How to realize ELO in a multiplayer game anyway?

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Frederick Scott wrote:
> I don't know what you mean by saying it doesn't "rate negative performances".
> It rates everything. It may not use some performances if they're not on
> your top eight list but a player doing poorly certainly pays opportunity
> cost for it if nothing else: his score _could_ raise and it doesn't. This
> is a cost.

Of course it is an opportunity cost, but in the other system it would be
a "direct" cost.

> In any event, you also don't explain how you figured out that because
> the current system may not rate some tournaments that all that stuff
> that bothered you about ELO makes no difference in the current system.
> That makes no sense. All that stuff creates good scores and it creates
> lousy scores. You need to explain the distinction you're making in
> much more concrete terms.

See below ...

> Sure. But you're naive if you thinking playing experimental decks makes
> no difference in the current system - even if you play more than
> eight tournaments.

Yeah but it is a psychological difference. Opportunity costs are more
difficult to see and have a more long-term effect. In the current system
if you score a bad result you don´t realize the effect immediately, on
the other hand with an ELO system you have a direct negative impact,
both on the rating and most likely on the players motivation.

Of course this point is only valid from my position where player
motivation (also drawn from rating) is more important than "good"
rating. You seem to be more in favor of "good" rating than player
motivation.

--
johannes walch

 

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"Johannes Walch" <johannes.walch@vekn.de> wrote in message
news:dd7g5k$s5m$1@news01.versatel.de...
> Frederick Scott wrote:
>> I don't know what you mean by saying it doesn't "rate negative performances".
>> It rates everything. It may not use some performances if they're not on
>> your top eight list but a player doing poorly certainly pays opportunity
>> cost for it if nothing else: his score _could_ raise and it doesn't. This
>> is a cost.
>
> Of course it is an opportunity cost, but in the other system it would be
> a "direct" cost.

Distinction irrelevant. Cost is the noun.

>> In any event, you also don't explain how you figured out that because
>> the current system may not rate some tournaments that all that stuff
>> that bothered you about ELO makes no difference in the current system.
>> That makes no sense. All that stuff creates good scores and it creates
>> lousy scores. You need to explain the distinction you're making in
>> much more concrete terms.
>
> See below ...

I see no explanation for this below. All of the stuff that you complained
about making a difference in the ELO system several posts back makes just
as much of a difference under the current system. The deck order, the
metagame issues, the opponents, the round of play - all of that stuff is
just as relevant to the current system as for ELO, for better or worse.

>> Sure. But you're naive if you thinking playing experimental decks makes
>> no difference in the current system - even if you play more than
>> eight tournaments.
>
> Yeah but it is a psychological difference. Opportunity costs are more
> difficult to see and have a more long-term effect. In the current system
> if you score a bad result you don´t realize the effect immediately, on
> the other hand with an ELO system you have a direct negative impact,
> both on the rating and most likely on the players motivation.

What you're essentially arguing for, as far as I can tell, is the ability
to "take a tournament off" (I think is kind of an American way of saying
it). That is, have the ability to show up and do something that essentially
doesn't count. Except it does under the current system from the standpoint
of, if you are able to play the tournament, your rating would be better off
if you played the tournament seriously. Yes, I can understand that it may
"feel" better if someone doesn't see their number move downward on the day
they play. If that's your reason for liking it, that's not a thing I
can dispute.

> Of course this point is only valid from my position where player
> motivation (also drawn from rating) is more important than "good"
> rating. You seem to be more in favor of "good" rating than player
> motivation.

Exactly.

Fred

 

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Archived from groups: rec.games.trading-cards.jyhad (More info?)

Frederick Scott wrote:
> "Johannes Walch" <johannes.walch@vekn.de> wrote in message
> > Of course it is an opportunity cost, but in the other system it would be
> > a "direct" cost.
>
> Distinction irrelevant. Cost is the noun.

Distinction very relevent. Opportunity cost + direct cost > opportunity
cost. Size of the cost matters.

Also, the fact that the cost will be wiped clean 18 months from now
matters.

> What you're essentially arguing for, as far as I can tell, is the ability
> to "take a tournament off" (I think is kind of an American way of saying
> it). That is, have the ability to show up and do something that essentially
> doesn't count. Except it does under the current system from the standpoint
> of, if you are able to play the tournament, your rating would be better off
> if you played the tournament seriously.

If it's a large enough tournament to be worth more than you've earned
in your current best 8, sure. Otherwise, the opportunity cost won't
even show up until one of those slides off the 18-month window.
Depending on how soon that's going to happen, the opportunity cost may
only sting for a few months, as the current tournament will be wiped
out eventually. If you're going to be attending many larger tournaments
before those few months hit, you can probably reduce the opportunity
cost to zero (if the current tournament is small enough in comparison).

