Mon, 15 Dec 1997 19:16:00 -0500
From - Thu Jan 08 14:45:29 1998
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Date: Mon, 15 Dec 1997 19:16:00 -0500
From: Robin Hillyard
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Subject: Lehmans, newbies, etc.
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Recently there was a thread (amongst the many Lehman-related threads)
regarding the effects that new players to OKB (newbies) have on stats
(note that I am not talking here about novice, i.e. new players to
duplicate - or even rubber - bridge).
I admitted that I don't like to play too many boards with a newbie if he
or she is clearly not playing at a level commensurate with a 50%
rating. (It's never happened that a real expert newbie has partnered me
but I supposed I would be obliged to point out to him after a few boards
that I would be unfairly impacting his stats). Anyway, I was taken
(mildly) to task for this attitude because I generally won't give them
more than four boards (I don't normally give them less, either). I
would love to be able to welcome them with open arms and not care about
the effect on my lehmans. [OK, so maybe I take them too seriously - I
admit it!]
The suggestion which I've made here in the past would allow just that.
In prior postings I have spelled out the (simple) modification to the
algorithm in mathematical detail (which has probably not helped my cause
much). This time, I'd like to demonstrate how it might work in
practice. These results are based on a simulation (using an excel
spreadsheet) which I'll send you if you're interested. In the
simulations a new player sits down with three other players of average
ability (ie. 50% guessers, having 50% ratings). However, the new player
is only a 40% guesser (that's to say on key decisions, he only makes the
right bid/play 40% of the time). Of course, he has a 50% rating too, to
begin with. They play 5 bds, then break up. This happens ten times
each week. The newbie's partner is always the same person, but the
opponents are different each time (and always 50% guesses/ratings). The
simulation goes on for 10 weeks. Before the simulation, newbie's
partner has played 500 boards (ie. he's been on OKB about 10 weeks,
say). Here are the results (the top row is the week number, the second
is the newbie's rating at the end of the week, and the third is the
partner's rating at the end of the week):
Using existing Lehman formula:
1 2 3 4 5 6 7 8 9 10
47.3% 46.5% 44.1% 43.0% 42.7% 42.9% 42.0% 41.4% 41.2% 40.9%
49.7% 49.6% 49.0% 48.6% 48.5% 48.6% 48.2% 47.9% 47.8% 47.6%
Using proposed modified Lehman formula:
1 2 3 4 5 6 7 8 9 10
44.8% 44.7% 41.8% 40.7% 40.6% 41.0% 40.1% 39.5% 39.4% 39.1%
50.0% 50.0% 49.7% 49.5% 49.5% 49.6% 49.3% 49.1% 49.0% 48.9%
Note that with the existing lehman formula, newbie gets to 41% rating
fairly slowly (still not there after 10 weeks). The partner drops to
47.5% by that time. With the modified formula, the newbie gets quite
quickly to around 40% (actually a little lower) while the partner is
much less affected (finishes around 49%). The numbers end up perhaps a
little lower than expected largely because this was a random simulation
and the pair actually achieved an overall result of 44.85% against the
constantly average opponents (where perhaps 45% might have been
expected). On the other hand, there is no perfect correlation between
guessing ability (the input to the simulation) and Lehman rating (the
output) although I have found a pretty good correspondence with other
simulations I've done.
Note also that if I had chosen a different number for the partner's
history (say 2000 boards instead of 500) the partner's rating would be
affected even less with the modified formula. In fact with 2000 bds
history, pd's rating would drop only to 49.8% and newbie's would drop to
39.2%.
If you're interested pls post here and copy me too. I'm willing to send
the spreadsheet(s) if you're interested.
spider
--
==============================================================================
Robin Hillyard (781)
275-3286