Quick note: For those unfamiliar with the FSI, it is a weekly survey asking fans to rate their feelings about each game and the season so far on a 0-100 scale. To catch up check out my blog here: http://mgoblog.com/diaries/onefootin
Who has it better than us? Well, according to my calculations, more than half of the Big Ten has it better right now. And I’m going to bet you won’t like who’s on top.
Let’s take this in two parts.
The Outback Bowl
First, there was that bowl game. As Figure 1 makes clear, this game felt bad. In fact, at a satisfaction level of 17.6 on our 0-100 scale, it felt worse than every regular season game except the Michigan State game.
This isn’t too surprising. It was bad enough to lose when favored by 7 points against an uninspired-looking South Carolina team that had just fired its offensive coordinator. It got worse when Michigan, leading 19-3, managed to fumble at the 5. It bottomed out when it turned out that was just the beginning of the second half Errorpalooza. Watching Michigan self-immolate while the Gamecocks scored 23 unanswered points was deeply aggravating, to put it mildly.
Figure 1: Outback Bowl Game Satisfaction.
(On a scale of 0 to 100, where 0 is the worst you ever felt after a game and 100 is the best you ever felt after a game, where would you rate your feelings about the Outback Bowl?)
X-axis is game satisfaction and Y-axis is # of respondents
Adding insult to injury, the loss to the Cocks took most of the remaining mojo from the fan base regarding the season as a whole. Season satisfaction clocked in at 24.9 – its lowest point of the season. 8-5 doesn’t feel good, as it turns out.
Figure 2: Season Satisfaction after the Outback Bowl.
(On a scale of 0 to 100, where 0 means the season went horribly and 100 means the season went perfectly, how do you feel Michigan's season went?)
X-axis is season satisfaction and Y-axis is # of respondents
Calculating B1G Fans’ Season Satisfaction
Okay, now for part two. Michigan’s season was unsatisfying but perhaps – out of a morbid sense of curiosity – you are wondering how Michigan fan satisfaction stacks up against other fan bases around the league.
Modeling Satisfaction from Our Data
Since I did not survey non-Michigan fans directly I used a regression analysis of our Michigan fan data to come up with a formula for calculating satisfaction for other fan bases. This approach comes with clear limitations. First, since we only have one season of Michigan data we don’t even have a perfect model of how Michigan fans will react to all situations. Just to take a couple of examples, we have no data on how fans respond to an unexpected victory over a ranked opponent, nor any idea how season satisfaction would look during a season where Michigan outperformed overall expectations. For that reason, our regression model is certainly far from perfect.
Second, even if our model were perfect for Michigan fans, it is very likely that other fan bases would react somewhat differently to the same situations. Given historical circumstances (spoiler alert!), Purdue’s fan base is likely to be happier with a 7-6 record on the season than Michigan’s is with 8-5. And though all teams have rivalries, we probably shouldn’t assume that all fans feel the same about them. I am pretty convinced, for example, that Sparty and Buckeye fans get more satisfaction from beating Michigan than the other way around.
With these caveats in mind, I still think we can provide a pretty reasonable estimate of B1G fan base satisfaction based on how Michigan fans responded during the season. For Michigan fans, based on 2605 responses over 13 games, the basic equation for game satisfaction is: 49.63 + (1.03 x Margin of Victory/Defeat) + (0.28 x Margin vs. Vegas) – (20.8 x Surprise Loss).
Margin of Victory/Defeat, clearly, is just measured by how many points more/less Michigan scored than its opponent. This captures both whether a game is a victory or defeat as well as its intensity. Margin vs. Vegas is how many points more/less Michigan scored than its opponent relative to the Vegas line. This captures general fan expectations about how the game went, which as we have discussed in past weeks is a critical component of how people feel about the outcome of a game. Surprise Loss is a variable I threw in because it was clear that unexpected losses – i.e. where Michigan was favored to win by Vegas – hurt more than usual.
In English, the model assumes satisfaction is about 50 points on our 100-point scale and then slides things up or down based on whether Michigan won or lost, by how much, and by how much relative to expectations. An additional point of margin in a victory adds about one point to fan satisfaction (vice versa for a loss). For every touchdown by which Michigan beats the Vegas spread you can add another 2 points of satisfaction, while a surprise loss sucks about 21 points of satisfaction from the average fan.
According to the magic of statistics this formula explains 70% of the variation in individual game satisfaction ratings. In the land of predicting individual opinions, 70% is pretty darn good, especially since all we have is data about the games and we don’t have any information on the respondents (Imagine, for example, trying to predict presidential popularity from economic conditions but without any information on respondents’ political affiliations).
Table 1 below illustrates how well the formula does predicting the typical fan’s satisfaction compared to the average satisfaction measured by the survey for each game. Though the predicted satisfaction misses big in a couple cases, overall it tends to come pretty close, with an average absolute difference of less than six points across all 13 games. After a few more seasons worth of data the predictions should get better.
