| 1 |
Thx @Sprung.
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1 |
Thx @Sprung.
|
| 2 |
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2 |
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| 3 |
[spoiler]Btw
the
full
probability
information
you
get
from
a
team
rating
system
(
e.
g.
our
elo
system)
for
a
FFA
is
a
NxN
matrix
P',
where
P'_(
k,
l)
is
the
probability
that
team
l
wins
vs
team
k.
If
we
define
P
as
the
(
N-1)
xN
probability
matrix
that
we
get
by
leaving
out
the
diagonal
in
P'
(
because
the
diagonal
describes
probabilities
that
teams
win
vs
themselves
=
0.
5)
,
[/spoiler]we
can
describe
the
above
result
for
the
probability
that
team
k
wins
the
game
as
simply
[b]||P_k||_1
/
||P||_1[/b],
where
P_k
is
the
k-th
column
of
P
and
||.
||_1
the
sum
of
all
components,
because
||P||_1=N*(
N-1)
/2.
|
3 |
[spoiler]Btw
the
full
probability
information
you
get
from
a
team
rating
system
(
e.
g.
our
elo
system)
for
a
FFA
is
a
NxN
matrix
P',
where
P'_(
k,
l)
is
the
probability
that
team
l
wins
vs
team
k.
If
we
define
P
as
the
(
N-1)
xN
probability
matrix
that
we
get
by
leaving
out
the
diagonal
in
P'
(
because
the
diagonal
describes
probabilities
that
teams
win
vs
themselves
=
0.
5)
,
[/spoiler]we
can
describe
the
above
result
for
the
probability
that
team
k
wins
the
game
as
simply
[b]||P_k||_1
/
||P||_1[/b],
where
P_k
is
the
k-th
column
of
P
and
||.
||_1
the
sum
of
all
components,
because
||P||_1=N*(
N-1)
/2.
(
The
column
P_k
is
the
vector
p
in
my
first
post.
)
|
| 4 |
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|
4 |
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| 5 |
[spoiler]The whole calculation here is much more general than the elo system. It could even be applied consistently on a probability matrix calculated by an artificial neural network balancing system that yields non-transitive team to team effectivities (team 0 will probably win vs team 1, 1 will probably win vs 2, 2 will probably win vs 0).[/spoiler]
|
5 |
[spoiler]The whole calculation here is much more general than the elo system. It could even be applied consistently on a probability matrix calculated by an artificial neural network balancing system that yields non-transitive team to team effectivities (team 0 will probably win vs team 1, 1 will probably win vs 2, 2 will probably win vs 0).[/spoiler]
|
| 6 |
I hope this solution will be implemented. The current implementation seems to be incorrect. It may fulfill some of the conditions, but current FFA teams' expectation value of elo change is probably far from zero and it would be nice to see reasonable !predicitons. Every team would have to be treated individually in the code. Maybe I can help with that.
|
6 |
I hope this solution will be implemented. The current implementation seems to be incorrect. It may fulfill some of the conditions, but current FFA teams' expectation value of elo change is probably far from zero and it would be nice to see reasonable !predicitons. Every team would have to be treated individually in the code. Maybe I can help with that.
|
| 7 |
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7 |
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| 8 |
Even though it may sound impossible, I will probably soon release a further generalization of the elo system that allows for giving every team in any team FFA (including normal teams and 1v1) a real winning probability of 1/N no matter how unbalanced the teams seem to be.
|
8 |
Even though it may sound impossible, I will probably soon release a further generalization of the elo system that allows for giving every team in any team FFA (including normal teams and 1v1) a real winning probability of 1/N no matter how unbalanced the teams seem to be.
|
Elo Calculation for (Team) FFA currently wrong?