Joe Calzaghe's unbeaten record - the facts and the maths

[chinny]

I was under the impression that he had calculated the odds as you would do with an accumulator bet?? I.e. If you were to put a £1 accumulator bet on three even money football games. Then if game 1 comes in you get your stake back, plus your £1 winnings, meaning £2 goes onto the second game. If that comes in you get your stake back (£2), plus your winnings which is £2, meaning you've got £4 on the final game which would mean you getting £8 back if the 3rd game comes in (£4 stake and £4 winnings).

This to me would be a reasonable way of trying to evaluate how good Joe's achievements are statistically, by working back through all the odds and calculating what the odds would have been before his very 1st fight if you'd have put a £1 on and you could glance into the future and knew all his opponents and their odds - and would be really interesting to compare against the likes of RJJ until he got beat!!

Yep, I had. Thank you, you get it. Just like an accumulator. Using my assumptions the accumulator for 46 fights would be around 10-1

[Wax On]

If that's the way you worked it out, then I think it's a great idea. The odds a fighter has been when he is about to take on opponents throughout his career is a really good indicator of how much risk he has taken (or not taken).

If you worked this out for every fighter's last 20 fights (i.e. an accumulator style bet based on what return you'd get for them winning every one) then it would serve as a brilliant comparison between fighters based on how much risk the bookies actually thought they were taking at the time.

i.e. Calzaghe's would be boosted by the fact that he was a dog against Lacy, but because more often than not he has gone into fights as overwhelming favourite till recently, his odds for the last 20 fights may be accumulated odds of say 8 or 9 to 1.

Whereas someone like Pacquio who has probably had about 20 evenly matched fights in a row would probably have had accumulated odds of about 20 or 30 to 1. But then again, he lost along the way.

Would love to do this for some of the top fighters of our generation and see who it said was the bravest in terms of matchmaking v their fight record. Would make a great article I reckon.

[nobby_nobbins]

I think it's impressive that Calzaghe has managed to retain his winning record given the fragile state of his hands. He has broken his hands more than once against decent "B" class opponents like Robin Reid, but has gritted it out to the end. Just making it to the final bell with a broken hand is a colossal achievement in my book, but actually winning the fight strikes me as quite extraordinary.

[Phenomenal-Nutrition]

So if you beat 10,000 over 20years who are all 100-1.....

[chinny]

If that's the way you worked it out, then I think it's a great idea. The odds a fighter has been when he is about to take on opponents throughout his career is a really good indicator of how much risk he has taken (or not taken).

If you worked this out for every fighter's last 20 fights (i.e. an accumulator style bet based on what return you'd get for them winning every one) then it would serve as a brilliant comparison between fighters based on how much risk the bookies actually thought they were taking at the time.

i.e. Calzaghe's would be boosted by the fact that he was a dog against Lacy, but because more often than not he has gone into fights as overwhelming favourite till recently, his odds for the last 20 fights may be accumulated odds of say 8 or 9 to 1.

Whereas someone like Pacquio who has probably had about 20 evenly matched fights in a row would probably have had accumulated odds of about 20 or 30 to 1. But then again, he lost along the way.

Would love to do this for some of the top fighters of our generation and see who it said was the bravest in terms of matchmaking v their fight record. Would make a great article I reckon.

Exactly

[Latuch!]

There’s a lot of rubbish spouted on here and elsewhere about Joe Calzaghe’s record. I’ve done a bit of maths which I reckon proves just how incredible it is that he has remained undefeated at this level (even taking account of how poor some of his opponents have been).

I’ve used probability to work out just how unlikely it is even for an elite fighter like Joe to go 46 fights unbeaten

I’ve assumed some hopefully realistic odds for JC’s fights – don’t forget this is at the time he fought them - and I’ve tried to be harsh to Joe’s opponent. Stay with me on this.

