( o ) ABCDEs - Ranking puzzle...( o )

[Decebal]

1) How would you rank fighters A, B, C, D and E if:

A could beat B, D and E but not C
B could beat C and D, but not A or E
C could beat A and E, but not B or D
D could beat C and E, but not A or B
E could beat B, but not A or C or D?

2) should fighters be ranked according to the names they have beaten on their resume in the past or just according to their likely present form, based on showings in recent fights and effects of recent fights on their likely present state?

[JohnThomas1]

Well A beats 3 of em so that's gotta be good.

[Decebal]

Well A beats 3 of em so that's gotta be good.

come on, mate...what order A to E?

[McGrain]

This is like a puzzle I would do on a really long train journey.

[Decebal]

This is like a puzzle I would do on a really long train journey.

Yeah, well, better sort it out theoretically now, before you have to sort it out practically, in a couple of days!;)

[McGrain]

Yeah, well, better sort it out theoretically now, before you have to sort it out practically, in a couple of days!;)

It's far easier when you have a solid perception of a given fighter.

Nevertheless i'd be up for it, but I have to go to the dentist now fortunatley :lol:

[Decebal]

Nevertheless i'd be up for it, but I have to go to the dentist now fortunatley :lol:

:rofl


:oops:

[Mendoza]

How would you rank fighters A, B, C, D and E if:

A could beat B, D and E but not C
B could beat C and D, but not A or E
C could beat A and E, but not B or D
D could beat C and E, but not A or B
E could beat B, but not A or C or D?

#1 = Fighter A. he is 3-1, and lost to C on a style match up.

#2 = Fighter C. He is 2-2, but beat fighter A ( 3-1 ) who was the best of the five.

#3 = Both fighter D and B are 2-2. Neither beat fighter A, who was the best of the bunch. I think Fighter B was better than fighter D because he beat him head to head. However, fighter B lost to fighter E, who was 1-3! Both these guys are journeyman.

#4 = Fighter E. He is 1-3

Here is how I would rank them:

A
C
B
D
E

[Decebal]

I've added another crucial question...would love to see your answer.:good

[cross_trainer]

1) How would you rank fighters A, B, C, D and E if:

A could beat B, D and E but not C
B could beat C and D, but not A or E
C could beat A and E, but not B or D
D could beat C and E, but not A or B
E could beat B, but not A or C or D?

Since these guys are presumably completely equal except for who they've beaten, they should be ranked as follows:


A -- Because he beat 3 of them.
C -- Because he could beat the guy who could beat 3 of them.
B -- He could beat two guys who beat 2 opponents
D -- He beat one guy who beat 2 opponents and one who could beat 1
E -- He beat only one guy.


2) should fighters be ranked according to the names they have beaten on their resume in the past or just according to their likely present form, based on showings in recent fights and effects of recent fights on their likely present state?

They should be ranked according to present effectiveness, BUT past performances can occasionally be useful in judging that effectiveness. Thus, Wlad's trail of destruction in the heavyweight division prior to beating Peter is relevant in showing that his recent performances have not been a fluke.

[China_hand_Joe]

Since these guys are presumably completely equal except for who they've beaten, they should be ranked as follows:


A -- Because he beat 3 of them.
C -- Because he could beat the guy who could beat 3 of them.
B -- He could beat two guys who beat 2 opponents
D -- He beat one guy who beat 2 opponents and one who could beat 1
E -- He beat only one guy.



They should be ranked according to present effectiveness, BUT past performances can occasionally be useful in judging that effectiveness. Thus, Wlad's trail of destruction in the heavyweight division prior to beating Peter is relevant in showing that his recent performances have not been a fluke.

I got the same as you.

The only thing for consideration is, was C's victory over A due to a stylistic advantage?

[cross_trainer]

I got the same as you.

The only thing for consideration is, was C's victory over A due to a stylistic advantage?

The same question could be posed for all of the wins.

Like you, I would say that a win over the best of the bunch, in the complete absence of more information about the fighters, is more important than winning over two 2-2 guys.

[Decebal]

I will post what I consider to be the right answer, including the reasoning behind it, to anyone, if you're interested; just pm me please!:good

[Decebal]

I think these are important questions...let's sort these things out before you all get going!:good

[Decebal]

I have added a poll, to allow us to keep track of things!:good

[Decebal]

Thank you, tobkhan...!

[TBooze]

A is tops as he is 3-1

B is second: he is 2-2, but beats C and D who are also 2-2

D is third: he is 2-2, but loses to B, but beats C

C is fourth: he too is 2-2 but loses to both his peers B and D

E is fifth as he is 1-3

It must be assumed all fighters were of very similar ability, thus no win means more than any other, other than in breaking a tie against your peer.

