Bouting inside clubs for optimum increase of fencing ability

[PeterGustafsson]

Hi!


This might be better placed in Coaches Corner, but I will post it here since CC seems to have a small readership. Moderators, please move if appropriate to do so.

How should fencers be paired so that the increase in fencing strength is optimised?

Assume that:
1. The relative fencing strength for all fencers in a club is known.
2. The pairings in training bouts in club training can be decided upon, and enforced, by club leadership.
3. Pairings unwanted by fencers will not lead to membership loss, at least not in the short term.
4. The fencer/coach ratio is so high so that coach time is at a very high premium.
5.The fencer/strip ratio is so high so that all pistes should be used at all times, not doing so is a waste of resources.
6. The fencing strength of an individual fencer can be represented by a number (or a vector with real numbers as components, if you want to make the analysis more complex and realistic!)

Personally, I believe that a fencer increases most in ability if he bouts against someone who is a bit, but not too much, better than himself. If he bouts against someone much his inferior he will be wasting his time, and maybe pick up bad habits to boot. If he bouts against someone who much better than himself he be crushed, and probably not learn much - at least in the short term. Furthermore, if two equally weak beginners bout against each other they will probably not learn all that much unless they are supervised.

First question: what is the appropriate metric that we shall optimize? There are several possibilities:

1. The total arithmetic sum of the fencing strengths of all fencers in the club should be maximized.
2. The maximum fencing strength of the best club member should be maximized.
3. The weakest fencing strength of any one club member should be maximized.
4. The largest increase in fencing strength for any one member should be maximized.
5. make up your own metric!

Of these alternatives, #2-4 essentially deal with one fencer, treating the rest of the club as props to his development. While that may be the correct choice in some settings, they present by order of magnitude easier optimization problems than metric #1, making them - in this context - uninteresting problems. Metric #1 has the added benefit that it limits intra-club controversies.

The simplest approach would be to match every fencer against the fencer who is weakest among those who are better than him. The problem with that approach is that the club scrub and champion only get one bout. If they are set against each other, the resulting bout will add very little to the total club strength

For example: Assume that the club has 6 members, one of each rating. The training time only allows for 6 training bouts. (That would be an truly unusual club, but I set the values as simply as possibly to illustrate my concepts, and still make the optimum bout order calculation nontrivial.) The simplest approach would then give the following training bout order:
1. U-E
2. E-D
3. D-C
4. C-B
5. B-A
6. A-U

As you see, bout#6 does very little for the club. Compared to bouts #1-5, it is essentially a time filler.

What would be - in your opinion - a better bout list, given the club membership and bout number constraints?

A wider problem: Assume that a coach knows the stuff posited in the first assumption list. How would one then go about calculating the optimum bout list?

One thinkable solution: Run a round-robin competition involving all the club members. From those results, then choose the bouts which have the lowest results differential, subjected to the constraints that not more than a set number of bouts can be selected, and that any one fencer can not feature in more than some maximum of those bouts, and that any one fencer can not feature in less than some maximum of those bouts. This should weed out many of the bouts which clearly do not belong in the optimum training bout list, but it is not guaranteed to produce a global optimum.

Do you see any downsides with this approach? Can you outline a better algorithmic solution?


Have a nice time!

Peter Gustafsson

[Allen Evans]

Originally Posted by PeterGustafsson

Do you see any downsides with this approach?

Yes. Convincing fencers to follow this metric.

AE

[brutus]

YEs you get better by fencing better fencers, but onyl to a point, you also need to fence people worse - the 'bunnies' - as you will ultimately come up against them in competition and it is a different way of fencing when facing a bunnie!

[PeterGustafsson]

Hi!

Originally Posted by Allen Evans

Yes. Convincing fencers to follow this metric.

AE

Well, you are breaking one of the stated assumptions then. If that assumption is not put in place, the bout selection problem becomes infinitely more difficult, but not more interesting, IMO. To solve that one only has to add leadership.

