Let's get to know our upcoming opponent the Wisconsin Badgers!
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Note: the methodology for determining the total wins differential distribution has been updated below, after some further discussion with J. that can be found in the comments section. Have a look!
Week 4 Total Wins Update
“Break their hearts my pride and hope, break their hearts and have no mercy.”
- Miss Havisham, from Charles Dickens’ Great Expectations
Four weeks now into the season finds us ostensibly at the conclusion of non-conference play, with only one OOC game remaining to be played conference-wide. The statistical sample size has grown 100% since the last diary, and the quality of competition has arguably improved as well, which also spurs the accumulation of more statistics since fewer games are lapsing into garbage time midway through the second quarter. To that extent, the influx of fresh, objective statistics diminishes the influence of the more subjective preseason ratings. Suffice it to say, the ratings at this point are more meaningful than not...
The impetus of this diary is the desire to characterize the competitive landscape of the Big Ten Conference through the synthesis of total win probability distributions for each of the teams. The distributions are derived from the relative expected points ratings from Bill Connelly (S&P+), ESPN (FPI), and occasionally Ed Feng (The Power Rank). The key is that the ratings are mapped into expected points, which can be further translated into win probabilities. Each of these three ratings are generated from their respective advanced statistical analyses, metrics and secret sauces. In doing so, they achieve varied results ... some more pleasing than others depending on your point-of-view.
Anyway, here you will find further ruminations on said statistics into still more statistics as a means for enabling further discussion, jumping to conclusions, flying off of the handle or goading your rival. Also included in this round is another look at the all-important head-to-head win-differential probability distribution for the matchup between a select pair of contenders in the B1G East.
Schedules, Spreads & Win Probabilities
Having reached the conclusion of the non-conference segment of the season, it seems reasonable to make one last pass over the analyses of the overall schedules and sum things up before diving into the conference segment, more of which will be known next week after all teams have played at least one conference game.
B1G East Schedule Rundown
The table of schedules below shows the overall schedules for all seven teams in the B1G East based on the Bill Connelly’s S&P+ weekly ratings. The last table simply shows a rank-ordering of the B1GE teams based on their expected in-conference win totals, it’s not a projection of divisional standings based on projected wins, losses, and tie-breakers.
Still on the heels of its demolition of Boomer Sooner, the Buckeye's can now lay claim to being the only team in B1G East that is favored in all of its remaining games. Without playing a game this past week, OSU has overtaken U-M not only in the S&P+ ratings (in which U-M was #1 last week) but also in total expected wins, edging the Wolverines by less than 0.2 wins. The only game U-M is not a favorite in is in Columbus at the end of November. Both U-M and OSU expect to have nearly 11 wins. What had appeared to be potentially tough road games for OSU - at Wisconsin, Penn State & Michigan State - have now softened considerably into the double-digit/two-score margin realm. In light of Wisconsin’s demolition of MSU, the Spartans’ prospects for B1GE contention have dropped as precipitously as those of the Nittany Lions’. Together PSU & MSU can now be lumped with Indiana and Maryland into a second tier of teams vying for bowl-eligibility with expected totals between 6.2 and 6.7 wins. Of that group, as of now, PSU is an underdog in only two more games; Indiana, three; Michigan State, five; and Maryland, seven. Through the wonder of statistics however, Maryland is at the top of the tier in terms of expected wins, and conversely Penn State is at the bottom. Regardless, six of seven teams in the Big Ten East may well become bowl eligible. This would be something quite significant toward laying claim to the title of most powerful division in all the land.
Here is a link to a similar table of schedule win probabilities based on FPI Ratings.
The FPI results differ to some extent, most notably in that Michigan actually registers the highest expect win total of just under 10.8 wins, edging OSU by 0.2 wins. FPI results show both U-M and OSU with greater than 10 expected wins. As with S&P+, FPI results also show OSU to be favored in all of its remaining games; U-M is an underdog in the one game. The second tier of bowl-contenders in the FPI rundown has three teams: PSU, MSU and Maryland. PSU is an underdog in only two more games; MSU, three; and Maryland, six. Maryland however, leads in expected total with just under 6.6 wins, with PSU and MSU trailing within 0.3 wins of Maryland. Indiana drops off another 1.3 wins and not likely to have a winning season per FPI.
B1G East Expected Overall Wins
The bar plots below show the expected total overall wins distributions for teams in the B1G East, in alphabetical order. Noted above each bar is the probability for that number of wins (you may need to click & embiggen to read it). The bar with the highest value is the most likely outcome (the mode). Also marked on each plot is the expected overall win total (the mean). The last line plot is just an overlay of the same data from the other seven bar plots.
