Hello gnubg users,
I have a question about the relationship between “Error total (MWC)”
(Err%) and “Luck total (MWC)” (Lck%).
Before I continue, some definitions to make sure I got this correctly:
- Err%(A) is the equity (in Match Winning Changes) that player A dropped
in the match, both chequer play and cube actions. This is expressed in
Match Winning Chances (MWC) and has always a negative sign.
- Lck%(A) is the equity player A gained/lost each time he rolled the dice.
This too is expressed in MWC, can have positive or negative sign.
- AR is the actual result in MWC, 50% if I win, -50% if I lose.
- Each of those variables above are non normalised.
Example from a recent match I have played:
PlayerA PlayerB
-------- --------
Err% −39.614% −64.202%
Lck% +37.250% −2.534%
AR 50% −50%
Now, the question.
I would think AR to be:
R = Lck%(A) − Lck%(B) + Err%(A) − Err%(B)
or in longhand, I expect “Result − Luck” to be equal to “Skill”; and vice
versa “Result − Skill” to be equal to “Luck”.
But this seems not to be case:
# From the perspective of PlayerA
Result = 50%
Luck = 37.250% + 2.534% = 39.784%
Skill = −39.614% + 64.202% = 24.588%
Implied skill (Result − Luck) = 50% − 39.784% = 10.216%
# ↑ This is “Luck adjusted result” − 50%.
Implied luck (Result − Skill) = 50% − 20.588% = 29.412%
I expected some minor discrepancies between the two numbers, because (if
I understood the calculation correctly), luck evaluations would have to be
done 1-ply deeper than error evaluations to perfectly match.
But there has to be something else that eludes me, right? What other factors
make one method of estimating skill so different from the other?
Thanks in advance, happy rolls
—F