While leadership is an interesting topic in an of itself, it is not part of the optimization issue that I started the thread with.

In high-level settings there is an easy remedy to your problem - state that fencers will train in the bouts listed by the national trainer, on pain of losing their training stipend and national team berth. Problem solved!


Have a nice time!

Peter Gustafsson

[PeterGustafsson]

Hi!

Originally Posted by brutus

YEs you get better by fencing better fencers, but onyl to a point, you also need to fence people worse - the 'bunnies' - as you will ultimately come up against them in competition and it is a different way of fencing when facing a bunnie!

In other words, the shape of the improvement function(own fencing strength, opponent fencing strength) is such so that it is nonzero for a large span of opponent(fs) if own(fs)=large.

Interesting observation, but the really good fencers should still mostly fence against those who present a challenge to them.

The optimization problem still stands, though.


Have a nice time!

Peter Gustafsson

[Monash_Armourer]

There is a local competition held by one of the "bigger" clubs in melbourne that kind of uses a handicap system for fecners to try and even things up, so essentially anybody can fence anybody.

For example:
A 13 year old that has been fencing for 1 year draws against my coach who is consistently rated in the top 4 foil fencers in Australai. Scores might start at 13 - 0 or even 14 - 0 in favour of the kid.

Somebody who has been fencing for 5-6 years and is a fairly competent fencer might start at 5 - 0 against my coach.

Two fairly evenly matched fencers might start out at 0 - 0 or maybe 1 or 2 points up at the beginning of the bout.

I fence somebody who is quite a decent fencer, but in another weapon, it might start 2 to 6 - 0 against me.

Two evenly ranked fencers, but one who is consistnatly tripped up by the other in bouts for whatever reason might start between 5 and 10 to 0.

It's an diea, not a perfect one though. but it's a start. Takes lots of things into consideration as well, such as experience, age, fitness and tournament rankings. Deciding handicaps in particular instances might be tricky.

The idea is that a 10 year old who has been fencing for a year, can potentially beat a top ranked fencer is one reason why the idea might be appealing to some though.

Food for thought.

[veeco]

With your model, the top fencers would get to fence very short bouts, and the weaker fencers would tend to fence very long bouts. Doesn't solve the optimization problem, especially in light of the fact that the strip usage must be maximized.

It's also bad to fence bouts that don't have as many touches as they do in real competition.

[the ancient one]

Try a team format. For your 6 fencer scenario:

Team 1
A D U

Team 2
B C E

Psychologically I think this works; some fencers have a higher motivation to "not fail the team" than they have for their own benefit. If the rankings are predictive Team 2 has a very slight advantage and The A in Team 1 must mentor the D and the U to higher performance, Team 2 has to work to avoid the upset.

You don't have to conclude the matches in one session.

[glowstix]

Originally Posted by PeterGustafsson

Hi!
If he bouts against someone much his inferior he will be wasting his time, and maybe pick up bad habits to boot. If he bouts against someone who much better than himself he be crushed, and probably not learn much - at least in the short term.

what if these two opponents are the only ones you have at your club on most days??

[qatet]

Originally Posted by glowstix

what if these two opponents are the only ones you have at your club on most days??

Create situations for yourself. Work on setting them up for hits with different tactics, take parries you wouldn't usually take, hit to lines you don't usually use, start with a different scores (you're already down by several touches), tell yourself that the ref always see your beat attack as your opponent's parry riposte. You don't event have to tell them what you're doing, you could just keep it private, if you thought that telling them that you're limiting your actions would insult them. If they're so far behind you that the bouting isn't useful at all, create drills to do with them. By building their skills you create better training for yourself.

[PeterGustafsson]

Hi!

Originally Posted by Monash_Armourer

There is a local competition held by one of the "bigger" clubs in melbourne that kind of uses a handicap system for fecners to try and even things up, so essentially anybody can fence anybody.

For example:
A 13 year old that has been fencing for 1 year draws against my coach who is consistently rated in the top 4 foil fencers in Australai. Scores might start at 13 - 0 or even 14 - 0 in favour of the kid.

