Advancement scenarios

I've been looking into the advancement scenarios from group play (advancing to the knockouts). To study this I've written some code that simulates the World Cup tournament. It's nothing sophisticated; it uses ELO ratings to determine match results, playing all the group matches and then the knockout rounds. I did a Monte Carlo run (10,000 tournaments) and generated statistics from that. The results seem reasonable. For example, here are a selection of teams; I'll list how often they win their group and how often they advance to the semifinals in my simulation, compared to the implied probabilities from the DraftKings Sportsbook: What I'm trying to show here is that the simulation produces reasonable results. It's not the best simulation, but it's good enough for my intent, which is to analyze broad trends in the tournament. I'll start with the advancement scenarios at the end of group play. Here's what I found (from 10,000 simulations): Probability of advancing, based on points in group play: Three points is the dividing line, so let's go into detail with that. Here's the probability of advancing, for all teams that finished in 3rd place with 3 points, base on their goal difference: Bottom line: Four points gets you through (almost always). two points doesn't (almost always). Three points may, depending on GD. Now let's step back and look at things before the final round of group games is played. After the each team has played two games, here are the averages. Of the 48 teams: (Note that in the scenarios marked with an asterisk, the teams still have something to play for, even though they have clinched advancement (i.e., improving or keeping their place in the group for a more-desirable knockout match) Bottom line: A vast majority of teams will have something to play for in the final round of group games. (Granted, some of those "still in the hunt" teams will have mathematical hopes only. For example, if Jordan goes into its final match needing a 4-goal win over Argentina). More analysis to come.

I was not aware that they had changed this rule regarding the head-to-head results taking precedence over goal difference. Notably, this was not the case during the qualifiers. This rule has long been in place at the Euros and it's mostly fine, I think.

View attachment 330050 Three points is the dividing line, so let's go into detail with that. Here's the probability of advancing, for all teams that finished in 3rd place with 3 points, base on their goal difference: View attachment 330051 More analysis to come.I am surprised that 3 points and a minus 3 goal diff still probably sees a team advance. And a -2 GD raises the changes to over 70%. Doesn't that go against what we've seen in WC history (granted not a huge sample size)?

I am surprised that 3 points and a minus 3 goal diff still probably sees a team advance. And a -2 GD raises the changes to over 70%. Doesn't that go against what we've seen in WC history (granted not a huge sample size)?Good point. I noticed this too but didn't write about it in my original post because it was already too long lol. The 3 recent Euros had 3rd-place qualifying. 44% of teams with 3 points advanced. The GD cutoff was between -1 and -2. So, in real life it's harder to advance than my model. But as you say, small sample size. Throw in the 2019 and 2015 women's World Cup, and the numbers get closer to my sims. 53% of teams with 3 points advance. The tipping point is right at -2 GD. I thought about the older men's World Cups (86-94) but that was a while ago, and some of them had still 2 points for a win, so it got messy. Interestingly, in the U20 World Cup it's very had to advance with 3 points (27%). I think that's because there is a wide range of quality - several of the 'minnows' were truly bad teams, and so it was easier to get 4 points. Maybe that's how this World Cup will be? I suspect two things explain the difference between my sim and empirical evidence. First, small sample size (random variation). Second, teams strategize to advance (e.g., playing for a draw if they know that will get them through), and that might skew the results. My sim doesn't do this - for example, if Algeria just needs a draw to advance, my code doesn't have them play defensively - they just play a normal match. Any, thanks for bringing this up. It'll be interesting to see how it turns out.

[Gory details about tiebreaker change] This World Cup is different than previous ones because: 1) 48-teams means 8 of 12 3rd place teams qualify for the knockouts, with a massive 495-element table to determine who they play, 2) for the first time, FIFA is using head-to-head as the first tiebreaker (i.e., UEFA rules). Since 3rd place teams can now advance, most teams are not eliminated even if they lose their first two games. That's because a 3rd place team with 3 points has a reasonable chance of advancing (depending on goal difference, of course). Even if you lose your first two games, winning your last gives you 3 points, and you're in the running. With an exception. There's a chance that a team with zero points after two games is already eliminated. That's because of the new tiebreaking rules. A team can win their final match and finish with 3 points, but be stuck in last place. Here's an example: Group B Mexico 3, South Africa 0 Korea Republic 2, Czechia 1 Mexico 1, Korea Republic 1 Czechia 1, South Africa 0 Standings: Mexico - 4 pts Korea - 4 pts Czechia - 3 pts South Africa - 0 pts Even if South Africa wins their final match, the best they can do is tie Czechia on points (assuming Czechia loses). And since SA lost to Czechia, SA loses the tiebreak and will finish 4th. Under the old tiebreaking rules, they could have theoretically passed Czechia on goal difference. The same is true at the other end of the standings - team A can clinch first place with 6 points, if the second place team has 3 and team A has already defeated them.