There is always a danger in assuming equal probability of victory/loss for each
game in a series unless it is played by robots.  However, I broke down and
decided to do a rigorous number crunch since Stephen Leroy pointed out some
errors I made in my initial, but unposted, calculations that I used to come up
with my argument.  (Sue me, I haven't seen stats since high school :-)
 
Continuing on the assumption of equal probability for each game in the series
and staying with the given probablity (there is nothing magical about 0.3, it
is entirely arbitrary), the following numbers can be obtained:
 
Single elimination: 30% chance underdog wins
                    70% chance favorite wins
2 out of 3:         21.6% chance for underdog (8.4% less than single format)
 
3 out of 5:         16.3% chance for underdog (5.3% less than 2 of 3, 13.7%
                                               less than single elimination)
 
4 out of 7:         12.6% chance for underdog (3.7% less than 3 of 5, 9.0% less
                                               than 2 of 3, 17.4% less than
                                               single elimination)
 
5 out of 9:         9.9% chance for underdog
 
Look what happens to the numbers when we take a mismatch (say 10% chance for
underdog in a single game) and an even match (say 49% chance for "underdog" in
a single game)
 
 
                         chance for underdog
single game              49%            10%
 
2 out of 3               48.5%          2.8%
 
3 out of 5               48.1%          0.8%
 
If the games are evenly matched, there is almost no difference in the
likelihood of an "upset."  The more of a mismatch is present, the more to the
advantage of the underdog is the single-elimination format.  For my original
30% assumption, we cut the chance of an upset by 28% going from a single
elimination to a best of 3 format.  In the 10% assumption, we cut the
probability of an upset by 72% from single to best of 3, and for the 49% case,
the probability is cut by only 1%.
 
The question comes down to, how evenly matched are the first and second-round
games?  Are they on the whole more like the 49% case or like the 10% case?
Since it is not possible to quantify these probabilities without having the
teams play each other a few hundred times, any answers to these questions are
mere speculation, but whether or not you favor single-elimination may be
largely a function of how even you believe that teams are in the early rounds.
 
Since games are not decided merely by chance, this whole thread has limited
application by itself.  (One more log on the fire however :-).  If one takes a
team with a two-week layoff, against a 30% underdog, in a neutral arena, on bad
ice, it does become apparent--in my opinion--how the single elimination format
is a great disadvantage and disservice to the favored team.
 
 
 
 
--
Dave [log in to unmask]
Cornell '91 OSU Med '95
Let's Go Red!