The primary question revolves around what are U-M's chances of making it to Indy for the B1G Championship Game? With only two games remaining, the possible scenarios for any team to advance have been reduced to a mere half dozen. These are described in the table below, with the attendant likelihood, and who the B1GE representative would be. The pathways by which U-M, MSU or PSU can advance have essentially coalesced into a single sequence of events for each. OSU, sitting in the proverbial catbird seat, has 3 potential scenarios by which it might advance:

Scenario
S&P+

Probability
FPI

Probability
B1GE

Champ
UM wins out

& MSU loses ≥ 1
31.9%
20.1%
U-M
 
MSU wins out
12.0%
16.0%
MSU
 
MSU loses 1 to PSU
& UM loses 1 to PSU
1.5%
0.7%
PSU
 
OSU wins out
36.0%
49.1%
OSU
OSU loses 1 to UM

& UM loses to PSU
15.0%
11.1%
OSU
OSU loses 1 to MSU

& MSU loses to PSU
3.6%
3.1%
OSU
OSU Total:
54.6%
63.3%
 

So, the thing that jumps out from these lists now is that the single most likely S&P+ and FPI scenarios are the ones by which OSU advances, which is a change from last week. Per S&P+, the likelihood of OSU advancing is 54.6% (or about 4:5), and 63.3% (about 4:7) as per FPI. U-M is still hanging in there with S&P+ with a 31.9% or about 2:1 chance, but with FPI, it’s a 4:1 shot at 20.1%. MSU is about 7:1 for S&P+ and 5:1 with FPI. PSU, needing both to win out and have OSU to lose out, is at 66:1 per S&P+, to 140:1 per FPI.

MP&THG Black Knight Hopping

So just to get a complete picture of how all of these probabilities (and those for the rest of the B1G) impact the projected end-of-season conference standings and prospects for U-M to win a B1G Championship, here you go, first with the standings resulting from the S&P+ predictions:

B1G East
B1G
Overall
W
L
W
L
Michigan*
7
1
10
2
Ohio State
7
1
11
1
Michigan State
6
2
10
2
Penn State
4
4
7
5
Maryland
2
6
4
8
Rutgers*
1
7
4
8
Indiana
1
7
5
7

* - winner of tie-breaker

B1G West
B1G
Overall
W
L
W
L
Iowa
8
0
12
0
Wisconsin
7
1
10
2
Northwestern
4
4
8
4
Illinois *
3
5
6
6
Nebraska
3
5
5
7
Minnesota
2
6
5
7
Purdue
1
7
2
10

Note that these standings incorporate the individual game win probabilities, which does not coincide with the most likely scenario described above, for the principal reason being that U-M is expected to win both its remaining games, yet in total, would be expected to lose one.

And now, here are the standings resulting from the FPI predictions.  These standings, despite using individual game win probabilities, still happen to coincide with the most likely scenario playing out:

B1G East
B1G
Overall
W
L
W
L
Ohio State
8
0
12
0
Michigan State *
6
2
10
2
Michigan
6
2
9
3
Penn State
4
4
7
5
Maryland
2
6
4
8
Rutgers
1
7
4
8
Indiana
0
8
4
8

* - winner of tie-breaker

B1G West
B1G
Overall
W
L
W
L
Iowa
8
0
12
0
Wisconsin
7
1
10
2
Northwestern
5
3
9
3
Nebraska
3
5
5
7
Minnesota **
2
6
5
7
Illinois *
2
6
5
7
Purdue
2
6
3
9

Yours in football – Go Blue!

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