| 1 |
In the end we have the following types of systems (apart from probability system, TrueSkill and ANN):
|
1 |
In the end we have the following types of systems (apart from probability system, TrueSkill and ANN):
|
| 2 |
\n
|
2 |
\n
|
| 3 |
[b]Team Elo System[/b] given by a function g to transform to playerstrength and h for the team size dependency: {{{ playerstrength = g(elo)
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3 |
[b]Team Elo System[/b] given by a function g to transform to playerstrength and h for the team size dependency: {{{ playerstrength = g(elo)
|
| 4 |
teamstrength = (sum of team's playerstrength)*h(n)
|
4 |
teamstrength = (sum of team's playerstrength)*h(n)
|
| 5 |
team
elo
=
f(
teamstrength)
}
}
}
n
is
the
number
of
players
in
a
team
(
can
be
different
for
any
team)
and
N
the
number
of
teams.
Win
probabilities
are
calculated
with
my
team
FFA
generalization
of
the
elo
system.
|
5 |
team
elo
=
f(
teamstrength)
}
}
}
n
is
the
number
of
players
in
a
team
(
can
be
different
for
any
team)
and
N
the
number
of
teams.
Win
probabilities
are
calculated
with
my
[url=http://zero-k.
info/Forum/Thread/20712]team
FFA
generalization[/url]
of
the
elo
system.
|
| 6 |
\n
|
6 |
\n
|
| 7 |
The current system uses g(elo)=elo and h(n)=1/n (but a wrong FFA calculation). Systems that I developed earlier use h(n)=1/sqrt(n) or h(n)=0.5+0.5^n. @Sprung 's system uses g(elo)=B^(elo-eloShift) and h(n)=1/n.
|
7 |
The current system uses g(elo)=elo and h(n)=1/n (but a wrong FFA calculation). Systems that I developed earlier use h(n)=1/sqrt(n) or h(n)=0.5+0.5^n. @Sprung 's system uses g(elo)=B^(elo-eloShift) and h(n)=1/n.
|
| 8 |
\n
|
8 |
\n
|
| 9 |
[b]Teamstrength System[/b] given by the same but without the calculation of team elo. Win probabilities are distributed proportional to teamstrengths. Shifts in the elo scale should not change the result. From this invariance g(elo)=B^(elo-eloShift) can already be concluded and from this follows the equivalence to the team elo system for N=2 but not for more teams. This is still true for any h.
|
9 |
[b]Teamstrength System[/b] given by the same but without the calculation of team elo. Win probabilities are distributed proportional to teamstrengths. Shifts in the elo scale should not change the result. From this invariance g(elo)=B^(elo-eloShift) can already be concluded and from this follows the equivalence to the team elo system for N=2 but not for more teams. This is still true for any h.
|
| 10 |
\n
|
10 |
\n
|
| 11 |
So
g(
elo)
=B^(
elo-eloShift)
with
h=1/sqrt(
n)
should
be
an
interesting
system.
I
don't
know
which
of
both
probability
calculations
should
be
used
for
N>2.
|
11 |
So
g(
elo)
=B^(
elo-eloShift)
with
h(
n)
=1/sqrt(
n)
should
be
an
interesting
system.
I
don't
know
which
of
both
probability
calculations
should
be
used
for
N>2.
|
math bork 2nd try