In soccer, a single goal has enormous value. In fact, we can put a number on that value. I’ve written about this before in posts on the most common scores in soccer or posts about the point value of goals. In a game where over 50% of matches involve fewer than 3 goals, and the most common score line is a goal difference of 1 (rather than 3 or 4), being ahead or behind is a big deal. Another way to see this is to remember that teams that are ahead at the half have roughly a 75% chance of winning the match.
Being ahead is vital not just because it makes wins more likely, statistically speaking. It's also interesting for soccer analysts because it does something to the dynamics of the game. It can change a match on a time and how teams are playing, either to protect a lead or get back into the game. At a minimum, having one team ahead creates psychological pressure on the team that’s behind, and it puts the team that’s ahead in control of the match. Put simply, it provides them with leverage. We can also define leverage statistically as “the likelihood of winning, given the score and the time remaining in the game” (I borrowed the definition from behindthenethockey.com's ingenious Gabe Desjardins).
The value of being ahead or the difficulty of being behind can thus be expressed in numbers. Here, I measure leverage by the expected odds of winning the match, given a particular score line at halftime. Because winning is about having a positive goal difference, we can calculate the expected frequency of a win, given different goal differentials. Below I show win frequency as a function of goal differential (GD), for the four best leagues in the world (Bundesliga, EPL, La Liga, and Serie A) from 2005/06 to 2009/10 combined. This large sample of matches should provide a really solid statistical indication of how much leverage top professional teams have over their opponents, depending on where they stand at that point in the match.
A tie at the half gives each team about a thirty percent chance of winning the match - it's wide open. The graph also shows that teams have zero leverage when GDs range from minus 5 to minus 2, while teams have maximum leverage (or close to it) with GDs of plus 3 to plus 5.
This also tells us that the real action in terms of leverage is in the range of minus 1 to plus 1.
The first thing that's noticeable is that goal differences of -1 and +1 are not the same. While being down one goal gives teams win leverage of less than 10%, being up one goal gives them almost 70% leverage. That's a huge difference. (And being up two goals at the half means roughly 90% leverage.) Given these numbers, a lead by just one goal at half time really puts a team in the driver's seat.
You might be worried that leverage varies by league. But it doesn't, as the next graph shows: (halftime) leverage is roughly the same in each of the leagues.
So do home teams have more leverage? Here are the numbers for the leagues and five seasons combined, split up by home and away teams. To make things easier to compare, dots of the same color represent the same leverage situation.
Clearly, home teams have significantly more leverage than away teams across the score lines (with the exceptions of GDs of -5 to -3 and +4 and +5, as before). The difference in leverage between teams playing home and away is .08 at a GD of -1 (.14 v. .06), .14 when the game is tied (.38 v. .24), and .14 at +1 (.75 v. .61 ). So home teams have slightly more leverage when they're down a goal than away teams and lots more leverage when they're up one or even just tied.
Leverage is real; ask any player (or fan, for that matter) whether it feels different to be ahead a goal or behind one. And leverage is useful, soccermetrically. Of course, with lots more detailed data, we could expand these measures to see how leverage changes at different points during the match. More finely grained data also would allow us to see how leverage changes during the course of the match and perhaps move back and forth between teams, and it would give us a way of measuring a team's overall leverage score for the match. In a future post, I'll take a look at how leverage plays out differently for different teams.
Being ahead is vital not just because it makes wins more likely, statistically speaking. It's also interesting for soccer analysts because it does something to the dynamics of the game. It can change a match on a time and how teams are playing, either to protect a lead or get back into the game. At a minimum, having one team ahead creates psychological pressure on the team that’s behind, and it puts the team that’s ahead in control of the match. Put simply, it provides them with leverage. We can also define leverage statistically as “the likelihood of winning, given the score and the time remaining in the game” (I borrowed the definition from behindthenethockey.com's ingenious Gabe Desjardins).
The value of being ahead or the difficulty of being behind can thus be expressed in numbers. Here, I measure leverage by the expected odds of winning the match, given a particular score line at halftime. Because winning is about having a positive goal difference, we can calculate the expected frequency of a win, given different goal differentials. Below I show win frequency as a function of goal differential (GD), for the four best leagues in the world (Bundesliga, EPL, La Liga, and Serie A) from 2005/06 to 2009/10 combined. This large sample of matches should provide a really solid statistical indication of how much leverage top professional teams have over their opponents, depending on where they stand at that point in the match.
A tie at the half gives each team about a thirty percent chance of winning the match - it's wide open. The graph also shows that teams have zero leverage when GDs range from minus 5 to minus 2, while teams have maximum leverage (or close to it) with GDs of plus 3 to plus 5.
This also tells us that the real action in terms of leverage is in the range of minus 1 to plus 1.
The first thing that's noticeable is that goal differences of -1 and +1 are not the same. While being down one goal gives teams win leverage of less than 10%, being up one goal gives them almost 70% leverage. That's a huge difference. (And being up two goals at the half means roughly 90% leverage.) Given these numbers, a lead by just one goal at half time really puts a team in the driver's seat.
You might be worried that leverage varies by league. But it doesn't, as the next graph shows: (halftime) leverage is roughly the same in each of the leagues.
So do home teams have more leverage? Here are the numbers for the leagues and five seasons combined, split up by home and away teams. To make things easier to compare, dots of the same color represent the same leverage situation.
Clearly, home teams have significantly more leverage than away teams across the score lines (with the exceptions of GDs of -5 to -3 and +4 and +5, as before). The difference in leverage between teams playing home and away is .08 at a GD of -1 (.14 v. .06), .14 when the game is tied (.38 v. .24), and .14 at +1 (.75 v. .61 ). So home teams have slightly more leverage when they're down a goal than away teams and lots more leverage when they're up one or even just tied.
Leverage is real; ask any player (or fan, for that matter) whether it feels different to be ahead a goal or behind one. And leverage is useful, soccermetrically. Of course, with lots more detailed data, we could expand these measures to see how leverage changes at different points during the match. More finely grained data also would allow us to see how leverage changes during the course of the match and perhaps move back and forth between teams, and it would give us a way of measuring a team's overall leverage score for the match. In a future post, I'll take a look at how leverage plays out differently for different teams.