Rest of Handicap system description

Well, this handicap system is an interesting training tool, but not quite was I was looking for.

The handicap system described by you is intended to, I presume, maximize the training effect of a given bout once it has been decided that that bout should take place.

What I was looking for was a bout selection algorithm, so that the best possible bouts can be chosen in order to maximize total training effect for a training session, given the constraint of a limited number of bouts.


Have a nice time!

Peter Gustafsson

[PeterGustafsson]

Hi!

Originally Posted by glowstix

what if these two opponents are the only ones you have at your club on most days??

Well, then you have a situation where the number of possible opponents is the constraining factor. In my threadstart scenario, the strip time is the constraining scenario. Different problem, well worth of its own thread.


Have a nice time!

Peter Gustafsson

[PeterGustafsson]

Hi!

Originally Posted by veeco

With your model, the top fencers would get to fence very short bouts, and the weaker fencers would tend to fence very long bouts.

In this sentence, does "your model" refer to the "ring-with-A/U" bout selection, or does it refer to the bout selection according to previous poule results? In either case, I do not see why the bout length should correlate with fencer strength. Care to explain why?

Originally Posted by veeco

Doesn't solve the optimization problem, especially in light of the fact that the strip usage must be maximized.

I put forth the "ring-with-A/U" bout selection algorithm as a obvious and simple - but flawed - bout selection algorithm.

The 2nd proposed solution, bout selection according to previous poule results, seems intuitively better to me, since it weeds out some blowout bouts which will not have much training value. What flaws - in more detail - do you see, and can you give an example?

Originally Posted by veeco

It's also bad to fence bouts that don't have as many touches as they do in real competition.

Well, I hand intended all training bouts to be of regulation length. One possible way to conserve strip time would be to have a point spread limit - once the points differential in a training bout reaches 3 points, the bout is ended. The last 2 points in a 5-0 blowout add little to the traning effect, and can be demoralizing to the loser.


Have a nice time!

Peter Gustafsson

[PeterGustafsson]

Hi!

Originally Posted by the ancient one

Try a team format. For your 6 fencer scenario:

Team 1
A D U

Team 2
B C E

Psychologically I think this works; some fencers have a higher motivation to "not fail the team" than they have for their own benefit. If the rankings are predictive Team 2 has a very slight advantage and The A in Team 1 must mentor the D and the U to higher performance, Team 2 has to work to avoid the upset.

You don't have to conclude the matches in one session.

This solution presupposes 9 bouts, which breaks the 6-bout constraint. The multi-session feature resolves that, in a way. However, if one uses your team idea but limits it to a 6-bout match, how should those bouts be chosen?

A simple but nonideal solution: Start out with 3 evenly matched bouts, and then let the trailing team chose the bout pairings for bouts#4-6. Like this:
Bout#1: U-E
Bout#2: D-C
Bout#3: A-B
Assume that A made a big comeback, so team 2 is trailing. They will then chose:
Bout#4: U-B
Bout#5:?
Bout#6:?

The obvious drawback to this is that if team 1 is trailing, fencer A will be chosen for bouts#4-6. If team 2 is trailing, fencer U will be chosen for bouts #4-6. In either case, it can be concluded that fencer D will not get a 2nd bout unless either fencer A or U is chosen for both bout#4 and 5.

This makes for a reasonably even team match, but bouts#4-6 will not be evenly matched, since there is a motive for both teams to select the most mismatched bout in their favor.

An improvement would be to forbid that the trailing team chooses the U-B or A-E bouts, since they are most mismatched of the 6 possible bout choices for bout #4-6. There are still 4 bout possibilities to choose from for the last 3 bouts.


Have a nice time!

Peter Gustafsson

[PeterGustafsson]

Hi!

