Here's another installment of "what is the point value of goals?" It's one thing to see how many points are associated with different numbers of goals, or to see if first or second half goals generate more points (they don't). But these analyses leave open the question of whether goals produce different amounts of points, depending on when the situation the team finds itself in - whether it is behind, tied, or ahead.
To see if this is the case, I calculated the point values of goals, depending on the score at halftime. As before, these calculations are based on data from the Big 4 leagues and for the last five seasons (2005/06 to 2009/10).
To see if this is the case, I calculated the point values of goals, depending on the score at halftime. As before, these calculations are based on data from the Big 4 leagues and for the last five seasons (2005/06 to 2009/10).
As they do on many other dimensions of soccer statistics, the leagues look very similar to one another. And at first glance, it appears that goals are most valuable when teams are ahead - that is, scoring no or just one goal when ahead still gives teams an expected point value of 2 to 2.7 points, while scoring no goal or just one when behind produces an expected point value of 0 to about .3 points. But this will hopefully surprise no one - teams that are ahead at the half are more likely to win (about 75% of them do), so these numbers aren't really reflections of the value of the goals but simply a reflection that teams that are behind lose more and teams that are ahead win more.
Across the leagues, the average values look like this:
More generally, the marginal point values of goals diminish rapidly for teams that are ahead at the half, and diminish for teams tied at the half as well, though not as steeply. Finally, the marginal point value of goals are most unlike the other two sets of values when teams try to come from behind. The numbers show that a goal is most valuable in terms of generating points for teams when we go from 1 goal to 2 and from 2 to 3 goals; going from 1 to 2 goals increases the team's predicted point value by 1.08, and from 2 to 3 generates an additional .9 points (so about 1 point each).
Across the leagues, the average values look like this:
To put things in perspective, recall from the earlier post that the average point value of goals overall ranges from .28 (0), 1.14 (1), 2.15 (2), 2.67 (3), 2.90 (4), to 3 (5+ goals). So one goal virtually ensures at least one point, while more than 2 gets teams closer to 3 points. But, as the numbers in the table show, that's certainly not the case when a team is behind; one goal generates about 1/3 of a point, and it takes four to five goals to ensure three points for the team that's behind at the half.
But recall also that what we really want to know is the "marginal" value of each additional goal - how many more points do you get when you score 2 (or 3 or 4) relative to 1 (or 2 or 3)? These numbers are shown in the next table. Turns out, a single second half goal (or going from 0 to 1 goals) is most valuable when teams are tied (1.31 points), and least valuable when the team is behind (.36). This is sensible, given that a single goal may take you to a draw when you're behind and put you on the road to victory when you're tied.
More generally, the marginal point values of goals diminish rapidly for teams that are ahead at the half, and diminish for teams tied at the half as well, though not as steeply. Finally, the marginal point value of goals are most unlike the other two sets of values when teams try to come from behind. The numbers show that a goal is most valuable in terms of generating points for teams when we go from 1 goal to 2 and from 2 to 3 goals; going from 1 to 2 goals increases the team's predicted point value by 1.08, and from 2 to 3 generates an additional .9 points (so about 1 point each).In contrast, going from 4 to 5 goals only increases the predicted point value by .15. This is logical: teams that have already scored 4 in the second half are highly likely to win, so scoring one additional goal is nice, but doesn't really make it more likely that the team will take away points. In contrast, scoring a goal when the team has scored 1 or 2 increases a team's chances significantly (by about a point), while going from 3 to 4 is worth about half that.