The current system lets people run abnormal decks in small tournaments
for essentially zero cost, provided they do well enough at enough
larger tournaments. This is only really a benefit for those who attend
many large tournaments, as it allows them to work the kinks out of new
ideas in a tournament environment without affecting their ratings.

You could realize a similar benefit under ELO if you could arrange
tournaments where you played only against those with a much greater
rating than your own (in which you tried to work out the kinks in your
deck) and then a bunch of normal tournaments to smooth out the
inevitable (but small) ratings drop that would result. This seems like
a much more difficult thing to do (and not even possible for the
top-ranked players), though it has the benefit of netting you a huge
rating increase if your wierd new idea works terrifically the first
time you try it.

Whether this benefit is worthwhile is an excercise best left to the
reader.

John

 

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<jnewquist@difsol.com> wrote in message
news:1123536335.557640.273370@g44g2000cwa.googlegroups.com...
>
> Frederick Scott wrote:
>> "Johannes Walch" <johannes.walch@vekn.de> wrote in message
>> > Of course it is an opportunity cost, but in the other system it would be
>> > a "direct" cost.
>>
>> Distinction irrelevant. Cost is the noun.
>
> Distinction very relevant. Opportunity cost + direct cost > opportunity
> cost. Size of the cost matters.

Maybe, but no one has yet stated why the size of the direct cost alone
should be relevant.

> Also, the fact that the cost will be wiped clean 18 months from now
> matters.

Huh? Why? This point comes completely out of left field. Even under ELO,
old results diminish in importance on a curve approaching nothingness as
newer results are recorded. I'm not sure what point you're trying to make,
here.

>> What you're essentially arguing for, as far as I can tell, is the ability
>> to "take a tournament off" (I think is kind of an American way of saying
>> it). That is, have the ability to show up and do something that essentially
>> doesn't count. Except it does under the current system from the standpoint
>> of, if you are able to play the tournament, your rating would be better off
>> if you played the tournament seriously.
>
> If it's a large enough tournament to be worth more than you've earned
> in your current best 8, sure.

If you're talking about people at the top of the ranking chart, perhaps.
I was making more general comments about average players who aren't going
to have a best eight list which can't be cracked by a first place finish in
any given tournament they happen to be at. I'm pretty sure Johannes was
also speaking about the rank and file players, not the elite. Otherwise
his reasoning doesn't make much sense.

> The current system lets people run abnormal decks in small tournaments
> for essentially zero cost,

It does not. If you're attending an X-sized tournament, you'd have to
have eight better finishes currently on your chart and keep eight better
finishes on your chart for the next 18 months than you could possibly get
from winning it. That means eight first place finishes at a tournament of
size X or correspondingly higher*** for lesser finishes. Of course, don't
forget that in those eight finishes, it's a good idea to have won every
single game and done a complete sweep of all players in each victory or
you could conceivably do better than this and thus pay opportunity cost
if you fail to try.

(*** - For these purposes, you'd have to consider that a 3R+F tournament
would be "larger" than a 2R+F because the extra round allows for a higher
potential point total. This roughly corresponds to the higher potential
yield in finalist points offered by a larger tournament, so it's a fair
way of thinking about that issue.)

> You could realize a similar benefit under ELO if you could arrange
> tournaments where you played only against those with a much greater
> rating than your own (in which you tried to work out the kinks in your
> deck) and then a bunch of normal tournaments to smooth out the
> inevitable (but small) ratings drop that would result.

No, you can not - at least, not in theory. All games ought to be just
as important as all other games. You apparently misunderstand ELO. If,
for instance, you arranged to play only against those with a much higher
rating than your own then in theory you should have a much lower chance of
getting a positive result, exactly balancing the potential payoff you'd
get. There's no reason you wouldn't lose the same ratings points playing
your experimental deck against great players or bad players or anything
in between.

(What actually might make a difference is whether you play *against* other
players who were using experimental decks and thus possessed ratings
higher than they merited under the circumstances. Alternatively, you might
have the misfortune of running up against players who were coming out of
a period of playing experimental decks and now could be more formidable
than their recent play record justified - either because they had
successfully tuned the deck in question or because they had given up on it
and switched to a more dependable deck. But assuming you face opposition
at random as you play tournaments, this should cancel itself out over
many results.)

Whether the theory works or not depends (as a wrote in reply to Robert
Goudie's post last week) on whether one's chance of beating another
player of a given accurate ranking is truly a straight-line curve or
not. That might be a questionable premise, I'd agree. But I'd have to
hear some convincing argument why it would be a terribly curved line
to believe ELO wouldn't normally give at least a pretty good number
corresponding to player's skills. The current system makes no pretence
of rating only skill so there's obviously no comparison. And the real
issue is what it truly does rate - which, AFAICS, is nothing.