What these new distributions show is that Michigan and Ohio State are tied for the highest modes with 11 wins, with OSU tilting slightly to 12 wins, and Michigan toward 10 wins. The next highest modes are Indiana and Maryland’s 7 wins, followed by PSU and MSU with 6 win modes. Thus far, U-M and OSU are the most significant contenders to win the division by a wide margin. OSU now has the edge for the best chance of having an undefeated season at 27.0% (up from the 2.0% before beating the Sooners) or about 3:1 odds, followed by Michigan with an 18.3% likelihood (9:2 odds). At this point, the overlaid S&P+ distributions have clearly coalesced into the Big Two, the Middle Four, and the Black Sheep... er… Knights.
Here is a link to a similar plot of conference win distributions based on FPI ratings.
The FPI results, contrary to past tendencies, now favor Michigan to slight extent as mentioned above, but not enough to separate modes. Both teams register a mode of 11 wins with both teams tilting to the lower side, with 20.6% chance to win out for Michigan, and 18.3% for Ohio State. From there, a clear separation of 4 wins exists to the next closest contenders, Penn State and Maryland, with modes of 7 wins. MSU claims the fourth place mode of 6 wins.
B1G West Schedule Rundown
The next table of schedules shows the overall schedules for the B1G West based on the Bill Connelly’s S&P+ weekly ratings. Again, the last table simply shows a rank-ordering of the B1GW teams based on their expected win totals - it’s not a projection of divisional conference standings per se.
The results of the S&P+ analyses has the contenders in the B1GW, in order of overall expected wins, being Wisconsin, Nebraska, Minnesota and Iowa. Notwithstanding Iowa’s OOC loss, all four are tightly grouped, within 0.5 wins of each other with less that 0.1 wins separating Wisconsin from Nebraska. No team is favored in all of its remaining games, nor is any team is expected to have a double-digit win total. Nebraska and Wisconsin are underdogs in 2 games apiece, whereas Minnesota and Iowa are underdogs in 3 games, with Nebraska and Iowa a 50/50 pick’em matchup. Iowa is also a 50/50 matchup with Penn State.
Northwestern thus far has managed to re-establish itself as a doormat for the B1GW. Now favored in only 2 remaining games, the Wildcats hopes of a bowl-bid have evaporated, its prospects having dropped to levels not seen since the early 80’s. OK, maybe it’s not that bad - there’s still Illinois and Purdue, whom the Cats are favored to beat. At this point though, Illinois is expected to win more games than Northwestern, but is also favored in only two. Meanwhile, Purdue is favored in none of its games for the remainder of the year, yet through the wonder of statistics is expected to win more games than either Northwestern or Illinois.
Here is a link to a similar table of schedule win probabilities based on FPI ratings.
FPI also expects the same four teams to have winning records. In order of expected wins, they are now Nebraska, Wisconsin, Iowa and Minnesota. Nebraska is the leader per FPI, showing a nearly 0.6 win edge over The Badgers. Iowa is another 1.0 wins back. The Gophers are another 0.8 wins behind the Hawkeyes. No team is favored in all of its games or even expected to have a double-digit win total. Iowa, however, is an underdog in the fewest remaining games: one. Nebraska and Wisconsin are both three-game dogs; and Minnesota, a five-game dog.
The bottom line remains that the B1GW race will be very competitive. The consensus at this point is that Nebraska, Iowa and Wisconsin are all evenly matched teams within about 0.3 games of each other, with Minnesota lurking in its Gopher hole poised to trip up anyone looking past them.
B1G West Expected Overall Wins
The bar plots below show the expected overall win distributions for the B1G West teams, in alphabetical order.
The story here is how virtually indistinguishable the distributions of Nebraska and Wisconsin are, both with a mode of 9 wins. Minnesota follows closely behind with a mode of 8 wins, and Iowa with a 7 win mode. It appears highly unlikely that any team will have an undefeated season. Wisconsin has the best chance of a one-loss season at 6.4%, followed by Nebraska at 6.1% and Minnesota at 4.8%.
Here is a link to a similar plot of conference win distributions based on FPI ratings.
The FPI results tell a similar story, but with a modest amount of separation between Nebraska, Wisconsin. Both have the same mode of 9 wins, with the Huskers distribution leaning toward 10 wins, and the Badgers leaning toward 8. Iowa - with its OOC loss - is discounted 1 win, but in terms of the B1GW race the Hawkeyes are right there with Wisconsin. Minnesota lags the other three with a mode of 7 wins. The other three do not have promising post-season prospects. With modes ranging from 3 to 5 wins for the group, it’s Purdue that has the best chance of a post-season bid (20%).
