by Dr Adrian Worton
It's the best time of year right now, as the Snooker World Championship returns. As usual (but perhaps not forever), it takes place in Sheffield's Crucible Theatre.
I've attended a few famous sporting venues and occasions - Wembley, Murrayfield, Anfield, Old Trafford, Glebe Park, The Ashes, the Olympics, etc. But it was visiting the Crucible for the first time that I found the most breathtaking. Perhaps it's the dated seat covers, but you immediately feel connected to the sport's rich history. You immediately feel what it would be like to watch that 1985 final from your seat. The modest size of the venue means wherever you sit you feel a part of the match. Fans at football matches can yell at the top of their voices and not influence a jot, whereas at the Crucible you can't open a bag of sweets without getting told off on international TV (the trick is to wait for the applause).
It's the best time of year right now, as the Snooker World Championship returns. As usual (but perhaps not forever), it takes place in Sheffield's Crucible Theatre.
I've attended a few famous sporting venues and occasions - Wembley, Murrayfield, Anfield, Old Trafford, Glebe Park, The Ashes, the Olympics, etc. But it was visiting the Crucible for the first time that I found the most breathtaking. Perhaps it's the dated seat covers, but you immediately feel connected to the sport's rich history. You immediately feel what it would be like to watch that 1985 final from your seat. The modest size of the venue means wherever you sit you feel a part of the match. Fans at football matches can yell at the top of their voices and not influence a jot, whereas at the Crucible you can't open a bag of sweets without getting told off on international TV (the trick is to wait for the applause).
One of the most famous aspects of the Crucible is its eponymous curse: no first-time winner has defended their title. Last year was the first since 2019 that we had a new champion - Luca Brecel - so inevitably there was a lot of talk about the curse heading into this championship. Luca is someone who has defied history, such as in his record comeback in last year's semi final, but he still succumbed to the curse as he lost a thrilling opening day match 10-9 to Dave Gilbert.
To be clear, not many people expected Luca to win this year's tournament; you could back him at 18/1 pre-tournament which implies a likelihood of roughly 5%. But there have been more likely victors; the last first-time winner was Judd Trump, who was the 11/4 favourite (around 33%) to defend his crown. The curse is notable because of the cumulative effect of all the unsuccessful defending champions.
However, I have heard some people connected to snooker - commentators, pundits, etc - dismiss how noteworthy the Crucible Curse is. There are a lot of players and you can't expect one specific player to win.
So, in this article we are going to try and quantify how unlikely it is that the curse is still standing.
The Champions
First of all, we need to know how many opportunities there have been for someone to defend their first Crucible title. The wording is important here - we are including players such as Ray Reardon and Alex Higgins who won world titles before the championship was held at the Crucible, as they all failed to defend their first title won at the Crucible.
Here is the Crucible roll of honour:
To be clear, not many people expected Luca to win this year's tournament; you could back him at 18/1 pre-tournament which implies a likelihood of roughly 5%. But there have been more likely victors; the last first-time winner was Judd Trump, who was the 11/4 favourite (around 33%) to defend his crown. The curse is notable because of the cumulative effect of all the unsuccessful defending champions.
However, I have heard some people connected to snooker - commentators, pundits, etc - dismiss how noteworthy the Crucible Curse is. There are a lot of players and you can't expect one specific player to win.
So, in this article we are going to try and quantify how unlikely it is that the curse is still standing.
The Champions
First of all, we need to know how many opportunities there have been for someone to defend their first Crucible title. The wording is important here - we are including players such as Ray Reardon and Alex Higgins who won world titles before the championship was held at the Crucible, as they all failed to defend their first title won at the Crucible.
Here is the Crucible roll of honour:
So that's 21 winners. And that allows us to make some quick estimates at the Crucible curse's likelihood.
Probability distributions
Basic uniform
Let's start with the simplest calculation: there are 32 players, so let's say the chance of a specific player winning the event is 1/32. Therefore, the probability of our 21 champions all failing to win the year is:
Probability distributions
Basic uniform
Let's start with the simplest calculation: there are 32 players, so let's say the chance of a specific player winning the event is 1/32. Therefore, the probability of our 21 champions all failing to win the year is:
(1 - 1/32)^21 = (31/32)^21 = 0.96875^21 = 0.513388
Therefore, using a basic uniform distribution, the probability of the Crucible curse occurring is 51.3%. So more likely than not.
