Sports

Separating the Fans from the Stadium: Stadium Size, Attendance, and Home-Record in College Football
Today we’re looking at the interwoven relationships between stadium-size and attendance and a team’s performance at home and away. We’ll look at how this relationship changed in 2020 when fans were not able to attend most games.

We’re going to try to separate the attendance from the venue size to see if having a packed house makes a difference, regardless of a team’s overall strength.

First, a few primers to understand the data we’re dealing with.

Let’s look at the distribution of venue sizes in college football.

Distribution of venue sizes in College Football. The most common stadium-size is 30,000 seats.

The most popular stadium size appears to be right around 30,000 seats. I’m not sure if this is a rounding thing, or if it just a nice number that a lot of teams settled on. Either way, there are a handful of college football cathedrals, with 90,000+ capacity, but most are under 60,000.

And, believe it or not, the size of your stadium matters. There is indeed a relationship between stadium size and the performance of your team at home, although this can almost certainly be chalked up to the best, most-historic teams in college football growing their stadium size over time to accommodate the demands of their fans. And whether that drives good recruits and good results, or vice-versa, the best teams typically play in the largest stadiums (in the past 20 years).

Boxplot of stadium capacity and home winning percentage. There is a slight positive relationship, and as stadium capacity increases, the uncertainty of results is narrower and teams tend to have a winning season at home.

As you can see, there is a slight positive relationship, and as stadium capacity increases, the uncertainty of results is narrower and teams tend to have a winning season at home. However, actual attendance at these games appears to be a more important factor.

Boxplot of average home attendance and home winning percentage. There is a large uptick in winning percentage when you gather at least a handful of fans.

Now we have to take this with a grain of salt, because attendance data can be murky. Some games have no attendance data at all. Others may be way off. It’s impossible to be certain, but there’s at least some positive trend between fans showing up to your games and playing well at home. This shouldn’t come as much of a surprise, although it is surprising that the difference between 50,000 fans and 100,000 seems negligible, indicating that the home field advantage of some of the largest brands in college football might not be all it’s cracked up to be. Of course, the biggest teams are also probably playing some pretty tough opponents in those mega stadiums.

Boxplot with average percent of stadium capacity filled for each team rounded to the nearest tenth, and home winning percentage on the y axis. There is, again, a positive relationship. Average attendances below 50% or above 100% were filtered out for low sample size.

When we put all of these relationships—stadium capacity, raw attendance, and percent of the stadium filled—side by side, we see that they all have a pretty similar relationship to one another and a pretty similar relationship to wins.

Side-by-side scatterplots of capacity, attendance, and percent of total capacity on the x-axis vs. home winning percentage on the y-axis. All have similar positive linear relationships.

Empty Stadiums

Let’s quickly take a look at how this changed in 2020. We saw previously that there is some relationship between stadium size and home record, but most of that is likely attributable to the people inside that big stadium, not just the stadium itself. In 2020, look at how that advantage disappeared as those intimidating and loud fans became smiling cardboard cutouts.

Multiple scatterplots of stadium capacity and home winning percentage, grouped by season from 2000 – 2020. In 2020, the relationship between these two variables went from slightly positive to almost 0.

In almost every season since 2000, the correlation between stadium size and home record was between .2 and .4 and once as high as .41. In 2020, it dropped to historical lows of just 0.08, or almost no relationship between how big a stadium a team was in and how well they played at home. The factor that changed here, of course, was the fans, not the stadiums. And this data includes even the teams that allowed fans for some or all of 2020, so the correlation could have been even worse than this.

So from this plot alone we can see that fans matter a lot more than the stadium size.

So next, let’s try to tease out how much each of these factors matters in the grand scheme of winning football games at home.

Controlling For Team Strength

In order to accurately access the importance of stadium capacity and fan attendance, I need to control for something important: overall team strength. And by control, we really just mean including it as a factor in our regression model. Because without it, the model might confuse stadium size with being more important than it is, simply because it doesn’t know that better teams tend to have bigger stadiums to begin with. By adding in a variable that indicates how good a team is, we can look at similarly-ranked teams and see if their stadium-size has an impact on their performance, given that their overall team strengths are similar.