[Decebal]

Some good answers; some - clearly wrong!:deal

[Decebal]

Any more takers? Too difficult for you?

[Decebal]

2-3 takers! Very brave!

[Decebal]

I will post my answer in 24 hours!:D

[Vockerman]

I find myself in the unenviable position of disagreeing with my esteemed colleague Cross Trainer - which I have found in the past to be a position fraught with peril - so I will be a little more mathematical to attempt to justify my rankings. Please bear with me.

If I have made an error in my analysis I respectfully invite you to please point it out to me.

My central premise is simple -
No one boxes to lose :hey

So IF wins are all that matter

A is first he has three wins.

B,C and D each have 2 wins - what do we do now?

Quality of opposition - count the wins their opponents have (wins are all that matter) -
B has wins over guys that have combined 4 wins (C has 2 wins D has 2 wins)
C has wins over guys that have 4 wins (A has 3 and E has 1)

So they are still tied

D has wins over guys that have 3 wins (C has 2 and E has 1) so he has an even record with B and C over the weaker opposition and should go behind B and C.

Between B and C they have even scores of wins and even strength of opposition ( 4 wins by guys they beat ) so it comes down to head to head in which B takes it by virtue of his win against C

E is the weakest with no real argument for avoiding last place.

A B C D E

IF WINNING IS ALL THAT MATTERS :good

[Decebal]

Well no one boxes to lose :hey

So IF wins are all that matter

A is first he has three wins.

B,C and D each have 2 wins - what do we do now?

Quality of opposition - count the wins their opponents have (wins are all that matter) -
B has wins over guys that have combined 4 wins (C has 2 wins D has 2 wins)
C has wins over guys that have 4 wins (A has 3 and E has 1)

So they are still tied

D has wins over guys that have 3 wins (C has 2 and E has 1) so he has an even record with B and C over the weaker opposition and should go behind B and C.

Between B and C they have even scores of wins and even strength of opposition ( 4 wins by guys they beat ) so it comes down to head to head in which B takes it by virtue of his win against C

E is the weakest with no real argument for avoiding last place.

A B C D E

IF WINNING IS ALL THAT MATTERS :good

Does it no matter whom they win against, though? Methinks so...good effort, but have another go!:good

[C. M. Clay II]

Since these guys are presumably completely equal except for who they've beaten, they should be ranked as follows:


A -- Because he beat 3 of them.
C -- Because he could beat the guy who could beat 3 of them.
B -- He could beat two guys who beat 2 opponents
D -- He beat one guy who beat 2 opponents and one who could beat 1
E -- He beat only one guy.

I agree with this.

[Decebal]

I agree with this.

Unfortunately, it's wrong...:|

[Decebal]

Hint: use logic and a systematic approach to find the right answer...don't simply use your gut instinct!:good

[ironchamp]

1) How would you rank fighters A, B, C, D and E if:

A could beat B, D and E but not C
B could beat C and D, but not A or E
C could beat A and E, but not B or D
D could beat C and E, but not A or B
E could beat B, but not A or C or D?

2) should fighters be ranked according to the names they have beaten on their resume in the past or just according to their likely present form, based on showings in recent fights and effects of recent fights on their likely present state?

My analysis:

#1 - Fighter "A" seems to be the best fighter of the bunch, my guess is that he's probably the most talented of the group and the most consistent fighter who just didnt match up very well with "C"

#2 - I give fighter "C" second place. Given that we don't have a body of work to go by, his wins over the best and worst fighter of the group means, at the very least, he appears to be a competant contender that can rise to the occasion but clearly has his limitations hence the losses.*

#3 - Third Place goes to Fighter "B" the dangerous but inconsistent puncher. I label him a puncher and Based on his losses more so than his wins. He lost to the best and worst fighters. His loss to A was not so surprising given A's superior ability. But his loss to E is clearly a case of fighters blowing "give me" fights. Punchers tend to be more inconsistent than boxers. A limited puncher can concievably beat good fighters (C,D) based on his physical attributes but will fall short against an elite fighter with stellar chin (A). Furthermore they are likely to come in over confident against lesser fighters (E).*


#4 - Fighter "D" has a win over C and E showing that he can beat a Trial Horse and a decent contender. Probably a semi skilled fighter with an average chin to the extent that he lost to the best fighter and he lost to a dangerous puncher. His losses are respectable. Why does he come in 4th? because Fighter "C" edges him based of his win over the best fighter and Fighter "B" edges him because of thier head to head match up.

#5 - I think its pretty obvious that Fighter "E" comes in last. Though we shouldnt speculate that he's a terrible fighter.