The maths

Going in, the Lacy and Kessler fights were pretty much pick ‘em, evens

Next up is Hopkins where Joe is say 2-1

Joe is hot favourite in the RJJ fight (3-1 on)

Then the next layer, lets say (don’t forget this is at the time)

Eubank 3-1 on
Sheika 3-1 on
Brewer 3-1 on
Mitchell 3-1 on
RJJ 3-1 on
Reid 3-1 on

Next rung

Bika 4-1
Woodhall 4-1

All other defences (12) I assume are 5-1 on , still huge odds for a 2 horse race

That’s 23 fights

I’ll assume odds of 8-1 on for the other 23. At the time some of these were pretty tough (eg Mark Delaney)

Conclusion
Even allowing for the fact that Joe (might be easier to depersonalise this and call him fighter x) is a hot favourite elite fighter, he still had only a one in 10 chance (9.1 to 1 to be exact using these assumptions) of remaining undefeated all this time.

QED

This is a GREAT idea to compute it, however your computation is not correct!!

The probability FACTORISES, so the correct number is

2/3*[(3/4)^7]*[(4/5)^2]*[(5/6)^12]*[(8/9)^23] = 0.0004254363,

which is about 2351 to 1 in terms of odds.

[chinny]

about 2351 to 1 in terms of odds.

Please think before you post. I'll explain this one more time in layman's terms.
Wax on was right to liken all this to an accumulator bet, ie if an event is evens and two of them happen then the odds lengthen. JC is at least evens in all his fights. Sum all the cumulative odds of him winning and you get about 10 to one (9-1 to be exact).
Here are the workings.

1 RJJ 0.33
2 Hop 0.33
3 Kessler 0.50
4 Lacy 0.50
5 Eubank 0.33
6 Sh 0.33
7 Br 0.33
8 Mit 0.33
9 Reid 0.33
10 Bika 0.25
11 Woodhall 0.25
12 Oth 0.20
13 Oth 0.20
14 Oth 0.20
15 Oth 0.20
16 Oth 0.20
17 Oth 0.20
18 Oth 0.20
19 Oth 0.20
20 Oth 0.20
21 Oth 0.20
22 Oth 0.20
23 Oth 0.20
24 bum 0.13
25 bum 0.13
26 bum 0.13
27 bum 0.13
28 bum 0.13
29 bum 0.13
30 bum 0.13
31 bum 0.13
32 bum 0.13
33 bum 0.13
34 bum 0.13
35 bum 0.13
36 bum 0.13
37 bum 0.13
38 bum 0.13
39 bum 0.13
40 bum 0.13
41 bum 0.13
42 bum 0.13
43 bum 0.13
44 bum 0.13
45 bum 0.13
46 bum 0.13

9.11

[Latuch!]

about 2351 to 1 in terms of odds.

Please think before you post. I'll explain this one more time in layman's terms.
Wax on was right to liken all this to an accumulator bet, ie if an event is evens and two of them happen then the odds lengthen. JC is at least evens in all his fights. Sum all the cumulative odds of him winning and you get about 10 to one (9-1 to be exact).
Here are the workings.

1 RJJ 0.33
2 Hop 0.33
3 Kessler 0.50
4 Lacy 0.50
5 Eubank 0.33
6 Sh 0.33
7 Br 0.33
8 Mit 0.33
9 Reid 0.33
10 Bika 0.25
11 Woodhall 0.25
12 Oth 0.20
13 Oth 0.20
14 Oth 0.20
15 Oth 0.20
16 Oth 0.20
17 Oth 0.20
18 Oth 0.20
19 Oth 0.20
20 Oth 0.20
21 Oth 0.20
22 Oth 0.20
23 Oth 0.20
24 bum 0.13
25 bum 0.13
26 bum 0.13
27 bum 0.13
28 bum 0.13
29 bum 0.13
30 bum 0.13
31 bum 0.13
32 bum 0.13
33 bum 0.13
34 bum 0.13
35 bum 0.13
36 bum 0.13
37 bum 0.13
38 bum 0.13
39 bum 0.13
40 bum 0.13
41 bum 0.13
42 bum 0.13
43 bum 0.13
44 bum 0.13
45 bum 0.13
46 bum 0.13

9.11

Thank you for your explanation, however you are completely wrong.

If you toss a coin 10 times, the probablity of heads is each time 0.50, and the probablity of getting 10 heads in a row is (1/2)^10 = 1/1024 = 0.001 (approximately) and the odds are 1024 to 1.

However your calculation in this case would give you 1/5:
coin 0.50
coin 0.50
coin 0.50
coin 0.50
coin 0.50
coin 0.50
coin 0.50
coin 0.50
coin 0.50
coin 0.50
cumulative = 5
so 5:1
which is clearly wrong.

