Oxford mathematician predicts football's next G.O.A.T. after Ronaldo vs Messi debate
With Cristiano Ronaldo and Lionel Messi approaching the end of their respective careers, Oxford mathematician Dr Tom Crawford has looked at the next generation of greats
by Tom Victor · The MirrorAfter years of debating which of Cristiano Ronaldo and Lionel Messi was the best player in the world - if not of all time - the time has come to pass the torch.
Both superstars are in the twilights of their respective careers, with Ronaldo in Saudi Arabia and Messi in the United States. Neither is in the mix for the 2024 Ballon d'Or, with those still plying their trade in Europe leading the way.
Ronaldo has given his predictions when it comes to the next generation. He predicted Kylian Mbappe, Erling Haaland, Jude Bellingham, and Lamine Yamal to be in the mix for the next few years, though it's another man - Real Madrid star Vinicius Junior - who appears to be the front-runner for the 2024 award.
It may well be the case that no player from the current generation comes close to the otherworldly goal numbers posted by Messi and Ronaldo throughout their careers. However, according to University of Oxford mathematician Dr Tom Crawford, the numbers suggest some have a better chance than others.
Back in 2021, Dr Crawford worked with LiveScore to develop his G.O.A.T. (Greatest of all time) Index. The mathematical model helped him pick out the greatest player of all time, based on factors including goals, trophies and individual awards, with Ronaldo coming out on top.
Crawford's background is in mathematical modelling in relation to his specialist field of pollution in the ocean. However, the premise is something he's able to carry into football for his next project - predicting the next G.O.A.T. based on current achievements and projections for the future, focusing on players aged 25 or under.
"The whole point of mathematical modelling is you can apply it to anything - so i'm like 'i know how mathematical modelling works, let's apply it to football," Crawford tells Mirror Football. "It's just 'here is data I have, just like I have data about the river and the earth. Here's data I have on players, can I try to make predictions and understand what might happen in the future?'."
He has previously worked on other football projects, including in the areas of scouting and penalty placement. "It's all a sense of 'take past data, try to make predictions of future things based on equations and understanding of the sport and of the earth," he adds.
Who do you expect to become football's next G.O.A.T. contender? Have your say in the comments section
After beginning with a longlist of 30, Crawford was able to get a feel for which players scored highly in certain categories. The process has been streamlined since he created the original 2021 model, with the first phase seeing candidates judged on goals, assists, club titles, international titles and individual awards.
Phase two sees him introduce the G.O.A.T. Curve, which predicts future success. Messi and Ronaldo have different-shaped curves, so it was a case of understanding which superstar's career each of the next generation players resembles, and then applying the maths based on that.
A score is calculated for each player, based on their potential to hit a score of 100 - equivalent to a Messi or Ronaldo level career. In Crawford's findings, each player's highest and lowest value is calculated, with an average of the two then taken: while only one player on the shortlist has a potential peak of 100 (more on that later), several others can touch the high 90s if things go to plan.
"The Messi G.O.A.T. Curve is just a straight line, pretty much - a consistent number of points every season, and that tends to work for any player who starts their career at a big club and plays from a young age," Crawford explains. "Lamine Yamal is a perfect example of someone who is very likely to follow the Messi shaped curve.
"Then you have the Ronaldo G.O.A.T. Curve, which is the other option. This is more like an elongated S shape - the mathematical name is called a sigmoid - [which] is slow growth at the beginning, then a steep rise in the middle and slow growth towards the end"
An example of a player who is closer to the Ronaldo curve, he notes, is Jude Bellingham. The Real Madrid star wasn't posting significant goal numbers early in his career, enjoying his first double-figure season in his fourth year as a pro before finding another gear - exactly the same at the Portugal international.
With goals valued so highly, are more defensive-minded players ruled out of the picture? Not quite. Crawford recognises it's more difficult for them to claim top spot, but not impossible - and argues that's exactly how it should be.
"There absolutely is [space for a defensive player to do it]," he says. "Based on this algorithm, this index defining the best player, there absolutely is. I think it's interesting that Pedri comes in the top 10, because he's probably the least attacking.
