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.

NCAA Basketball

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.

Home Advantage in Sports

To conclude, let’s review some things that we know about home advantage.

• Home advantage exists but its effect varies between sports. This brief study has demonstrated that the size of the home advantage differs between MLB and college basketball. The effect in basketball is strong — a former BGSU coach used the expression “steal a win” whenever BGSU won an away game — he understood the difficulty of winning on the road.
• It is not obvious what causes the home advantage, but some authors think they know the cause. Perhaps a more interesting question is what causes the home advantage. A lot of reasons can be proposed, but Wertheim and Moskowitz believe that home advantage is generally caused by referee bias. I think one can document this umpire effect in baseball — for example, I believe the size of the zone can vary between home and visiting players. I wrote a short article for Significance Magazine on this “why home advantage” issue.
  
  Called Strikes: Here is an illustration of this referee effect in baseball where I show contour lines of the called strike region equal to a probability of a strike equal to 0.5, 0.7, and 0.9 for home and away batters on a 0-2 count during the 2019 season. The strike zone looks a little larger for the visiting batters which benefits the home team.

• Home advantage is a bias effect. Some years ago, I considered the home advantage for individual players. Is there evidence that particular players can have larger “true” home advantages than other players? What I found was that the answer is no. Home advantage is one example of a bias that appears to affect all players the same way. This is consistent with the opinion of Bill James on the subject. We both think that most situational effects like the home/away effect, opposite arm/same arm effect are the same for all hitters.

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