Re: 700/23 vs 700/25 tires ?

On Mar 3, 5:40 pm, Tim McNamara <tim...@xxxxxxxxxxxxx> wrote:
 "b...@xxxxxxxxxxxxxxxxx" <bjwei...@xxxxxxxxx> wrote:

Suppose that my buddy Greg is in the same category as me but is
actually a decent racer (even if a little obsessed with the economic
treatises of Salma Hayek) and he has a 25% chance of winning each
race that he enters in a 40-race season.  (Let's assume that each
race is similar and statistically independent, but he only wins
sometimes due to the vagaries of random race circumstances.)

Greg has only three other competitors in his class?  That's the only way
he'd have a 25% chance of winning each race.

This is statistically illiterate. You believe a version
of the RBR joke that whenever there are two
outcomes, the chances are always 50/50.

One could imagine that in a given race, there's
2 racers with a 25% chance of winning, 2 with
a 10% change, 4 with a 5% chance, 10 with
a 1% chance, and 10 with no chance at all.
This is far closer to the reality I've seen than
everyone having an equal chance.

The exact numbers don't matter. Frank's
A/B test is incapable of determining the
difference in 40 races between someone
who has a 5% chance of winning and
someone who has a 10% chance, because
the statistics aren't good enough. Yet that
is a difference that would be significant
to a racer.

Again, this is not an argument that there is
some magic piece of equipment that will
double your winning chances. It's an
argument that even if you train your ass off
and improve your chances of winning by
a fair fraction, merely counting the number
of wins in a season is not going to tell whether
you actually improved, unless you did something
extreme like move from being a backmarker to
winning half your races. Failing that, you have to look
at more than a discrete set of binary win/loss
outcomes. (By that I mean you could look at
your power, your speed on hills, your average
finish place, and so on.)




<snip>

This is why I'm saying that Frank's idea of an A/B comparison of race
outcomes is worthless - it's not sensitive enough to tell us what we
want to know. That doesn't mean that we can't measure effects.

Ben, this is what I and Frank have been trying to tell you all along.  
You can't identify any effect of these things in the outcomes of races.  
You've just demonstrated that.  Congratulations!

No, that's not what Frank has been saying.
Frank has been saying that these things are
in fact negligible - that they don't make a
difference. I'm saying that his proposed
experiment doesn't have a large enough
sample size to tell whether any effect, including
reasonable training effects, makes a difference or not.

There is a difference between existence of
an effect and detectability of an effect. Because
Frank didn't work out the sensitivity of his
proposed experiment, it was only good for
posturing on Usenet. For example, it could
never have been used to, for example, write a
physiology paper on the effect of a training method.

Suppose that I take 10 cyclists and have half
of them do a program of lactate threshold intervals
(2x20 min or similar). Then I count their wins
over a ~40 race season. That gives me 200 outcomes
in the sample and 200 in the control group. That
experiment is not going to be large enough to tell
me whether LT intervals help, unless there's an
insanely large difference. For example, even if
the LT group won 20 races and the control group
won 10, it would only be a 1.9-sigma effect.
(You can check these numbers via the formulae on
the Wikipedia binomial distribution page.)

It would be better to do something like measure
their power outputs, a non-discrete set of outcomes.
In fact, that is what physiologists do, and that
is how we prove scientifically what common sense
tells us, that training helps. Similarly,
if we cared about equipment differences, we
could measure power differences, as has been
done with tires and with aero drag.

If you and Frank continue to never work anything out
by the numbers, but wait for me to feed to examples
and then try to complain about the specific
percentages I chose, you aren't ever going to learn
anything about how one scientifically verifies or
refutes common sense - which is wrong sometimes.

Ben
.

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