| 1 |
Finally rewrote things so I can quickly try different fudges to the win probability function from here: https://trueskill.org/#win-probability.
|
1 |
Finally rewrote things so I can quickly try different fudges to the win probability function from here: https://trueskill.org/#win-probability.
|
| 2 |
\n
|
2 |
\n
|
| 3 |
Anyway, I figured I'd concentrate on the way that the team skill delta was calculated (delta_mu), as that felt the most tangible to me and also logically something that will vary between different kinds of games (chess, football, zero-k etc). After trying various fudges, I found that a simple mean of the individual player scores got a far better score than the sum. Even a small factor (0.9 or 1.1x) away from the mean reduced the score.
|
3 |
Anyway, I figured I'd concentrate on the way that the team skill delta was calculated (delta_mu), as that felt the most tangible to me and also logically something that will vary between different kinds of games (chess, football, zero-k etc). After trying various fudges, I found that a simple mean of the individual player scores got a far better score than the sum. Even a small factor (0.9 or 1.1x) away from the mean reduced the score.
|
| 4 |
\n
|
4 |
\n
|
| 5 |
Example,
2v2-4v4
games,
ranking
from
all
games:
|
5 |
Example,
2v2-4v4
games,
ranking
from
[s]all
games[/s]
(
edit:
oops,
I
meant
2v2-4v4
games)
:
|
| 6 |
\n
|
6 |
\n
|
| 7 |
||win_probability function||score||
|
7 |
||win_probability function||score||
|
| 8 |
||base||-0.0181||
|
8 |
||base||-0.0181||
|
| 9 |
||my fudge (`(p + 0.5)/2`)||0.0297||
|
9 |
||my fudge (`(p + 0.5)/2`)||0.0297||
|
| 10 |
||@Brackman's suggestion from https://zero-k.info/Forum/Post/250763#250763||score: -0.0862 (1)||
|
10 |
||@Brackman's suggestion from https://zero-k.info/Forum/Post/250763#250763||score: -0.0862 (1)||
|
| 11 |
||delta mu from mean||0.0315||
|
11 |
||delta mu from mean||0.0315||
|
| 12 |
||0.9x delta mu from mean||0.0312||
|
12 |
||0.9x delta mu from mean||0.0312||
|
| 13 |
||1.1x delta mu from mean||0.0313||
|
13 |
||1.1x delta mu from mean||0.0313||
|
| 14 |
\n
|
14 |
\n
|
| 15 |
(1) should be *4? that gives 0.0222
|
15 |
(1) should be *4? that gives 0.0222
|
| 16 |
\n
|
16 |
\n
|
| 17 |
The delta mu from mean peak is so tightly centered around the exact mean that it can't be a coincidence. It seems likely to be a property either of the win_probability function or the scoring function? This seems to work very well for 1v1 games too, increasing the score from about 0.1 to 0.14. I haven't checked anything else yet.
|
17 |
The delta mu from mean peak is so tightly centered around the exact mean that it can't be a coincidence. It seems likely to be a property either of the win_probability function or the scoring function? This seems to work very well for 1v1 games too, increasing the score from about 0.1 to 0.14. I haven't checked anything else yet.
|
| 18 |
\n
|
18 |
\n
|
| 19 |
None of these changes affect the success rate of the function.
|
19 |
None of these changes affect the success rate of the function.
|
| 20 |
\n
|
20 |
\n
|
| 21 |
For clarity my delta mu from mean function below:
|
21 |
For clarity my delta mu from mean function below:
|
| 22 |
\n
|
22 |
\n
|
| 23 |
```
|
23 |
```
|
| 24 |
delta_mu = mean(r.mu for r in team1) - mean(r.mu for r in team2)
|
24 |
delta_mu = mean(r.mu for r in team1) - mean(r.mu for r in team2)
|
| 25 |
sum_sigma = sum(r.sigma ** 2 for r in itertools.chain(team1, team2))
|
25 |
sum_sigma = sum(r.sigma ** 2 for r in itertools.chain(team1, team2))
|
| 26 |
size = len(team1) + len(team2)
|
26 |
size = len(team1) + len(team2)
|
| 27 |
denom = math.sqrt(size * (ts.beta ** 2) + sum_sigma)
|
27 |
denom = math.sqrt(size * (ts.beta ** 2) + sum_sigma)
|
| 28 |
return ts.cdf(delta_mu / denom)
|
28 |
return ts.cdf(delta_mu / denom)
|
| 29 |
```
|
29 |
```
|
Evaluating rating systems