Uniform seeds
The above method is clearly very simplistic. You would think that the person who won the previous event would be a better player than an average player in the competition. So let's just look at the seeds (the top-ranked 16 players). Only twice in 47 editions has the a seeded player not won the title. To put it another way, for a given World Championship, there is a 95.9% chance it was won by a seed.
The defending champion is always one of the 16 seeds (see note at the bottom). So we could say the odds of them winning is 95.9% multiplied by 1/16. So therefore, the probability that none of our 21 have ever triumphed is:
Uniform seeds
The above method is clearly very simplistic. You would think that the person who won the previous event would be a better player than an average player in the competition. So let's just look at the seeds (the top-ranked 16 players). Only twice in 47 editions has the a seeded player not won the title. To put it another way, for a given World Championship, there is a 95.9% chance it was won by a seed.
The defending champion is always one of the 16 seeds (see note at the bottom). So we could say the odds of them winning is 95.9% multiplied by 1/16. So therefore, the probability that none of our 21 have ever triumphed is:
(1 - (0.959 x 1/16))^21 = 0.94005^21 = 0.273011
Using a uniform distribution among the seeds gives us a 27.3% chance for the curse. So we're now into the territory of 'unlikely'.
These uniform distributions treat our 21 winners as equal, but they are clearly not. Not to pick on anybody, but it was more likely that Stephen Hendry would retain his 1990 title than Graeme Dott would retain his 2006 triumph. So let's have a look at stratifying our winners based on their individual likelihood of beating the curse.
Ranking
We have already used players' rankings to a degree, with our uniform seeds option. There, we calculated the probability of a top 16 player winning the tournament and applied that to every defending champion.
Let's do the same, but make it more granular. Let's look at how many wins each ranking position has obtained:
These uniform distributions treat our 21 winners as equal, but they are clearly not. Not to pick on anybody, but it was more likely that Stephen Hendry would retain his 1990 title than Graeme Dott would retain his 2006 triumph. So let's have a look at stratifying our winners based on their individual likelihood of beating the curse.
Ranking
We have already used players' rankings to a degree, with our uniform seeds option. There, we calculated the probability of a top 16 player winning the tournament and applied that to every defending champion.
Let's do the same, but make it more granular. Let's look at how many wins each ranking position has obtained:
For consistency and speed, we have used the old-fashioned method (up to 2010) whereby players' ranking is the position they ended up at by the end of the previous season.
Primarily thanks to messyrs Davis and Hendry, players ranked 1st have won the World Championship 15 times, or 31.9% of the time. So a given player ranked 1st would have approximately a 31.9% chance of winning the title.
It feels silly to say that the 3rd ranked player (6 titles) actually has more of a chance of winning than the 2nd ranked player (3 titles), so we will group the rest of the top 16. Players ranked 2nd-5th account for a total of 16 titles, 34.0%. So players ranked in this range have a 8.5% chance of winning.
The rest of the top 16 (6th-16th) provide a total of 14 titles (29.8%), meaning those players have a 2.7% chance of winning.
This is where our 21 first-time winners ranked going into the following year's event:
Primarily thanks to messyrs Davis and Hendry, players ranked 1st have won the World Championship 15 times, or 31.9% of the time. So a given player ranked 1st would have approximately a 31.9% chance of winning the title.
It feels silly to say that the 3rd ranked player (6 titles) actually has more of a chance of winning than the 2nd ranked player (3 titles), so we will group the rest of the top 16. Players ranked 2nd-5th account for a total of 16 titles, 34.0%. So players ranked in this range have a 8.5% chance of winning.
The rest of the top 16 (6th-16th) provide a total of 14 titles (29.8%), meaning those players have a 2.7% chance of winning.
This is where our 21 first-time winners ranked going into the following year's event:
So we have four ranked 1st, thirteen ranked 2nd-5th and four ranked outside the top five. Therefore, our new Crucible Curse calculation is as follows:
(1-0.319)^4 x (1 - 0.085)^13 x (1 - 0.027)^4 = 0.06058
So, factoring in the relative strengths of the 21 first-time Crucible winners we have a probability of 6.1% for the Crucible curse. This is much lower, and I feel more accurately reflects how much of a quirk the curse is. It is pretty unlikely, but it is short of the 5% theshold that is considered "statistically significant".
