On 7/27/2023 1:37 PM,
[email protected] wrote:
We all know the role that luck plays in the game.
But, assuming that we can rely on the bots (a very reasonable
simplifying assumption in my view), how should we assess
match performance?
The answer is actually blindingly obvious -- simply observe how
much MWC (match-winning-chances) a player sacrifices.
Bob Koca and I argued this point on BGOnline many years ago,
so I basically agree with you.
We got considerable pushback. The counter-argument that I found
to be most reasonable is that if what you're trying to do is to
estimate *how skillful each player is*, then EMG greatly reduces
variance while (probably) introducing only a small amount of bias.
Here's an illustrative example. Suppose that an 11-point match
at some stage reaches 3-away/3-away. Player A blunders horribly
in the first game of the match, but plays very well in the
3-away/3-away game. By MWC standards, Player A plays very well.
But now imagine that, hypothetically, the 11-away/11-away game
and the 3-away/3-away game were switched. You might infer
that in this scenario, Player A would blunder horribly in the
3-away/3-away game but play the 11-away/11-away game very well.
(This is certainly not a watertight inference. There are
psychological factors at play---maybe Player A's blunders are
a function not of the decisions that arise but of "nerves" in
the first game of a match---plus what is "correct" at 3-away/3-away
is not necessarily "correct" at 11-away/11-away. Nevertheless,
I think it's a reasonable supposition.) In this hypothetical
scenario, Player's A's performance is much worse, because
blunders at 3-away/3-away are more costly than at 11-away/11-away.
We could say that Player A was "lucky" that the tough decisions
arose in the first game rather than later on in the match.
In the long run, we expect that this sort of "luck" will even out,
but it could take a lot of matches for that to happen. All those
EMG shenanigans are a form of (biased) variance reduction, to try
to get a more accurate estimate of skill from less data.
I think this argument is reasonable as far as it goes. If you're
trying to award BMAB titles based on performance, then using EMG
is probably going to yield more sensible results---the benefits
of variance reduction probably outweigh the drawbacks of bias,
especially because there probably isn't going to be that much
*systematic* bias (EMG will probably be biased in one direction
for some matches and biased in the other direction for other matches).
On the other hand, this still doesn't give us a good argument for
using EMG for assessing *who played better* in a particular match.
For this, I agree that MWC is still a more logical choice than EMG. Unfortunately, I think that people have gotten so used to EMG that
they will probably balk if MWC and EMG give different answers to
the question of who played better.
---
Tim Chow
--- SoupGate-Win32 v1.05
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