### What happens to home advantage when one team is better?

In my last blog I took a first look at home advantage. I showed that home advantage is an important but declining factor in determining the outcome of matches. This is particularly true of the last 40 years, in which the proportion of home wins has fallen steadily and away wins are rising.

In this post I’m going to dig a little deeper into the data to see what we can learn about nature of home advantage.

To do this we have to first separate the impact of home advantage from the main factor that determines the outcome of a match: the relative skill levels of the teams. We generally expect the best teams in the league to beat the worst teams irrespective of where they play, but how does home advantage fit in with this? Does it only work when the home team is better? What happens when the away team is better? And what if the teams are evenly matched?

To answer these questions, I will first introduce a simple method for estimating

*superiority*– how much better is one team than their opponent? Then I’m going to use this measure to look in more detail at home advantage.### Quantifying Superior

A simple proxy for superiority is to use the difference in the number of points each team has accumulated since some point in the past. It seems natural to use the total points obtained in the last 38 games

^{1}, bridging the gap into the previous season. This ensures both teams played roughly the same opponents, home and away. Newly promoted teams – who, by definition, didn’t play games in that league the previous season – receive 1.05 points per game for the previous season (on average, newly promoted teams achieve around 40 points in their first season = 1.05 per game)

^{2}.

I then define

*rolling points difference*(*RPD*for short) as being the difference in the 38-game points total for the home and away team. For instance, the current rolling points difference between Swansea City and Chelsea (their next match, at Swansea) is -10 points, i.e., Chelsea have accumulated 10 more points than Swansea over the last 38 games.### Separating Home Advantage from Superiority

Figure 1 shows how the percentage of home wins, away wins and draws depend on the relative abilities of the two teams playing (as measured by RPD). As we move from the centre of the plot to the right, the home team is increasingly better than the away team. As we move to the left, the away team is increasingly better than the home team. The vertical dot-dashed line indicates when teams should be evenly matched. To create the plot, I’ve used all EPL matches in the last 20 years. The shaded areas show the 95% confidence region around each line.

So what does the plot tell us? First of all, RPD does a good job of measuring team superiority: the percentage of home wins rises steadily when the home team has a higher 38-game points total (positive RPD) and the percentage of away wins increases when away team has a higher points total (negative RPD).

Figure
1: home win, away win and draw percentages for matches as a function of the
rolling points difference (RPD)
between the teams. |

Second, the results confirm that the effects of home advantage are clearly present even when the teams are evenly matched: at RPD=0, the home win percentage is 41%, away win is 29% and draw is 30%. Home advantage doesn’t just amplify team superiority (as some have suggested), it clearly influences the outcome when the teams are evenly matched.

In fact, Figure 1 shows that home advantage is evident across the board: the home team wins significantly more often (59% of games) when the RPD is +20 than the away team wins when the RPD is -20 (44%).

The point at which the red and blue lines cross indicates where the home and away teams have an equal chance of winning the match. This occurs at an RPD of -10 points: that is, if the away team has accumulated 10 more points more than the home team in their last 38 games then they are just as likely to win the game. For comparison, 10 points is roughly equivalent to 4-5 places in the league table ranking at the end of a season

^{3}.
As far as I can tell, my analysis here is novel: it clearly demonstrates that home advantage is present irrespective of the quality gap between the teams.

As a final thought, Figure 1 provides a simple model for predicting the outcome of any give match. You simply calculate the RPD between the teams and read off the probability of a home win, away win or draw. I’m going to take a look at how well bookmaker’s odds forecast match outcomes in a future post.

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[1] In the EPL there are 20 teams, so each team plays 38 games per season.
[2] For example, if a newly promoted team has played 10 games and accumulated 15 points in the present season, it will receive a rolling 38-game total of 44: 15 points for the current season plus 28x1.05 for the previous season

[3] Some other things worth noting: A rolling points difference of -10 points also corresponds to the point at which the likelihood of a draw is maximized, which makes sense. Also, draws occur more frequently when the home team is better (to the right of the plot) than away wins; small teams will frequently ‘play for a draw’ (i.e. very defensively) when playing away from home.

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