*C and B to me are the only interchangable ones to me. A, D and E are the only ones whose places IMO should be 1, 4 and 5 respectively.

[Decebal]

My analysis:

#1 - Fighter "A" seems to be the best fighter of the bunch, my guess is that he's probably the most talented of the group and the most consistent fighter who just didnt match up very well with "C"

#2 - I give fighter "C" second place. Given that we don't have a body of work to go by, his wins over the best and worst fighter of the group means, at the very least, he appears to be a competant contender that can rise to the occasion but clearly has his limitations hence the losses.*

#3 - Third Place goes to Fighter "B" the dangerous but inconsistent puncher. I label him a puncher and Based on his losses more so than his wins. He lost to the best and worst fighters. His loss to A was not so surprising given A's superior ability. But his loss to E is clearly a case of fighters blowing "give me" fights. Punchers tend to be more inconsistent than boxers. A limited puncher can concievably beat good fighters (C,D) based on his physical attributes but will fall short against an elite fighter with stellar chin (A). Furthermore they are likely to come in over confident against lesser fighters (E).*


#4 - Fighter "D" has a win over C and E showing that he can beat a Trial Horse and a decent contender. Probably a semi skilled fighter with an average chin to the extent that he lost to the best fighter and he lost to a dangerous puncher. His losses are respectable. Why does he come in 4th? because Fighter "C" edges him based of his win over the best fighter and Fighter "B" edges him because of thier head to head match up.

#5 - I think its pretty obvious that Fighter "E" comes in last. Though we shouldnt speculate that he's a terrible fighter.






*C and B to me are the only interchangable ones to me. A, D and E are the only ones whose places IMO should be 1, 4 and 5 respectively.

Interesting analysis...I think about it in a different way!:good

[Decebal]

No more answers?

[Decebal]

Allright, allright! Here is my answer to this puzzle!

Let me first say that this has little to do with practical world ranking of fighters...it's just a bit of fun and a tribute to our very own :happy :happy :happy ESB Rankings Committee!:happy :happy :happy


1) How would you rank fighters A, B, C, D and E if:
A could beat B, D and E but not C
B could beat C and D, but not A or E
C could beat A and E, but not B or D
D could beat C and E, but not A or B
E could beat B, but not A or C or D?

Ok...this is how this thing works...Firstly, we use Occam's principle...keeping the number of awkward styles for the 5 fighters to a minimum.

First, you have to work out why C cannot be first...If he were, he would still be beaten by B and D...but these fighters were themselves beaten by A...clearly, if C gets beaten by such fighters, he cannot be the best...the only reason he beat A was styles!

Secondly, you work out that A has to be first...this is obvious...he was only beaten by C, because of styles.

Thirdly, you have to work out why B cannot be last...B beats both C and D so he cannot be that bad...why argue that B has an awkard style for C and D, but not A? There's no point in complicating matters unncessarily (Occam's principle)

Fourthly, you work out that E has to be last...the only reason why E beats B is because he is awkward for the style of B...he loses to everyone else, though...

So you have:

1.A
2.
3.
4
5.E

Next, you have to work out that C cannot be second...C beats A because he is awkward for A! If he weren't awkward, but in fact very good he would beat at least one of B or D too! And then, he would no longer be second, but first. But we have already established that C cannot be first. A is first!

We use the same argument to establish that B comes before D...the reason B gets beaten by E is that E is awkward for B...if E were in fact better than B, E would beat either C or D as well. But he doesn't, so he is not better than B. But B beats D! Sure, because he's better!

If C cannot be second, and B is better than D, then B has to come second!

1.A
2.B
3.
4.
5.E


Next, you establish that C has to come after D...not the other way around...it checks out! D beats C! Not the other way around! Also, fewer awkward style complications this way! C is not that good...he beats A only on styles...

So we have:

1.A
2.B
3.D
4.C
5.E


A - better than anyone, but gets beaten only by his styles nemesis - C...
B - wins/loses to form, but only gets beaten by his styles nemesis - E
D - wins/loses entirely to form! Kingpin of the system!
C - wins/loses to form, except he beats the Champ, A on styles.
E - wins/loses to form, except he beats B on styles...


This is the best I can do...maybe you can do better! :good

[Decebal]

Let me come clean and say that, at first, using my gut instinct, I thought the correct order would be:

1. A
2. B
3. C
4. D
5. E

...and my fantasy Legend for this was:

A - Calzaghe
B - Kessler
C - Bute
D - Mundine
E - Inkin

...kind of...(with the emphasis on: KIND OF...):D

[Vockerman]

My Dear Decebal,

First let me congratulate you on a most interesting puzzle, indeed anything that can get Cross Trainer, China_Hand_Joe and C.M. Clay II on the same side is a most remarkable topic!!