The method above of course isn't exact either. For example, we gave Trump a 8.5% chance of winning compared to the 33% the bookies gave him. If anybody can find pre-tournament odds for every World Championship, I would love to use those to find an even more accurate percentage. With Trump joined by Davis and O'Sullivan in having a fairly low percentage, maybe the outcome would be below 5%.
Other events
Another way to put the curse into context is to look at other events, and see if any of those have seen anything similar. Specifically, we are going to look at comparable events and see if any of the last 21 first-time winners of those went on to retain their first title. We will just look at individual sports with annual events, at the pinnacle of the sport. So for example, we won't look at athletics, as its biggest events are the Olympics (quadrennial) and World Championships (bienniel).
This isn't by any means an exhaustive list, just the events that came to mind first:
The method above of course isn't exact either. For example, we gave Trump a 8.5% chance of winning compared to the 33% the bookies gave him. If anybody can find pre-tournament odds for every World Championship, I would love to use those to find an even more accurate percentage. With Trump joined by Davis and O'Sullivan in having a fairly low percentage, maybe the outcome would be below 5%.
Other events
Another way to put the curse into context is to look at other events, and see if any of those have seen anything similar. Specifically, we are going to look at comparable events and see if any of the last 21 first-time winners of those went on to retain their first title. We will just look at individual sports with annual events, at the pinnacle of the sport. So for example, we won't look at athletics, as its biggest events are the Olympics (quadrennial) and World Championships (bienniel).
This isn't by any means an exhaustive list, just the events that came to mind first:
Event |
Sport |
Title defences |
Players |
World Drivers' Championship |
F1 |
6 |
Prost, Schumacher, Hakkinen, Alonso, Vettel, Verstappen |
Masters |
Golf |
1 |
Faldo |
PGA Championship |
Golf |
2 |
Woods, Koepka |
US Open |
Golf |
1 |
Koepka |
The Open |
Golf |
1 |
Harrington |
Australian Open Men's Singles |
Tennis |
6 |
Vilas, Kriek, Wilander, Edberg, Lendl, Courier |
Australian Open Women's Singles |
Tennis |
6 |
Graf, Seles, Hingis, Capriati, Azarenka, Sabalenka |
French Open Men's Singles |
Tennis |
3 |
Courier, Bruguera, Nadal |
French Open Women's Singles |
Tennis |
2 |
Graf, Seles |
Wimbledon Men's Singles |
Tennis |
5 |
Newcombe, Borg, Becker, Sampras, Federer |
Wimbledon Women's Singles |
Tennis |
4 |
Navratilova, Graf, V Williams, S Williams |
US Open Men's Singles |
Tennis |
5 |
McEnroe, Lendl, Edberg, Rafter, Federer |
US Open Women's Singles |
Tennis |
3 |
Graf, Seles, V Williams |
Steffi Graf was good, wasn't she?
So, every sport above has at least somebody who has defied its equivalent of the Crucible curse. In three of golf's majors there is just one player who has managed the feat, whereas in tennis every event has multiple who have managed it. It's a selection of famous faces, such as Graf, Roger Federer, Rafael Nadal, the Williams sisters, etc. Novak Djokovic is notable by his absence though.
I would argue that of the three sports above, the tennis competitions are by far the most similar to the Snooker World Championship, as they too are based on knockout matches. The open nature (pun unintended) of golf competitions strongly lends itself to a high variance in tournament winners, whilst F1 is mainly driven (pun also unintended) by the quality of the cars rather than the drivers.
Snooker
We can also look at snooker's other events to see if the sport itself lends itself to making title defences difficult. There are only two events that have a similar prestige to the World Championship - the UK Championship and the Masters. Most events also don't have enough former champions for a similar comparison.
Both the UK Championship and the Masters have had two first-time winners defend their titles. The UK has had the familiar duo of Steve Davis and Stephen Hendry, whilst the Masters had Hendry and Paul Hunter.
Snooker's Women's World Championship has had 15 different winners in total, 3 of whom defended their first title: Allison Fisher, Kelly Fisher and Reanne Evans.