To do this, I’m choosing to use a team’s away record as a proxy for overall team performance. I could use Elo ratings, or even AP Poll rankings, but I feel like away performances are fair because you have no home-field advantage and it’s just up to your team to perform. This assumes that the quality of away opponents is fairly evenly distributed among teams of different stadium sizes. This may not always be the case, but the majority of the season (3/4 of it) are reserved for in-conference matchups, which are the better games, and non-conference games, if they are easy opponents, are usually reserved for early-season home games (or that week where Alabama takes a week off in November to beat Grambling State by 80).

Just to confirm, how teams play at home and away are related, and this relationship is fairly strong.

Correlation between home winning percentage and away winning percentage, represented as boxplots for each 10% winning percentage. There is a fairly strong positive relationship between the two, with teams that win 90% or more of home games rarely losing more than 25% of their away matchups.

What Drives Home Game Attendance?

An interesting finding of my data exploration was that home attendance actually correlates more to away performances than home performances. The reasoning behind this might be that fans watch their teams play well on the road, and then get a desire to go see them in person when they’re home. If they watch their team on TV and they stink, they’ll be less motivated to go buy a ticket to see that trainwreck in person.

Home and Away winning percentages plotted against average percent of stadium capacity at home games. Performing well away from home actually leads to higher likelihood of sellout crowds than home performances.

So teams that play completely average and win 50% of games are better off doing so away from home, as it leads to nearly 15% higher home capacity than doing the same at home.

Building A Regression Model

Okay, let’s finally get into it and put some numbers to these relationships. We’re going to build a linear regression model to see if the relationship between stadium size and home record is significant, along with how significant the other factors like attendance and away record are in determining home record.

Since we’re trying to get an idea of how important each feature is in the regression, we need to ensure that no two variables are too highly correlated. I used Variance Inflation Factor (VIF) to determine this, and found that attendance and stadium size are too similar to use both (they are correlated at 90%), however stadium size and percent of the stadium filled on average are not, so I dropped raw attendance data and instead went with the following three variables:
- Stadium Size
- Average percent of capacity filled
- Away Record
I’m using this to predict a team’s average home record over the course of their games at that stadium. For this reason, I’m using a linear model since the response variable is continuous from 0 to 1. Note: in hindsight, the best model to use in this situation would be a Beta Regression, which is specifically for continuous response variable s between 0 and 1 like my situation, however not knowing much about it, I’m not going to get into it for the sake of simplicity. I’m not doing rocket-science here, after all.

Results of linear model. Only the team’s away record was significant.

After running the model with those three variables, we find that neither stadium size nor percent of capacity are significant factors when team strength (via away record) is included in the model. This indicates that regardless of the size of stadium a team plays in or how packed the house is on average, they will perform to their best abilities over time. This is fair, but what if we look at an individual game. Can we gain any predictive power by factoring in the crowd size or venue when trying to determine the outcome of one game?

This time, I chose to use logistic regression to see if a model that included the attendance, stadium capacity, and percent of the stadium filled could outperform one that solely relied on the Elo rating of the two teams. We’re using logistic regression because we’re trying to predict a simple True/False of whether the home team won the game or not. This data excluded 2020 because the attendance data is far from complete, so we’ll just assume it’s a normal year. And in a normal year, it turns out that none of those variables are useful relative to Elo ratings alone.

Results of logistic regression. Only the Elo rating was significant.

The size of the stadium was the closest variable to being significant, but I would guess that the model was recognizing some of the larger stadiums and starting to correlate that to a better outcome for the home team, when in fact the physical size and capacity of the venue doesn’t mean much. Similarly, the number of people in the stadium or percent of the stadium filled didn’t seem to matter either.
August 3, 2021
Home-Field Advantage in 2020? It’s Complicated

You’ve heard of home-field advantage, but it’s always in the context of the advantage that a home-crowd gives a team. But what if that stadium were empty? Well sure enough, we saw just that last year.

Home-field advantage changed in 2020. That’s for sure. But by how much and why is less certain. Take, for instance, the distribution of home records over the past 6 seasons. As you’ll see, 2020 saw more teams with weaker home records, some getting shut out completely, a rare occurrence in past years.

Density plot of home winning percentages in college football over the past six seasons. 2020 saw more teams with home records below 50%.

However, this doesn’t tell the full story, because, as we know, in 2020 teams played abbreviated schedules and dealt with last-minute cancellations, leading to a smaller slate of home games for some teams. Here’s the distribution of the number of home games played in 2020 vs. 2019.

Distribution of number of home games played and count of teams in 2020 vs. 2019. In 2019, every team played 5 or more home games while last year, 69 teams played 4 or less.

