| 1 |
Your argumentation would be correct in a normal strategy game, where teamstrength is the sum of playerstrengths. In ZK however there are extra coms. Thus teamstrength is the average of playerstrengths. 51.5% for team 3 is for no cooperation between team 1 and 2. If they cooperate, team 3's win chance will be higher (68.0%) because of extra coms.
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1 |
Your argumentation would be correct in a normal strategy game, where teamstrength is the sum of playerstrengths. In ZK however there are extra coms. Thus teamstrength is the average of playerstrengths. 51.5% for team 3 is for no cooperation between team 1 and 2. If they cooperate, team 3's win chance will be higher (68.0%) because of extra coms.
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| 2 |
For h=1/(number of the teams' coms) all cases are considered here.
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2 |
For h=1/(number of the teams' coms) all cases are considered here.
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| 3 |
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3 |
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| 4 |
[spoiler]As the teamstrength system rates teams with high elo deviation better, people with very high and very low elo will loose elo and people with normal elo will increase, if games are balanced with this system. Thus the current effect that there are people with team elo 2000 but not with 1000 could be compensated a little, if really only a little.[/spoiler]
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4 |
[spoiler]As the teamstrength system rates teams with high elo deviation better, people with very high and very low elo will loose elo and people with normal elo will increase, if games are balanced with this system. Thus the current effect that there are people with team elo 2000 but not with 1000 could be compensated a little, if really only a little.[/spoiler]
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| 5 |
Furthermore you could argue that probabilities should be proportional to squares of teamstrengths to better reflect team cooperations in FFA. But in order to leave at least 1v1 unaffected, you need to apply sqrt first : {{{ playerstrength = B^((elo-eloShift)/2)
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5 |
Furthermore you could argue that probabilities should be proportional to squares of teamstrengths to better reflect team cooperations in FFA. But in order to leave at least 1v1 unaffected, you need to apply sqrt first : {{{ playerstrength = B^((elo-eloShift)/2)
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| 6 |
teamstrength
=
(
sum
of
team's
playerstrength)
*h(
n)
|
6 |
teamstrength
=
(
sum
of
team's
playerstrength)
/n
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| 7 |
team elo = log_B(teamstrength^2)+eloShift }}} Instead of squares you can use a more general convex function phi (a strictly monotonic increasing diffeomorphism) with inversion theta, which is concave: {{{ playerstrength = theta(g(elo))
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7 |
team elo = log_B(teamstrength^2)+eloShift }}} Instead of squares you can use a more general convex function phi (a strictly monotonic increasing diffeomorphism) with inversion theta, which is concave: {{{ playerstrength = theta(g(elo))
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| 8 |
teamstrength = (sum of team's playerstrength)*h(n)
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8 |
teamstrength = (sum of team's playerstrength)*h(n)
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| 9 |
team elo = f(phi(teamstrength))}}} Then you can calculate probabilities either with team elo or proportional to phi(teamstrength). As g is convex and theta concave, the better rating of teams with higher elo deviation is partially compensated.
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9 |
team elo = f(phi(teamstrength))}}} Then you can calculate probabilities either with team elo or proportional to phi(teamstrength). As g is convex and theta concave, the better rating of teams with higher elo deviation is partially compensated.
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math bork 2nd try