Summary
The evidence is pretty clear that the Crucible curse is pretty unlikely. I can't easily find a comparable event with a similar record, and a fairly rough statistical analysis suggests it has a very low likelihood of occurring. But it's not outrageously unlikely, which feels about right.
All the talk coming into this year's World Championship suggests that the event will be moved away from the Crucible when its contract ends in 2027. I won't go into that, other than that I don't like the idea, as I suggested in the introduction.
If that is the case there are four more Crucible champions to come (including one from the current championship). With Brecel already out, that leaves three opportunities for somebody to win their first title and then defend it. Will somebody break the curse or will the Crucible remain undefeated? It would be a fitting legacy for the venue, but it would be exciting if somebody goes close.
(Very important) Addendum
Somehow, criminally, I have missed out Mark Selby (one of my favourite players!) from the list of Crucible winners! I'm so sorry, Mark!
Naturally, the inclusion of another player changes the calculations above:
As we now have 22 champions, it also means the number of successful first-time title defences in other events may be higher too.
So, every sport above has at least somebody who has defied its equivalent of the Crucible curse. In three of golf's majors there is just one player who has managed the feat, whereas in tennis every event has multiple who have managed it. It's a selection of famous faces, such as Graf, Roger Federer, Rafael Nadal, the Williams sisters, etc. Novak Djokovic is notable by his absence though.
I would argue that of the three sports above, the tennis competitions are by far the most similar to the Snooker World Championship, as they too are based on knockout matches. The open nature (pun unintended) of golf competitions strongly lends itself to a high variance in tournament winners, whilst F1 is mainly driven (pun also unintended) by the quality of the cars rather than the drivers.
Snooker
We can also look at snooker's other events to see if the sport itself lends itself to making title defences difficult. There are only two events that have a similar prestige to the World Championship - the UK Championship and the Masters. Most events also don't have enough former champions for a similar comparison.
Both the UK Championship and the Masters have had two first-time winners defend their titles. The UK has had the familiar duo of Steve Davis and Stephen Hendry, whilst the Masters had Hendry and Paul Hunter.
Snooker's Women's World Championship has had 15 different winners in total, 3 of whom defended their first title: Allison Fisher, Kelly Fisher and Reanne Evans.
Summary
The evidence is pretty clear that the Crucible curse is pretty unlikely. I can't easily find a comparable event with a similar record, and a fairly rough statistical analysis suggests it has a very low likelihood of occurring. But it's not outrageously unlikely, which feels about right.
All the talk coming into this year's World Championship suggests that the event will be moved away from the Crucible when its contract ends in 2027. I won't go into that, other than that I don't like the idea, as I suggested in the introduction.
If that is the case there are four more Crucible champions to come (including one from the current championship). With Brecel already out, that leaves three opportunities for somebody to win their first title and then defend it. Will somebody break the curse or will the Crucible remain undefeated? It would be a fitting legacy for the venue, but it would be exciting if somebody goes close.
(Very important) Addendum
Somehow, criminally, I have missed out Mark Selby (one of my favourite players!) from the list of Crucible winners! I'm so sorry, Mark!
Naturally, the inclusion of another player changes the calculations above:
- The basic uniform distribution changes from 51.3% to 49.7%, so just tipping it from being slightly more likely to occur to slightly more likely not to occur
- The uniform seed distribution moves down slightly from 27.3% to 25.7%.
- As Mark was ranked #1 coming into his 2015 title defence our final probability based on rankings gives him a 31.9% chance of retaining his title in 2015. That changes the overall Crucible curse probability from 6.1% to 4.1%, meaning the curse is indeed statistically significant!
As we now have 22 champions, it also means the number of successful first-time title defences in other events may be higher too.
Note
The defending champion is always top seed regardless of their world ranking. Strictly speaking, Shaun Murphy was ranked 21st going into his title defence, but that was when world rankings stayed the same over a full season. The year after he won the world title he also won the European Masters and reached at least the quarter finals in several events, so it seems fair to consider him at a level that would see him ranked in the top 16.
The defending champion is always top seed regardless of their world ranking. Strictly speaking, Shaun Murphy was ranked 21st going into his title defence, but that was when world rankings stayed the same over a full season. The year after he won the world title he also won the European Masters and reached at least the quarter finals in several events, so it seems fair to consider him at a level that would see him ranked in the top 16.
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