So more than half of D-I teams played 4 or less home games. This led to a lot of variability in their results. Almost every conference also played an exclusively conference-only schedule last year, upping the quality of their competition in those home games. Naturally, we’d expect their home-record to drop as the average quality of their opponent went up.

When we filter for only those teams that played at least six home games in 2020, we get a much different story.

Density plot for home winning percentage for the past six seasons, filtered for teams that played at least six games at home each season. 2020 has a higher density at the right side of the graph, and a lower density in the middle of the graph for 50% win rates.

Well now what? This looks like teams actually played better at home when they got their 6+ games in. And in fact, they did play better on average at home in 2020 than the overall average in the previous five seasons. Teams in 2020 won 71% of their home games when they played six or more of them. From 2015-2019, that number was 64%. The difference is statistically significant with 95% confidence.

That being said, when you include all teams, regardless of how many home games they played, the difference between home-records in 2020 was statistically significantly worse than the preceding five seasons. So when teams were able to get all their games in, they saw improved home-field advantage, and when they didn’t get their normal games in, they struggled at home.

So how can we make sense of this trend? I don’t know that we can entirely understand the difference. Only 28 teams out of 127 got 6 or more games in in 2020. 10 were from the ACC, and then a mix of Sun Belt, Independent, Conference USA, and a few Big 12 and American Athletic conferences. The overwhelming majority of these teams were from the South, where eased restrictions meant more fans at home games, which could have given them improved home-field advantage.

Elo Ratings between the two groups were almost identical going into 2020, but were 50 points higher when the season ended for the teams that played all their home games.

We also need to remember that conferences like the Big Ten only played 9 games, all in-conference. So we would expect their win percentage to decrease significantly in a season where they effectively lost one or two near-guaranteed home-wins against non-conference cupcakes. Who knows what would have happened with an extra three games. We saw teams start off slow and finish the season on a run, adjusting to the new normal of the 2020 season. We also saw teams fall off, falling victim to opt-outs, infections, and lack of motivation.

So while, in part, the full-season teams played better than usual, it is likely that had more teams gotten in a full-season’s worth of games, they would have dragged the home-field advantage down to below-average levels. There is no doubt that the overall landscape in college football favored the away team more than in any other season in at least the past 20 years.

This year, we’ll see how much that home-field winning percentage rebounds as fans return in full force in most stadiums. And we can’t wait to see it.

Have a theory about why those 28 teams played better at home in 2020? Email me at kyle@staturdays.com or tweet us @Staturdays on Twitter.

July 28, 2021
Predicting the Heisman Winner After Kyle Trask’s 3-Interception Loss
Kyle Trask was a “shoe”-in for Heisman. Now the shoe is on the other foot (Mac Jones’s).

The name Kyle had gotten a bad rap in the last year. People think that all we do is drink Monsters and pop wheelies on our ATVs with our cousins at the campground. Kyle Trask was supposed to show the world that us Kyles are so much more. That we could be Heisman-winners and SEC champions too. Not so fast my friend.

I cannot understate enough how consequential a single shoe has become to not only Kyle Trask’s Heisman campaign, but also Florida’s shot at a College Football Playoff spot.

For those of you who have no clue what I’m talking about (doubtful, but possible), it’s probably easiest if you just watch this video.

Let’s start with the latter: Florida were unlikely to beat Alabama as it were, with Elo giving them around a 20% chance to win the game (with the LSU loss). Had they done that, they’d easily be in the College Football Playoff. Now, it’s unclear if a two-loss Florida could get in regardless of the result of this game, unless they had a performance so dominant against the best team in the nation that it couldn’t possibly be a fluke. That is even less likely than them winning by any margin.

Now the Heisman. Trask was a 52% favorite to win the Heisman last week. After a 3-interception loss, Kyle Trask dropped all the way to 11% odds (+800). Mac Jones went to the 66% favorite, followed by Devonta Smith at 33%. We’ve been working on a model to predict Heisman winners for the past two weeks using a few data sources from collegefootballdata.com. As of last week, Kyle Trask had the best odds to be the Heisman winner. Now, Jones has closed the gap.

The two major stats that were negatively affected by that LSU loss were team record (8-2) and interceptions thrown (+3). Only one of those two is significant to determining the Heisman winner: team record.