Total Wins Differential
It goes without saying that when it comes to Michigan vs. Ohio State, every cotton-pickin’ percentage point counts in the hearts and minds of the MGoBlogosphere. So this next bit of analysis delves further into the statistics by calculating a win-differential distribution from the distributions of both teams. As a quick primer without getting into any equations: when considering the difference between two independent random distributions (meaning the distribution of all games that are not head-to-head), the variance of the difference is simply the sum of the two individual variances (squares of the standard deviations). In a similar sense, the mean of the wins-differential is simply the difference between the expected wins of the two teams. From there, the devil is in the details of apportionment of the resulting distribution according to the probabilities of the head-to-head matchup.
Michigan vs. Ohio State
The win-differential distribution simply shows the likelihood of a team (Michigan) finishing with a conference record that is however many games better or worse than another team (Ohio State). Keeping in mind that in the event of a tie, the winner of the head-to-head match up determines the tiebreaker, the probability of a tie in conference records (i.e. a win differential of zero), as well as the the probabilities of either team having a one-game lead going into the head-to-head (i.e. win differentials of +1 and -1), are then pro-rated in proportion to the win probability of the head-to-head game. So then the total likelihood of Michigan finishing ahead of Ohio State is the sum of all the maize-and-blue shaded bars (i.e. U-M wins however many more games that OSU), plus a proportional split of the -1, 0 and +1-differential bars. It’s worth noting that this total likelihood does not indicate the likelihood of making it to the B1G Championship, as it says nothing about how other teams in the B1G East do, or even how Michigan or Ohio State do in the absolute sense. For example, if both teams were to finish tied in the B1G at 6-3, which means that UM and OSU would be losing 3 games each, other teams are clearly winning those games - and so another team may well be the B1GE representative in Indy. Sort of common sense, but yea.
So, beginning with the results of the S&P+ analysis, the chart below shows that the most likely outcome (37.7% likelihood) is that U-M will finish in a tie with OSU heading into Columbus. Thus, as in days of yore, The Game would decide who plays for the B1G Championship. Looking at the tie-breaker scenario, OSU is favored (mostly due to home-field advantage) with a win probability of 62.2%, so it collects 23.4 points of the 37.7 points for the likelihood of winning coming in tied (finishing ahead one game). U-M collects the remaining 14.3 points.
The second most likely scenario, with a 24.8% likelihood, is that UM comes into Columbus one game ahead of OSU. Of this, OSU collects another 15.4 point share for the likelihood of winning coming in behind by one game (thus finishing in a tie, but OSU winning the tie-breaker).
The next most likely scenario, with a 21.4% likelihood, is that UM comes into Columbus trailing by one game. Of this, UM collects an 8.1 point share for its likelihood of winning (thus finishing in a tie, but UM winning the tie-breaker).
The other outcomes are relatively straightforward in that either team would have already clinched finishing the season ahead of the other team.
Continuing on, here is the same chart based on the FPI ratings following the week 4 results. These results show a much tighter race to the B1GCG between U-M and OSU, with the most likely outcome also being that the teams head into Columbus with the same record. In the head-to-head matchup, OSU’s home field advantage gives them a 56.2% likelihood to win the game. However, the distribution of potential outcomes shows that the race is a statistical dead heat despite the head-to-head advantage for the Buckeyes.
So there you have it. The Big Ten East is as competitive as ever, and Michigan football is poised once again to make a serious run at a Big Ten Championship for the first time since well, last year. The difference of course, is that in comparing last season to the current one, these numbers were not nearly so promising, as many were skeptical of Michigan achieving even 8 wins. Now it's the competition that will be looking to elevate its game to meet Michigan's, and in that way, things are right in world.
Yours in football, and Go Blue!
Interview with Wisconsin head coach Paul Chryst madison.com, 26 September:
Adding links as I go along, feel free to upload these to YouTube and embed them.
Wisconsin O vs. MSU D- https://db.tt/9TWb95JR
[More later, I'll bump the post as I add links]
So my LSA91 wife and I went to our first Big House game in a few years, and saw many things that impressed our creaky minds. Some were pretty self-explanatory and fun, like walking in behind the band, seeing a full student section (through the third quarter anyway), or watching the team demolish an opponent.
I'd love some more background on a few of the others - where they came from, etc. I tried googling, but I'm old. Can someone point me to a good page discussing or explain:
1) The third down chop/wiggle/"you suck" call. (Yes, self explanatory, but where did it come from and when.)
2) The student dance. (Same thing).
3) About 10% of the girls walking to the game were just about half-way to a halloween costume - typically knee socks and a night shirt or short shorts, but there were some cheer costumes, shiny skirts, etc. Is that a thing every game, and is it in college sports generally or just AA?
Just stumbled across this on the Twitter. Some really great ones in here.