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What is a better way to decide ties in a league - Goal Difference or Head-to-head results?? To some extent whether or not head-to-head results makes for a better tiebreaker than overall goal difference is really subjective. Both are used to pick the team that "performed" better, but each using different criteria for judging a team's performance. Which criteria is preferable is purely a matter of opinion, and circumstance.
Major critiques of each method IMO include:
Goal Difference: Tends to favour the "flat track bully", a team which does very well against "smaller" opposition.
Head-to-Head: Tends to favour the "lucky" team, a team which may not be really better, but got the lucky break in the crucial game. It makes one game more important than the rest, hence "luck" plays a bigger part.
A friend of mine, a sports statistician, ran a small simulation on this sometime back, and I quote:
One can assess the tiebreakers in terms of how well they do in picking the *better* team. This may be considered unfair though, as tournaments do not necessarily reward teams that *are* better, but rather those that happened to *play* better. However, tournaments exist for the purpose of determining the "best" team, so it makes sense that one should want to use a tiebreaker that does tend to favour the team that really is better.
The problem is that in real life it's not always possible to know for certain which team is better. It is possible though to run computer simulations using a model in which the relative strengths of the teams are known, and then compare the two tiebreakers to see how often they favoured the team that really is better. This is what I've done.
I used a fairly simple model for simulating game scores between teams of varying strengths (well, simple for those with a mathematics background, incomprehensible nonsense otherwise). I set it up like group play from Euro96, with four teams each of clearly different strengths. For simplicity sake, I only considered two-way ties, as three-way tiebreaking is tricky to
compare (and in four-way ties there's no difference between the two tiebreakers anyway). I considered all two-way ties, not just those for 1st or 2nd place.
I ran the model until I reached 10000 ties, and did this several times using different distributions of team strengths. In all cases, the Goal Difference tiebreaker favoured the better team far more often than did Head-to-Head. Typical results are:
Of the 10000 ties:
Head-to-Head broke the tie 43% of the time
Goal Difference broke the tie 73% of the time
When they did break the tie:
Head-to-Head favoured the better team 48% of the time
Goal Difference favoured the better team 63% of the time
When they both broke the same tie, but in different ways:
Head-to-Head favoured the better team 34% of the time
Goal Difference favoured the better team 66% of the time
Goal Difference clearly wins out here. And in runs in which I increased the difference in strength between the teams, Goal Difference performed even better, while Head-to-Head did even worse. In runs in which the teams were more closely matched, the two tiebreakers performed similarly, but Goal Difference still had a slight edge.
On the basis of these simulations, Goal Difference clearly favoured the better team, while Head-to-Head actually slightly favoured the weaker team. However, if people wish to believe that Head-to-Head is a better way of comparing how two teams *played*, then there's really no arguing with it. That's a matter of opinion. What I've shown is that Goal Difference is a better tiebreaker if you want to favour the teams that really *are* better, but not necessarily those that *played* better.
While I am not a big believer in simulation models on sporting events (often the assumptions dictate the results), I do lean towards the GD model of breaking ties for something like the World Cup. Not only it encourages teams to attack more and take a few risks against the "weaker" teams, it also reduces the pressure on the outcome of BIG games which again makes them play their natural game. But for something like domestic leagues and the CL, the Head-to-Head makes more sense, as there are home and away fixtures which give enough chance to the "better" team to win the Head-to-head.
What do you guys think??
Major critiques of each method IMO include:
Goal Difference: Tends to favour the "flat track bully", a team which does very well against "smaller" opposition.
Head-to-Head: Tends to favour the "lucky" team, a team which may not be really better, but got the lucky break in the crucial game. It makes one game more important than the rest, hence "luck" plays a bigger part.
A friend of mine, a sports statistician, ran a small simulation on this sometime back, and I quote:
One can assess the tiebreakers in terms of how well they do in picking the *better* team. This may be considered unfair though, as tournaments do not necessarily reward teams that *are* better, but rather those that happened to *play* better. However, tournaments exist for the purpose of determining the "best" team, so it makes sense that one should want to use a tiebreaker that does tend to favour the team that really is better.
The problem is that in real life it's not always possible to know for certain which team is better. It is possible though to run computer simulations using a model in which the relative strengths of the teams are known, and then compare the two tiebreakers to see how often they favoured the team that really is better. This is what I've done.
I used a fairly simple model for simulating game scores between teams of varying strengths (well, simple for those with a mathematics background, incomprehensible nonsense otherwise). I set it up like group play from Euro96, with four teams each of clearly different strengths. For simplicity sake, I only considered two-way ties, as three-way tiebreaking is tricky to
compare (and in four-way ties there's no difference between the two tiebreakers anyway). I considered all two-way ties, not just those for 1st or 2nd place.
I ran the model until I reached 10000 ties, and did this several times using different distributions of team strengths. In all cases, the Goal Difference tiebreaker favoured the better team far more often than did Head-to-Head. Typical results are:
Of the 10000 ties:
Head-to-Head broke the tie 43% of the time
Goal Difference broke the tie 73% of the time
When they did break the tie:
Head-to-Head favoured the better team 48% of the time
Goal Difference favoured the better team 63% of the time
When they both broke the same tie, but in different ways:
Head-to-Head favoured the better team 34% of the time
Goal Difference favoured the better team 66% of the time
Goal Difference clearly wins out here. And in runs in which I increased the difference in strength between the teams, Goal Difference performed even better, while Head-to-Head did even worse. In runs in which the teams were more closely matched, the two tiebreakers performed similarly, but Goal Difference still had a slight edge.
On the basis of these simulations, Goal Difference clearly favoured the better team, while Head-to-Head actually slightly favoured the weaker team. However, if people wish to believe that Head-to-Head is a better way of comparing how two teams *played*, then there's really no arguing with it. That's a matter of opinion. What I've shown is that Goal Difference is a better tiebreaker if you want to favour the teams that really *are* better, but not necessarily those that *played* better.
While I am not a big believer in simulation models on sporting events (often the assumptions dictate the results), I do lean towards the GD model of breaking ties for something like the World Cup. Not only it encourages teams to attack more and take a few risks against the "weaker" teams, it also reduces the pressure on the outcome of BIG games which again makes them play their natural game. But for something like domestic leagues and the CL, the Head-to-Head makes more sense, as there are home and away fixtures which give enough chance to the "better" team to win the Head-to-head.
What do you guys think??
Good point!