"One of the questions I remember being asked around the first G.O.A.T. Index was the weighting on goals. and I think it does come down to this idea that goals are what wins you football matches, which is what wins you trophies. So whilst defence wins championships and all that, if you do not score goals then you draw every game 0-0 with the world's best defence - you're probably not going to win anything.
"So i think it's just the way the game works, it's always going to be biased to attacking players. But what i would say here is, just outside of the top 10 you did have Eduardo Camavinga and Aurelien Tchouameni, pretty much holding players, and also Rico Lewis whio i guess is kind of a full back.
"They are all scoring very highly on club titles - Manchester City, Real Madrid winning lots of things. I think they're going to be let down on the goals and assists measures but can certainly score highly on club titles international titles and as a result potentially those individual awards. It's certainly not outside the realms of possibiliy that Rico Lewis in five years wins a Ballon d'Or."
Lewis' team-mate Erling Haaland is another who is let down in one particular category. He hasn't come close to winning a major tournament with Norway, and indeed he has yet to even qualfiy for one in three attempts."
"I don't think it's impossible, but it is going to hamper the ability, and i actually think that's correct in a way," Crawford argues. "All of the players who are in the greatest of all time discussion, anyone who's realistically in that discussion has won an international title with their national team. Pele, Ronaldo, Messi, other names you could throw in.
"It does kind of feel a bit unfair on Erling Haaland, perhaps, but at the same time to me it feels like to be in that discussion - we're talking of the best of the best of the best - that does feel like a key element of it. But on the other hand if you look at Erling Haaland for example, who is in fourth, the range of his score is coming out as between 67 and 95. so mathematically he could easily get 95, it's completely possible.
"He would have to have incredible season after season winning several more Champions Leagues, et cetera, but that is accounting for the fact that he hasn't won any international titles. And the model takes what we know and takes it into the future, so i can't say for certain the model has assumed he would never win one, but that is built into it.
"It's very unlikely, i think, that those predictions would assume he's going to win an international title. In theory it looks as though he could get as high as 95, which would put him very very close to the Ronaldo-Messi level. So it's possible but you need everything else to go right."
Back to that player with the potential to hit 100, then. It's not Mbappe, who remains the most likely to lead the way. Haaland's international limitations are likely to prevent him from hitting those Messi-Ronaldo heights, while Lamine Yamal - despite having a very high potential peak - also falls just short.
Instead, perhaps surprisingly, Julian Alvarez is the only one of the 10 with the potential to hit full marks. The reason is his strikingly impressive trophy cabinet - including a Treble with Manchester City and World Cup with Argentina - though a summer move to Atletico Madrid could see that slow down.
"I suppose the alvarez thing was the surprise for me," Crawford adds. "It feels like it makes sense when you actually think about it, though you wouldn't have named him.
"Almost every tournament he has played in, he has won that trophy. He's never necessarily a really key component in all of those victories, and he scores really badly on individual awards because he hasn't been singled out for that purpose. But just in terms of a trophy collection, it's very hard to argue against that.
"Mbappe could go as high as 97, this model is predicting, but Alvarez could go as high as 100. But there's a bit more uncertainty in Alvarez than there is for Mbappe - again because of those first few years and then the big increase when he moved to Man City and won all the titles with Argentina."
If that all sounds like it will be functionally if not literally impossible to match Messi and Ronaldo, we should probably just read that as a reminder of how the pair were posting numbers like never before. Between 2010 and 2018, both men scored more than 40 club goal in every single season, with Messi's 73 in the 2011-12 season the kind of campaign you had to see to believe.
"One thing that came out in the original G.O.A.T. Index calculation was how far ahead of everyone else Ronaldo and Messi were," Crawford notes. "Ronaldo and Messi were in the 90s, Pele was in the 80s, and then everyone else was like 30 and below...the drop off was huge."
Based on the numbers, the prospect of one of the current crop hitting those heights feels remote. There are still heights to be hit, though, and we have a decent idea of which players are the most likely to hit them.
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