I also think before I post and I also got a PhD in probability (and this is not a joke), so thanks for your explanation in layman's terms, it just showed me what kind of error you are making.

[chinny]

Thank you for your explanation, however you are completely wrong.

I also think before I post and I also got a PhD in probability (and this is not a joke), so thanks for your explanation in layman's terms, it just showed me what kind of error you are making.

I apologise for my insolence. I've just calculated if you bet £1 on Calzaghe's first fight and continued the accumulator through 46 and yes it will return £1000's.

Again, apologies to those who got this right when I was wrong and especially to you Latuch.

PHD in probability, who'd have bloody thought it!

[Latuch!]

Lets search for another JC coming and make thousends or millions on betting

[chinny]

Lets search for another JC coming and make thousends or millions on betting

imagine if you'd done that on Michael Spinks! (the only I guy I can think of off the top of my head who won all his fights except the last one)

[Latuch!]

Lets search for another JC coming and make thousends or millions on betting

imagine if you'd done that on Michael Spinks! (the only I guy I can think of off the top of my head who won all his fights except the last one)

for this reason never bet everything and save some £ at least to get drunk...

Naseem Hamed is also a good example, I wonder what were the odds for him going into the Barrera fight...

[jamesmcdonnell]

If you have a qualification in probability, then you must surely realise then there is a big difference between flipping a coin and a boxing match.

A coin doesn't have 'form' a boxer does, and therefore the odds are not rooted in probability, which is merely a mathematical expression, to compare a boxing match with a coin toss is clearly falacious.

[stujones]

And also James, based on the form/ability of both guys has a huge baring on the odds. For example, should Roy Jones and Joe Calzaghe fought the exact same guys in the same order - then the probablility for Joe to remain undefeated would have been less, because due to the bookies perceiving Roy to be the better the odds on him winning are alot better.

Plus the odds used in the original example are off the mark.

[Latuch!]

If you have a qualification in probability, then you must surely realise then there is a big difference between flipping a coin and a boxing match.

A coin doesn't have 'form' a boxer does, and therefore the odds are not rooted in probability, which is merely a mathematical expression, to compare a boxing match with a coin toss is clearly falacious.

The odds represent "market belief" (avarage belief of the betting comunity) of a probabiiity of an outcome of a boxing match before the match and in this sense the correspondance is clear and mathematically formalized. The probability is called "implied probability" and you can check it on some bookies pages.

If you have 3.0 on Valuev winning on points against Holy, this means that you get 2 extra punds for each pound put at exposure, so the implied probability that Valuev wins on points is about 1/3, and the implied probability, that the outcome is different from Valuev on points is about 2/3.

You can compute this implied probabilities of "Valuev points" and "outcome different from Valuev points" (denote it by p and 1-p respectively) by solving the equation
p*2 + (1-p)*(-1) = 0
So you win 2 pounds with probability p and lose 1 pound with probability 1-p.

In particular if you believe that the probability that Valuev wins on points is indeed bigger that the implied probability = p = 1/3, then you should bet on it (which I actually did), because if you are right you will win on avarage (as mathematically speaking, you have a positive expected value of your gain in this case).

You will be surprised how much mathemtics and probability the bookies use to modell a sporting event and calculate the probablities of each outcome to set initial odds. The odds are then driven by the market and thats why they change over time.

Here you have a company which is specialized in computing probabilities of different outcomes of sporting events. This company hires nearly 100 probabilists and statisticians.
http://www.atassltd.co.uk/
Bookies usually buy their initial odds from such companies as they do not have an appropriate research staff to compute these probabilities accurately.

[BigEars]

Boxing is a two horse race, and if you discount the lacy/delaney fights then isn't his odds at remaining defeated very high?

Nope otherwise accumulators on sports such as boxing and football wouldn't provide such favourable odds, the odds are so favourable because the more matches the chance of one finally losing is greatly increased.

[chinny]

If you have a qualification in probability, then you must surely realise then there is a big difference between flipping a coin and a boxing match.

referring to a PHD as 'a qualification' is like saying Julian Jackson could bang a bit

[jamesmcdonnell]

If you have a qualification in probability, then you must surely realise then there is a big difference between flipping a coin and a boxing match.