We built our model using data from 2004 through 2019, pairing up the most common passing, rushing, and receiving stats for each player with the eventual Heisman winner. This is inherently tricky because a Heisman winner is inherently rare. Out of about 42,000 player-season combos, there can only be 17 Heisman winners in that span. Despite that, we did a decent job of getting some fairly accurate Heisman odds historically, and the winner of the Heisman was the player with the highest odds in our model 11 out of 17 years.

The most important and significant factors that determined whether a player might win the Heisman ended up being:
- The team’s winning percentage in the regular season
- A player’s rushing yards relative to others at their position in that season
- Total Touchdowns per Game (it should be noted that total touchdowns for the season were pretty much equally significant, but since this season is shortened for some teams, we opted for the per-game stat)
Interestingly, our model still did better at identifying true Heisman candidates when we included more variables, even if they were statistically insignificant. Some of the variables we left in despite their perceived unimportance were:
- interceptions per game
- player position
- total yards per game
- Power Five conference indicator
The inclusion of these extra variables sniffed out a few clear outliers that weren’t even in consideration, namely the Cincinnati QB and RB, who have put up large numbers, but are not in a Power 5 conference, a defining characteristic of previous Heisman winners (despite that, P5 conference was still considered insignificant on its own, likely because so many Power 5 players do not win the Heisman each year, while many players who score 50+ touchdowns do (six out of 15, to be specific).

Cincy QB Desmond Ridder also threw .75 interceptions per game this year, a seemingly insignificant amount, but not when Fields, Trask, and Jones average .6, .5, and .3, respectively. It’s a tough world out there these days.

The results were fairly promising. Like I said, there are only 16 winners, and thousands of losers each season, so most players are going to have an essentially 0% chance of winning the Heisman. But when we look at the top 5 players in terms of Heisman probability each season, we see that the actual winner did in fact have much higher odds then the next four runner-ups, showing that our model is on the right track.

So the actual Heisman winner usually had the highest win probability to win the award on average, while the runner-ups came in around 12% probability.

Here is a look at how total TDs correspond to the probabilities to win the Heisman that our model gives.

This stat is clearly most important with QBs, as many of the Heisman-winning QBs had total TDs in the upper 40s or lower 50s. Matt Leinart and Troy Smith were two exceptions, with Leinart having the lowest predicted win probability of the players we looked at, undoubtedly helped by being the QB on an undefeated USC team that year.

So who are the Heisman favorites in our model this year?

The top five this year are:
1. Justin Fields (25.8% chance)
2. Kyle Trask (19.9%)
3. Mac Jones (17.3%)
4. Najee Harris (14.4%)
5. Kedon Slovis (6.7%)
Now remember, we are using per game numbers here, but we can almost certainly rule out Slovis and Fields who will only have played six games by the time the ballots are cast: enough games to warrant a playoff spot, maybe, but not a “Most Outstanding Player in College Football” trophy.

What you can take away from Fields sitting on top of our rankings is that he was on-track for a Heisman-caliber season.

Despite losing to unranked LSU in a three-pick game, Trask still leads in our odds thanks to his considerable lead in total TDs and TDs/game (4.2 for Trask to 2.8 for Jones). However, you have to feel like this conference championship game will decide things one way or another, with the top 2 QBs facing off head-to-head. They are, after all, separated by only 2.6 percentage points in our probabilities, and TDs aren’t everything, as we saw in the above plot.

For those wondering about DeVonta Smith, Alabama wide receiver, he comes in at #6, followed by Trevor Lawrence at #7. While Smith is certainly having a great year, he may be hurt by the fact that our 16 years of model-training hadn’t seen a WR win the Heisman once. That, and the fact that he has two teammates performing at equally, if not more historic levels.

Najee Harris is performing at Top-10 levels at his position in terms of total TDs, compared to other RBs in 2020. In terms of TDs per game, he is also in the top ten, though many others above him did better, none of which won the Heisman. However, only one of them was also on an undefeated team: Jaret Patterson of Buffalo (this year), who are in the MAC. So Najee has a chance, but it seems unlikely despite his outperformance of his peers. The less-prestigious Doak Walker Award (for the top back in College Football)? For sure.

Again, we have to discount Fields despite his stellar performance so far in the air and on the ground. You can see neither of the top QBs in contention have much of a run game, so it will come down to TDs and win percentage. I think Florida need to win on Saturday to get Trask his Heisman. Otherwise, it’s going to ‘Bama (but I won’t say who at ‘Bama).
December 19, 2020