Fred

 

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Frederick Scott wrote:
> <jnewquist@difsol.com> wrote in message
> news:1123536335.557640.273370@g44g2000cwa.googlegroups.com...
> >
> > Frederick Scott wrote:
> >> "Johannes Walch" <johannes.walch@vekn.de> wrote in message
> >> > Of course it is an opportunity cost, but in the other system it would be
> >> > a "direct" cost.
> >>
> >> Distinction irrelevant. Cost is the noun.
> >
> > Distinction very relevant. Opportunity cost + direct cost > opportunity
> > cost. Size of the cost matters.
>
> Maybe, but no one has yet stated why the size of the direct cost alone
> should be relevant.

Not size of direct cost. Size of cost. There's a lower cost for losing
a game/tournament when the direct cost is eliminated, provided the
opportunity cost hasn't risen by the same (or greater) amount. The
opportunity cost, as should be clear from the rest of my post, is
dependent on the number and size of tournaments you attend compared
with the size of the current tournament.

> > Also, the fact that the cost will be wiped clean 18 months from now
> > matters.
>
> Huh? Why? This point comes completely out of left field. Even under ELO,
> old results diminish in importance on a curve approaching nothingness as
> newer results are recorded. I'm not sure what point you're trying to make,
> here.

The reason it matters is that the cost may *never* be realized. In ELO,
it's realized *right now* and must be earned back through sufficient
play.

> >> What you're essentially arguing for, as far as I can tell, is the ability
> >> to "take a tournament off" (I think is kind of an American way of saying
> >> it). That is, have the ability to show up and do something that essentially
> >> doesn't count. Except it does under the current system from the standpoint
> >> of, if you are able to play the tournament, your rating would be better off
> >> if you played the tournament seriously.
> >
> > If it's a large enough tournament to be worth more than you've earned
> > in your current best 8, sure.
>
> If you're talking about people at the top of the ranking chart, perhaps.
> I was making more general comments about average players who aren't going
> to have a best eight list which can't be cracked by a first place finish in
> any given tournament they happen to be at. I'm pretty sure Johannes was
> also speaking about the rank and file players, not the elite. Otherwise
> his reasoning doesn't make much sense.

Okay. In case you hadn't noticed, I'm not so much defending his
reasoning as playing math major. You made some bad assumptions to
refute him, I'm correcting the assumptions. Whether a system which
allows the elite to experiment more (under certain circumstances) with
less (or no) penalty is good, bad, or unimportant, is a totally
philosophical discussion and I'm not really in it right now.

Meanwhile, I'm going back to the math.

> > The current system lets people run abnormal decks in small tournaments
> > for essentially zero cost,
>
> It does not.

If you snip the part where I say "provided they do well enough at
enough
larger tournaments," then you appear to have rebutted me. Meanwhile,
what I actually wrote is true, for some value(s) of "enough". I suppose
I should have said "small enough tournaments" and "large enough
tournaments" as well, but the point holds.

Under certain circumstances, in the current system, the opportunity
cost of playing poorly or trying something uncertain can be brought to
zero. This is different from ELO, where both a direct cost and an
opportunity cost are imposed on every game played for rating points. It
benefits those players who play (and do well) at many large tournaments
and also play small tournaments.

> (*** - For these purposes, you'd have to consider that a 3R+F tournament
> would be "larger" than a 2R+F because the extra round allows for a higher
> potential point total. This roughly corresponds to the higher potential
> yield in finalist points offered by a larger tournament, so it's a fair
> way of thinking about that issue.)

Yes, larger means points-wise larger, not necessarily body-count
larger.

> > You could realize a similar benefit under ELO if you could arrange
> > tournaments where you played only against those with a much greater
> > rating than your own (in which you tried to work out the kinks in your
> > deck) and then a bunch of normal tournaments to smooth out the
> > inevitable (but small) ratings drop that would result.
>
> No, you can not - at least, not in theory. All games ought to be just
> as important as all other games. You apparently misunderstand ELO. If,
> for instance, you arranged to play only against those with a much higher
> rating than your own then in theory you should have a much lower chance of
> getting a positive result, exactly balancing the potential payoff you'd
> get. There's no reason you wouldn't lose the same ratings points playing
> your experimental deck against great players or bad players or anything
> in between.
>
> (What actually might make a difference is whether you play *against* other
> players who were using experimental decks and thus possessed ratings
> higher than they merited under the circumstances. Alternatively, you might
> have the misfortune of running up against players who were coming out of
> a period of playing experimental decks and now could be more formidable
> than their recent play record justified - either because they had
> successfully tuned the deck in question or because they had given up on it
> and switched to a more dependable deck. But assuming you face opposition
> at random as you play tournaments, this should cancel itself out over
> many results.)


