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Minnesota Football: The Goldy Ratio - Ohio State

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A higher level mathematical and inferential review of certain topics that arose from snowy battle between Minnesota and Ohio State.

Jesse Johnson-USA TODAY Sports

Hey, remember when I did Charts & Chalk? Those were the days.

Game Theory'n

Many folks have questions/thoughts/#TAKES on Jerry Kill's decision to kick a field goal down ten points from the 17 yard line. The general commentary from the dissenters goes like this: you have the field position, so why not go for the more difficult of the two scores?

Here's my rebuttal. Winning percentage calculators like the one at Advanced Football Analytics have one fatal flaw in accounting for situations like this (other than the standard caveats that the NFL and CFB are not exactly the same game), which is Kill was not going for the win but a chance to tie at home. That scenario has a different distribution and associated probability than trying to win outright. Fundamentally the Gophers needed two scores, and the order of which those scores occurred is not particularly relevant. What is relevant and of far greater importance in late game scenarios is time, which is much more valuable than yardage given the situation (no timeouts, can stop the clock on first downs/spikes).

Rather than get into a discussion regarding the proper distribution of scores in end of game situations (I think it should be Poisson or discrete count vs. binomial) and the associated "expected points," we can spitball this by looking at a few scenarios. Recovering an onside kick when the opponent is expecting one happens only a fifth of the time, so the second score will be inherently more difficult and less likely than the first. Assuming an onside recovery at one's own 45, the "expected" point value doesn't change depending on the time available. That implies time isn't as important as spot, correct?

No, because the "expected" point value is not a function of time but of spot, yet moving into scoring position by advancing spot is a function of time. People understand the college clock rules by now, so having the option to not only stop the clock by getting out of bounds but spiking after a first down provides not only more opportunities to score a touchdown but also advance closer to the goal, making those scores more likely -- even marginally. In situations where you need a touchdown to tie, both of those developments are preferred over hitting a maximum of two first down yardage plays to set up a long field goal try with rapidly decreasing success rates. In crappy weather conditions, no less.

An adjacent but different argument is Minnesota wasted two downs that could have been used to advance the ball and get into better position for the more difficult 7 of the needed 10. This is a fair point, though much of what I outlined above still applies: you need two scores, and if you have one in the pocket, why not give yourself a chance with as much time possible for that more difficult score considering the amount of potential plays given the time remaining would still allow for a Hail Mary if it came to that?

Weather Advantage

Good question, Orson.

Urban Meyer has some opinions on the matter, interleaved with real politiking:

"This is a tough environment – it’s the first time I’ve ever been here… I don’t want to see this on the schedule for a while, certainly not again in November. ... I’d like to see any team in the country come up here and do this. Play here in November, against a very good team… Have at it."

A few weeks ago in M&B I suggested that a TCF Bank Stadium home field advantage (HFA) probably isn't a static 3 points, as is the rule of thumb for gamblers. I hypothesized that temperature, wind speed and other conditions may contribute a different advantage to Minnesota in say, November, than it would earlier in the season.

The impetus for my theory? Minnesota was 5-3 against the spread in November (now 7-3) at The Bank, including 2 straight up victories as a double digit underdog. Seven of the November games hit the under. Want even more scenarios? The Gophers are 6-2 ATS when then kickoff temperature at home is 40 degrees or less, and 4-2 ATS against FBS teams in night games played at The Bank.

Last week I built an inferential model using all FBS games played at TCF Bank Stadium, modeling margin of victory against the opponent and Minnesota's F/+ ratings, kickoff temperature, wind speed and several indicators such as night and rivalry games. After yet another game in November that hit the under and the Gophers won ATS, I decided it was time to present some findings.

A few things to keep in mind. #1, the sample size is small (36 games) and I'd like to see this data set after 50 games. #2, this is not a predictive model. I'm using ordinary least squares multiple linear regression to infer a linear relationship between margin of victory and the covariates, and how each of the covariates impact MOV while controlling for everything else.

Still, there is an interesting relationship between MOV and the game conditions at The Bank, which I simulated in the series of charts below by applying the model to a set of randomized temperature data. The x-axis plots temperature in degrees Fahrenheit, while the Y-axis represents the predicted MOV. For the first series of charts, I've held the wind speed constant while adjusting the opponent's F/+ rating.

TempPlot_OppFPlus_0

TempPlot_OppFPlus_Minus152

In each of the plots, you see the regression line at various levels of Minnesota F/+ ratings along with their 95% confidence interval bands. Note that the bands are wide, which is helpful to visualize from an inferential perspective (MOV doesn't vary exclusively on the set of attributes I've provided, after all) but not all that helpful for prediction.

You can see a few notable things from the charts. #1, that predicted MOV increases as the temperature gets colder. #2, the intercepts against weaker opponents (2nd chart) are almost double that of a foe with an F/+ rating of 0.

TempPlot_Rivalry

Now let's add the rivalry game factor into play, using constant wind speeds against but setting the rival's F/+ rating to 10. Notice how this plot looks nearly identical to the first despite a much tougher opponent. This reflects the data suggesting Minnesota plays better against rivals at home than non-rivals. Also note that the spread between regression lines is compact and relatively unchanged from the previous two plots.

TempPlot_Wind

Let's hold Minnesota and the opponent's F/+ rating constant, and vary the wind speed instead. The spread between the regression lines is wider than previous plots.

TempPlot_Night

Finally, the impact of comparing night games to non-night games at TCF Bank Stadium holding wind and F/+ ratings constant.

The purpose of this exercise is not make an predictive claims: incorporating this type of information into a forecasting model would require much more effort and data collection, plus some thoughtful consideration about it should be applied (correlation does not equal causation). It does, however, visualize how different environmental and conditional factors are related to game outcomes and the varying impacts of these randomized factors controlling for everything else.

Ultimately, we're trying to infer if something is real. I believe there's sufficient evidence to support the claim of a cold weather HFA at TCF Bank Stadium, which should lead to interesting discussions about variable HFA at other stadiums as well (similar to Park Factors in sabermetrics).