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How much luck do you need to win the World Cup?
00:08:59
Investigating the role of random chance in football
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Transcript23 lines
- [00:01]
A
Hello and thanks for downloading the More Or Less podcast. We're the programme that looks at the numbers in the news life and in that sport, that definitely starts with the word foot. And I'm Lizzie McNeil. Now, unless you've been blissfully far away from any screens, radios, pubs, flags or indeed people, you'll have noticed that there's been a bit more football around than usual. Yes, after five weeks and over 100 matches, we've reached the dramatic final of the 2026 World Cup. Doubtless, both teams have worked extremely hard to reach this point. But loyal listener Mike Gent got in touch to ask whether there might be another factor at play here. And no, we don't mean interfering state leaders. He wanted to know about luck.
- [00:49]
B
Given England and Scotland's sojourn in the World cup, it made me think, how much luck do you need to win the World Cup? Has anyone ever tried to quantify luck?
- [00:58]
A
So how important is luck in winning the World Cup? Does the better team always win? Or could a worse team steal victory from the jaws of defeat? First of all, we need to define what we mean by luck. So we armed ourselves with our trusty four leaf clovers, rabbit's feet and other totemic objects, and contacted Ian Graham, former head of research at Liverpool Football Club.
- [01:22]
B
Yes, a genuine luck is something completely outside a team's control. But that's not usually what we think about when we think about Leck. Leck really is a shorthand for things that are difficult to predict, things that are difficult to control.
- [01:38]
A
It happens that football is one of the least predictable ball sports there is,
- [01:43]
B
and the real reason driving that is the low scoring nature of the game. So in football, there's typically 2.5 to 3 goals per game, and whether a chance becomes a goal or not is very uncertain. If you compare that to a game like basketball, which has hundreds of scoring events per game, or a game like tennis, where has hundreds of points per tennis match. The low scoring nature of football leads it to being not very predictable, or we could say leads it to having a higher percentage of games whose outcome is more down to luck than down to skill.
- [02:22]
A
If this is true, and it really is based on luck, then you'd expect to see the underdog win in football more so than in other sports. So do you? Luckily for us, mathematician Luigi Nunez Vicente from Lehigh University ran a study to test just that.
- [02:39]
C
So we basically collected a major match data set with more than 5,000 matches involving 12 sports. All the competitions, World Cups and Olympics since 1970 until 2023 and these were 12 ball sports. Then we also developed what we mean by weak in a match. A team is weak if it is a certain number of positions that we calculated statistically below its opponent. And then we come up with an underdog achievement just by summing all the wins and the ties of the weak teams, divided by all the matches played by the weak teams. And that gave us a score, an underdog achievement score.
- [03:20]
A
And what were the results?
- [03:22]
C
We came up with two major conclusions. One is that indeed soccer is one of the sports with the highest underdog achievement. And secondly, it's one of the sports where there's a great influence of randomness, meaning luck.
- [03:37]
A
So how does that all play out in a tournament like the World Cup? Is it a bookie's dream of luck above all else? Well, according to David Sumter, professor of Applied Mathematics at Uppsala University, yeah, kind of.
- [03:51]
D
When I work together with football clubs, what I'll do is I'll say you really can't tell anything from a single match. We always work on the principle of looking at five matches and only after you've got five matches really, can you draw any conclusions about how well the team are performing. And in a World cup setting that's a very difficult truth because if you think about the last 32 down to the final, that's just five matches as well. So we really can't tell which are the best teams over those five matches. And a bit of randomness can knock out any one of those teams. So randomness is really the rule rather than the exception.
- [04:30]
A
So even if you are a highly skilled team, there are plenty of opportunities to be unlucky over five matches.
- [04:37]
D
My estimate would be if you're the best team in the tournament, you have a 20, 25% chance of actually winning that tournament. So you can think you do need, you know, 75% luck if you're going to win the tournament.
- [04:51]
A
So to answer our listeners question, you need a lot of luck in order to win the World Cup. Despite all the randomness at play in this year's World cup, there were still no underdogs in the semi finals. The last four teams in the tournament were were all the highest ranked ones. Could that be evidence that football is not so random after all?
- [05:12]
B
Yes and no. So I think this tournament's the first one where seeding has been in place that keeps the best teams apart until the semi finals. So it's hard to compare with previous tournaments. That being said, it's pretty unusual that this was the result. So we simulated the tournament 100,000 times. We found the most likely set of semi finalists was the set of semi finalists that was observed. But we also found there's only about a 0.9% chance that all four of those teams would qualify for the semi finals.
- [05:56]
A
But what about our listener's other question? How do we quantify luck and separate it from skill or. Well, one way to measure this is xg.
- [06:05]
B
So XG stands for expected goals. It's one of the worst names in sport. Think of it as chance quality. So there's a very low number of goals in football. So in order to get more data about each game, you can look at the number of shots each team takes. Each team takes about 10 times the number of shots than there are goals in a game.
- [06:30]
A
Or in other words, each shot only has a 1 in 10 chance of becoming a goal. But not all shots are created equal.
- [06:38]
B
So a penalty's got about a 78% chance of being converted. A typical shot from open play's got an 11% chance of being converted, and then a generic shot from open play on the penalty spot got about a 20% conversion chance.
- [06:54]
A
Each time a team takes a shot, you look at the chance the shot would have gone in, depending on where it's taken from, and you add it to the total xg. The final XG then tells you how many opportunities that team made at the goal, regardless of whether the cards fell in their favour and the shot became a goal. The team with the highest XG doesn't always win the game, but they will have had the most opportunities. Because of the randomness of football, the most reliable thing a player can do is to create chances to be lucky. Although, as David Sumter says, this isn't how the players are thinking about it.
- [07:31]
D
For them, it can't come down to luck. They have to fight to do their best. But despite them all doing deterministic things, they're kicking this spherical object around which starts to bounce around in some way that is better modeled as random. There's lots of collisions with the ball, bum, bum, bum, bum, and then the randomness is generated. And despite all of their best intentions to try and win, that randomness is always going to keep coming back to you. You can think of chaos theory and the weather, and you can think of, like, how long we can predict the weather into the future. And nowadays we can predict the weather despite the weather being chaotic, we can predict it about three days into the future. In a football match, you can only predict about 8, 9, 10 seconds into the future is pretty much random after those 10 seconds. So there's just this really high degree of randomness all of the time with those underlying scoring rates together produce these very random outcomes for the matches.
- [08:34]
A
Our thanks to Ian Graham, author of how to Win the Premier League, David Sumpter, author of Soccer Matics and Luiz Nunez Vicente. And that is all we have time for this week. We'll be back next week, but if you've seen a number you think we should take a look at, email us at more or lessbc.co.uk until next week. Goodbye.