A coin doesn't have 'form' a boxer does, and therefore the odds are not rooted in probability, which is merely a mathematical expression, to compare a boxing match with a coin toss is clearly falacious.

The odds represent "market belief" (avarage belief of the betting comunity) of a probabiiity of an outcome of a boxing match before the match and in this sense the correspondance is clear and mathematically formalized. The probability is called "implied probability" and you can check it on some bookies pages.

If you have 3.0 on Valuev winning on points against Holy, this means that you get 2 extra punds for each pound put at exposure, so the implied probability that Valuev wins on points is about 1/3, and the implied probability, that the outcome is different from Valuev on points is about 2/3.

You can compute this implied probabilities of "Valuev points" and "outcome different from Valuev points" (denote it by p and 1-p respectively) by solving the equation
p*2 + (1-p)*(-1) = 0
So you win 2 pounds with probability p and lose 1 pound with probability 1-p.

In particular if you believe that the probability that Valuev wins on points is indeed bigger that the implied probability = p = 1/3, then you should bet on it (which I actually did), because if you are right you will win on avarage (as mathematically speaking, you have a positive expected value of your gain in this case).

You will be surprised how much mathemtics and probability the bookies use to modell a sporting event and calculate the probablities of each outcome to set initial odds. The odds are then driven by the market and thats why they change over time.

Here you have a company which is specialized in computing probabilities of different outcomes of sporting events. This company hires nearly 100 probabilists and statisticians.
http://www.atassltd.co.uk/
Bookies usually buy their initial odds from such companies as they do not have an appropriate research staff to compute these probabilities accurately.

I would be very surprised - I have a friend who is a professional gamber, and former oddsmaker for a major bookmaker, and he told me that they don't have any such people on their payroll. They have experts in particular sports - who use their own statistical models - not mathematicians or probability gurus.

I know that probability has a major influence, because my mate comes round and bores me shitless insisting I give percentile values to various outcomes for each fight on a spreadsheet - I find it tedious myself - but he actually gets off on it the sad bastard.

[Loftgroov]

The opening analysis is badly flawed.

You don’t establish long-term probability based on the sequential addition of subjective odds for the outcome of each previous contest. Furthermore, bookmaker’s odds are just subjective probabilities.

[Latuch!]

They have experts in particular sports - who use their own statistical models - not mathematicians or probability gurus.

So if someone is an expert in particular sport and uses a statistical model additionally, then he is a statistician, isn't he?

I never said you take a probability guru who understands boxing as good as my grandmother to compute odds...

Have a look at job openings at the company I linked. They are looking for people who have a degree in statistics or mathematical modelling AND have a very sound knowledge in a particular sport.

[jamesmcdonnell]

They have experts in particular sports - who use their own statistical models - not mathematicians or probability gurus.

So if someone is an expert in particular sport and uses a statistical model additionally, then he is a statistician, isn't he?

I never said you take a probability guru who understands boxing as good as my grandmother to compute odds...

Have a look at job openings at the company I linked. They are looking for people who have a degree in statistics or mathematical modelling AND have a very sound knowledge in a particular sport.

Perhaps it has changed a little then in recent years - My Mate Stuart worked for various bookmakers, he had no background in mathematics - however, his old man was a bookmaker, so he didn't really need to I guess.

[prime]

Hopkins swerved Joe for 5M and took about $100,000 to fight some nobody! FACT! The only person who Joe could have fought was Ottke!! hopkins talks like a beast but runs and holds like a coward when the fight starts! he didnt take a forward step even after dropping Calzaghe. Please get real people.

[Dioufy]

Frank's a master at making people believe his man was avoided. Look at Calzaghe/Johnson, Calzaghe/Froch and Macca/Hide. The sad part is, I could name a hell of a lot more fights if I wanted to, but what's the point, Frank will probably sue my arse.

[banjo]

I've always been wary of that story but then again I've never read or heard anything about Hopkins denying the story. Lets put it this way, if it was me that was being accused of pulling out of a fight or turning down offers then I'd be straight out there to tell the truth.

[Dioufy]

I think Hopkin's is thick-skinned enough to ignore what Calzaghe, and mainly Warren, say about him.