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Douglas Zare writes:
> How much does luck and skill correlate?
They certainly aren't mutually exclusive. The luck in backgammon means
that the game isn't decided by who makes the first mistake. The luck
means that it matters how much better than your opponent you play, not
just whether you play better.
The flip side of the coin is that you can determine how much better
one player is than another by determining how much luck is needed for
each to win. This works if you measure luck in mwc in an unbiased
fashion, not in EMG or EMG/move.
> When two players are comparable in skill a -5 or -10 in luck rate
> (Snowie terms) pretty much decides who wins.
That might be reasonable for money play, if you play for a fixed
amount of time. In match play, you don't stop after a set period of
time, but after one side is ahead by 50% mwc.
If luck is properly measured, then between competent players, the
luckier would win the match over 99% of the time. The main reason you
can find examples that don't look like this is that Snowie's luck rate
is a bad measure.
A luck rate in EMG mainly tells how the match was won, i.e., what
match scores were hit, as well as how easy the takes were for any
doubles accepted. Suppose in a 3 point match player A wins 1 point,
then another single game. Then player B wins the Crawford game,
doubles player A in, and wins at DMP. Who was luckier? Player B,
obviously, unless A was playing absolutely terribly. Player B won. Who
had more luck in terms of EMG?
Perhaps player A, by about 0.200, and if the match took 200 moves the
luck rate for player A might be +1 millipoint per move. That's because
with perfect play, the luck in EMG for player A was +1 in the first
game, about +1.2 in the second game, -1 in the third game, and -1 in
the fourth.
When expressed in mwc, the luck for player B should be about +50%. It
is 50%+net skill. So, if player A made one little mistake and player B
played perfectly, the total luck for B was +49% mwc. If player A makes
the same mistake and then wins, the total luck for player A was +51%
mwc. Even though the luckier player wins, the weaker player needs more
luck to win, hence wins less often, since luck averages to 0.
> Same rolls, one checker play error. Still the luck rate is negative
> just because of one "tiny" misplay.
The luck for a roll is independent of how you play it. However, there
is no reason to expect the luck of a particular subsequent roll or
sequence (which you specified) to be the same, no matter how you play
this one.
If you win the opening roll, 2-1, splitting is about the same as
slotting. If I respond 4-3, this is a lucky roll for me if you have
slotted, since I get to hit. It is an unlucky roll for me if you have
split. Of course, to balance this, there are rolls which are luckier
if you have split than if you have slotted, such as 5-5.
I don't see any reasonable measure of luck that says, a priori, what
the luck was of the sequence 2-1, 4-3.
> I have a hard time figuring out if my play is improving or not just
> because my luck rate has been "awful" for so long. It might well be
> that my play has improved a lot, but because I was having a bad run
> I don't see as much gain as I should have. This is a bit of a
> motivation issue.
Why focus on the results or your luck rate? Much more useful is to
consider your error rate or your net skill advantage. It makes more
sense to ask whether you play as well when your luck so far in a match
has been bad as you do when your luck has been good.
Douglas Zare
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