I would like to take issue with you, sir, if I may, on one specific point in your system.

What we have been given is the results of a "Round Robin" tournament containing five contestants.

You have rated a person with a win over the last place guy and a win over a guy in the middle of the pack (Designated "D") IN FRONT OF a guy with a win over the tournament winner and the last place finisher (Designated "C"). I should say that the latter CLEARLY had the better tournament and I can certainly assure you that in a ELO rated event - like a chess tournament - "C" would have the higher rating (His even score with D and win against a higher rated player).

Is there a mathematical justification you have for choosing D over C that I have missed?

With respect, I appreciate the work you have done and the importance of the issue. I simply cannot find an objective mathematical model that reproduces your "ideal".

The introduction of the notion of "styles" to a tournament rating problem is quite unique.

Kind Regards,

Victor Von Vockerman

[Decebal]

My Dear Decebal,

First let me congratulate you on a most interesting puzzle, indeed anything that can get Cross Trainer, China_Hand_Joe and C.M. Clay II on the same side is a most remarkable topic!!

I would like to take issue with you, sir, if I may, on one specific point in your system.

What we have been given is the results of a "Round Robin" tournament containing five contestants.

You have rated a person with a win over the last place guy and a win over a guy in the middle of the pack (Designated "D") IN FRONT OF a guy with a win over the tournament winner and the last place finisher (Designated "C"). I should say that the latter CLEARLY had the better tournament and I can certainly assure you that in a ELO rated event - like a chess tournament - "C" would have the higher rating (His even score with D and win against a higher rated player).

Is there a mathematical justification you have for choosing D over C that I have missed?

With respect, I appreciate the work you have done and the importance of the issue. I simply cannot find an objective mathematical model that reproduces your "ideal".

The introduction of the notion of "styles" to a tournament rating problem is quite unique.

Kind Regards,

Victor Von Vockerman

Haha, hey, mate! No need to address me so formally!:good

You are undoubtedly right! It crossed my mind too that in a chess championship, C would get more points than his 4th place would suggest he should! And this goes for any method of ranking that goes by POINTS accumulated! And here was one of my points! I think this is the wrong way of going about ranking fighters.

In my opinion, they should be ranked according to how good they are at present, given their past couple of performances and likely form as a result of those fights (e.g. including injuries, becoming "shot" etc...)

Partly, the reason why I started this thread was to challenge those who will end up making ranking lists - they have to be aware of the weaknesses behind their own system of ranking, whatever it is!

I think that we are not running an ATP or ELO points systme when ranking...or are we/should we? This is because in boxing, more than in other sports, it matters much more HOW that win was earned, and the manner in which the fighters have fought! So it is much more an art than any points system would allow for.

As to this puzzle, the reason why D should be ranked above C is that D is a better fighter than C - beats him directly, and also, C's win over A shouldn't be overrated - it was as a result of his awkward style for A, not because he was that good! I think we have to accept, in boxing, that even a great Champ could be beaten by someone outside the very top, because of their very awkward style. But this shouldn't mean that that awkward fighter should be considered top, in a rankings list.

The theory of boxing ranking is tough...and I am not pretending that I have made any inroads - but I am trying to shed some light on some caveats...

I am aware that our top analysts will be able to do a great job by using their gut feel alone! This is why they are such good analysts in the first place. However, I think it would be useful if we established on what basis these rankings would be made, in the first place.

You see...the problem is this...a top analyst should be able to decide whether A beats C or not, and so on...like in the question. But even if he predicts all the various combinations perfectly, it doesn't mean that he will know how to rank them accordingly!

Say:

A stands for Calzaghe
B stands for Kessler
C stands for Bute
D stands for Mundine
E stands for Inkin....

amd say that

A could beat B, D and E but not C
B could beat C and D, but not A or E
C could beat A and E, but not B or D
D could beat C and E, but not A or B
E could beat B, but not A or C or D

....just like in the original question...and an analyst would correctly determine the outcomes of these fantasy match-ups...


....HOW should he rank them A-E?

You saw yourself how many different answers we got, when looking at things theoretically using GIVEN fight results (taken as a given by all). Now, if people don't agree whether Calzaghe would beat Kessler or the other way around, there is very little chance that they will come to the same conclusion about the ranking...

...Sure, this is inevitable...that is why we have quite a few - to even things out.

My point is, though...they have to think carefully about the assumptions that they make subconsciously, when ranking fighters...partly to this end, I have started this thread - to show people how many hidden assumptions there were - and how difficult it all is!

:good