# Home Advantage and Margin of Victory

#### Introduction – Home Advantage in Sports

As we all know, the home team tends to win in team sports. But the size of the home advantage differs between professional sports. For example, the home advantage of MLB games is relatively small, the home advantage in collegiate basketball games is high, and the home advantage in NFL games is somewhere between the home advantages in baseball and basketball.

Last Saturday, the BGSU men’s basketball team played its rival Toledo in the friendly confines of BGSU’s Stroh Center. Given that BGSU was having a great season, I thought beforehand they had a good chance of winning the game, especially since they were playing at home. They did win a close game decided in the final seconds. That raises the question — does the home team have an extra home advantage when the game is only decided by a few points?

#### Relationship with Winning Margin

Recently I started wondering about the relationship between home advantage and the winning margin in different sports. In particular …

• Do home teams have a special or larger-than-average advantage in close games?
• Are home teams more likely to win in one-sided games when the margin of victory is large?

Let’s explore the relationship of home advantage and winning margin in several sports. We’ll see some interesting patterns in this data.

#### Baseball

Let’s start with baseball games which I am pretty familiar. From Retrosheet, I collected all of the regular season games in the last 20 seasons from 2000 through 2019. For each of the possible winning margins 1, 2, 3, … runs, I found the proportion of games won by the home team. Here is the graph. For winning margins of 2 through 10, the home winning fraction is in the 0.52-0.53 range with the exception of 7 where the home winning fraction is actually under 0.5. (I don’t take this seriously — I think this is really just a byproduct of random sampling variation.) But the home advantage is really strong for one-run games. Why? Perhaps the advantage of batting last makes a difference? Maybe I am missing a possible explanation here.

Let’s move on to college basketball. The mRchmadness package contains all of the results of all Division I games played by women and men during the 2017 and 2018 seasons. I focused on only the home games played — the games played on neutral sites were excluded. Below I graph the winning margin against the proportion of home team winning for both men and women games. Here we see a very different pattern than what we see in baseball. The home advantage is actually smallest for tight games and the home advantage steadily increases as the winning margin increases. There is also an interesting difference between men and women games — the home advantage of women games doesn’t appear to be as sensitive as the home advantage of men games to the winning margin.

#### Inter-Conference Games

I thought about this pattern. Many of the early season games are played between teams from different conferences and the better school from the more prestigious conference will tend to host a game from the school from the less prestigious conference. This might explain the large home advantage for games with high winning margins.

To control for this situation, I focused on only conference games — here I am focusing only on men conference games among teams in the Big 10, ACC, and Atlantic 10 for the 2016, 2107, and 2018 seasons. There is some variability in these proportion values due to random sampling. But this also shows that the home advantage is smallest for close games and the home advantage does increase gradually as the winning margin increases.