Originally Posted by PeterGustafsson

One thinkable solution: Run a round-robin competition involving all the club members. From those results, then choose the bouts which have the lowest results differential, subjected to the constraints that not more than a set number of bouts can be selected, and that any one fencer can not feature in more than some maximum of those bouts, and that any one fencer can not feature in less than some maximum of those bouts. This should weed out many of the bouts which clearly do not belong in the optimum training bout list, but it is not guaranteed to produce a global optimum.

Here comes an example, the poule comes from Swedish ME championships 2007:

Poule no 10 V/M Indicator HS
GÓMEZ Andrés Fff X V2 V V 4 V 4/5 12 21
HEDENSKOG Filip Äfk 1 X 3 V 2 V 2/5 0 16
FAJERS Mattias Dif 0 V X 3 4 3 1/5 -8 15
BRAKANDER Lars Ufk 3 2 V X 0 V 2/5 -7 15
NERELL Magnus Saf V V V V X V 5/5 15 25
HEINERUD Lars Uf 0 2 V 4 0 X 1/5 -12 11

Imagine that all these fencers would have come from the same club, how should one have chosen the 6 bouts which would have given the best total training effect?

One possible solution:
Of these 15 bouts, 4 were won by a 1-point margin. If they are selected to the bout list, one gets:
Gomez - Hedenskog
Fajers - Nerell
Heinerud - Brakander
Gomez - Nerell

Now, both Gomez and Nerell have gotten 2 bouts (both have medalled in Sw. Championships, BTW). To choose the last two bouts, one might look among the bouts not featuring them. The poule results without them look like this:

Poule no 10
HEDENSKOG Filip Äfk X 3 V V
FAJERS Mattias Dif V X 3 3
BRAKANDER Lars Ufk 2 V X V
HEINERUD Lars Uf 2 V 4 X

This is 6 bouts, but one has already been selected. There are 3 bouts with a 2-point win margin, and 2 to be chosen. All feature Fajers. Which to deselect? Of the 4 so far selected bouts, 2 have Nerell as a winner, while Gomez and Brakander have one win each. The 3 bouts with 2-point margins feature Fajers, Brakander, and Heinerud as winners. If one deselects the Brakander - Fajers bout, one gets a bout list with 6 bouts, no blowouts, and all poule members as winners at least one time. Fajers (5th place) gets 3 bouts, while Brakander (4th) only gets one bout.

The total bout list, with poule results, looks like this:
Gomez - Hedenskog V2-1
Fajers - Nerell 4-V
Heinerud - Brakander 4-V
Gomez - Nerell 4-V
Hedenskog - Fajers 3-V
Fajers - Heinerud 3-V

The total win margin for these 6 bouts is 8 points. All six fencers feature in at least 1 tight bout.

If one would have chosen the "ring-with-A/U" bout selection algorithm, one would have gotten this bout list:
Heinerud - Fajers V-3
Fajers - Brakander 3-V
Brakander - Hedenskog 2-V
Hedenskog - Gomez 1-V2
Gomez - Nerell 4-V
Nerell - Heinerud V-0

The total win margin for these 6 bouts is 14 points, considerably worse than the result for the previous method. 3 bouts feature in both lists. Only 3 fencers feature in at least 1 tight bout.

If one would have done two rings, one weak and one strong, one would have gotten the following bout list:
Heinerud - Fajers V-3
Fajers - Brakander 3-V
Brakander - Heinerud 4-V
Hedenskog - Gomez 1-V2
Gomez - Nerell 4-V
Nerell - Hedenskog V-2
The total win margin for these 6 bouts is 10 points, an intermediate result. 5 fencers have at least 1 tight bout. There is a definite risk that this selection algorithm leads to a situation where the weaker fencers get stuck, since they never get to train against the better fencers.


Have a nice time!

Peter Gustafsson

[Zilverzmurfen]

Peter, I'm amazed that you find the time and effort to contemplate over these matters...

...I just get a headache looking at all these numbers!

[glowstix]

Originally Posted by PeterGustafsson

Different problem, well worth of its own thread.


Have a nice time!

Peter Gustafsson

well maybe you can humour me on another day...