Okay, whatever. It depends on your assumptions. I mean, if you assume
that even you're experimental deck is going to kick the ass of a bunch
of newbies, then you minimize rating flux by picking on them with it.
If you've already decided your first few games with it (in a tournament
setting) are lost, then you minimize the loss by picking a fight with
the biggest fish you can. If you're wrong in the first assumption,
however, you lose a whole lot of points to a bunch of new players,
whereas when you're wrong on the second assumption, you win big - it's
the "safer" bet.

My point had more to do with eliminating the *short-term* impact to
your rating. As you say, ELO will average it out in the long term.

>
> Whether the theory works or not depends (as a wrote in reply to Robert
> Goudie's post last week) on whether one's chance of beating another
> player of a given accurate ranking is truly a straight-line curve or
> not. That might be a questionable premise, I'd agree. But I'd have to
> hear some convincing argument why it would be a terribly curved line
> to believe ELO wouldn't normally give at least a pretty good number
> corresponding to player's skills. The current system makes no pretence
> of rating only skill so there's obviously no comparison. And the real
> issue is what it truly does rate - which, AFAICS, is nothing.

That's the issue you're really interested in, truly.

> Fred

 

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<jnewquist@difsol.com> wrote in message
news:1123545978.417040.313270@g43g2000cwa.googlegroups.com...
> The opportunity cost, as should be clear from the rest of my post, is
> dependent on the number and size of tournaments you attend compared
> with the size of the current tournament.
....

> Frederick Scott wrote:
>> <jnewquist@difsol.com> wrote in message
>> news:1123536335.557640.273370@g44g2000cwa.googlegroups.com...
>> > Frederick Scott wrote:
>> >> What you're essentially arguing for, as far as I can tell, is the ability
>> >> to "take a tournament off" (I think is kind of an American way of saying
>> >> it). That is, have the ability to show up and do something that essentially
>> >> doesn't count. Except it does under the current system from the standpoint
>> >> of, if you are able to play the tournament, your rating would be better off
>> >> if you played the tournament seriously.
>> >
>> > If it's a large enough tournament to be worth more than you've earned
>> > in your current best 8, sure.
>>
>> If you're talking about people at the top of the ranking chart, perhaps.
>> I was making more general comments about average players who aren't going
>> to have a best eight list which can't be cracked by a first place finish in
>> any given tournament they happen to be at. I'm pretty sure Johannes was
>> also speaking about the rank and file players, not the elite. Otherwise
>> his reasoning doesn't make much sense.
>
> Okay. In case you hadn't noticed, I'm not so much defending his
> reasoning as playing math major. You made some bad assumptions to
> refute him, I'm correcting the assumptions.

I made some assumptions that may be considered "bad" were they tested only
in the corner cases you're suggesting. In terms of the more general
conditions that matter to almost all players almost all of the time, I
guess I think it's picking nits to worry about.

> Whether a system which
> allows the elite to experiment more (under certain circumstances) with
> less (or no) penalty is good, bad, or unimportant, is a totally
> philosophical discussion and I'm not really in it right now.

More to the point, such a caveat would make his reason to favor the system
incredibly ludicrous - or incredibly self-serving. I don't think the
discussion would be 'philosophical'. 'Silly' is the adjective that comes
to my mind.

> Meanwhile, I'm going back to the math.
>
>> > The current system lets people run abnormal decks in small tournaments
>> > for essentially zero cost,
>>
>> It does not.
>
> If you snip the part where I say "provided they do well enough at
> enough larger tournaments," then you appear to have rebutted me.

All right, sorry. Missed it (my bad) and didn't think anyone would
really want debate it from such an angle. But sure, I now see what you
mean.

> Under certain circumstances, in the current system, the opportunity
> cost of playing poorly or trying something uncertain can be brought to
> zero. This is different from ELO, where both a direct cost and an
> opportunity cost are imposed on every game played for rating points. It
> benefits those players who play (and do well) at many large tournaments
> and also play small tournaments.

Those are pretty stringent requirements, however. You'd have to do
sufficiently well in at least eight of the larger tournaments to best any
possible finish you could make at the smaller ones you attended. I don't
think that's likely to be very easy. I guess I find it believable that
certain guys (and Johannes may be one of them) who are good enough and
energetic enough to be finalists in eight large tournaments over 18
months may earn enough finalist points to cover any sub-optimal game
results in those tournaments and make it impossible to improve on them
in smaller tournaments. That's not a viewpoint that the vast majority
of players ever need worry about, though.

Fred

 

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Here is a Multiplayer Elo Calculator.

It makes changes to the elo based on all of competitors simultaneously. You can see the overview of the math in the results.

 

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