Table One. Real vs. Predicted Michigan Fan Game Satisfaction
|Game||Actual Sat||Predicted Sat||Actual - Predicted|
The formula for season satisfaction is pretty similar. If you’ve been reading the diary this season you know that the average fan’s sense of the season is heavily tied to the game they just watched. As a result, assessments of the season varied a lot more on a weekly basis than they probably should have based strictly on the amount of new data coming in each week. The other significant variable in the season satisfaction formula, unsurprisingly, is the number of cumulative losses. Nothing says satisfaction like winning; nothing destroys it more than losing.
As a result, our season satisfaction formula after the 2017-18 season looks like this: 29.84 + (.62 x Game Satisfaction) – (3.388 x # Cumulative Losses). This model explains 73% of the variation in individual season satisfaction assessments over the 13 games of the season. Again, not too shabby. Table Two provides the summary.
Table 2 Real vs. Predicted Michigan Fan Season Satisfaction
|Game||Actual Sat||Predicted Sat||Actual - Predicted|
Who Has It Better Than Us? Season Satisfaction across the Big Ten
If you’re still with me, Table 3 brings home the sad fact: Michigan’s implosion in the Outback Bowl, combined with its five losses on the season, put Michigan fan satisfaction below all seven B1G teams that won their bowl games and even below Indiana, which lost to its rival Purdue to end its season.
Table 3 End of Season Fan Satisfaction in the B1G
|Team||Season Sat||Record (Ranking)||Final Game (Game Sat)|
|MSU||70.2||10-3 (15)||Beat #18 WSU 45-17 (81.5)|
|OSU||65.9||12-2 (5)||Beat #8 USC 24-7 (69.1)|
|Wisconsin||63||13-1 (7)||Beat #10 Miami 34-24 (61)|
|PSU||59||11-2 (8)||Beat #11 UW 35-28 (58)|
|Purdue||56.1||7-6||Beat Arizona 38-35 (75.2)|
|Northwestern||50.1||10-3||Beat Kentucky 24-23 (49.1)|
|Iowa||49||8-5||Beat Boston College 27-20 (58)|
|Indiana||31.4||5-7||Lost to Purdue 31-24 (40.7)|
|Michigan||24.9||8-5||Lost to South Carolina 24-17 (17.6)|
|Minnesota||14.9||5-7||Lost to Wisconsin 31-0 (14.2)|
|Rutgers||9.5||4-8||Lost to MSU 40-7 (10.9)|
|Nebraska||2.74||4-8||Lost to Iowa 56-14 (0)|
|Maryland||2.74||4-8||Lost to Penn State 66-3 (0)|
|Illinois||1.2||2-10||Lost to Northwestern 42-7 (8.4)|
There is plenty to quibble with about these satisfaction predictions. Looking at the final game satisfaction figures, for example, it seems to my eye that they are probably too low for teams that won a bowl game. For most fans, winning a bowl game is likely more satisfying than winning a regular season game for any given margin of victory and performance against the Vegas spread. And in particular I think the model clearly undervalues the impact of beating a highly ranked opponent in a bowl game, even in these cases where the B1G team was favored. As a result of this, those teams’ final season satisfaction ratings should probably be higher than they are predicted here.
The reason the model misses on this is simple: so far we have no Michigan bowl victories and zero victories over ranked opponents in our satisfaction database. Until we do we’re stuck guessing at how much those things affect the predictions. Likewise, since we only have one season’s worth of data we can’t model the effects of teams significantly outperforming (or underperforming) season expectations. Going 7-6 is worse than 8-5, but Boilermaker fans are looking at their 7 wins through a very different lens than Michigan fans are viewing 8 wins. Similarly, OSU is close to the top, but how satisfied can the Bucks really be at this point with a two-loss season? And what about Wisconsin? Was that a great season or was that like winning a silver medal and wishing you’d won the damn gold?
Looking at the results from 30,000 feet, however, they make sense. Thanks to the fact that game satisfaction is a big driver of how fans rate the season, the seven teams that won their bowl games generated higher season satisfaction scores than Michigan. It’s important to remember here that this is an analysis of fan satisfaction – the fact that the satisfaction rankings don’t mirror objective measures of season quality (i.e. win/loss records) is pretty much the whole point. Fans are emotional, irrational, and short-term thinking animals. We have the S&P to tell us how good teams are. We have the satisfaction index to have fans tell us how they feel about the teams.
For our grand finale, in case you want to compare Michigan’s roller coaster of satisfaction with others on a week-by-week basis, I leave you with the season trends for each of the B1G teams.
Michigan State (10-3)
Ohio State (12-2)
Penn State (11-2)