# blueollie

## Mathy post: women’s legs, polls, pigeons and expectations …

Workout notes: it was 75 F and yes, 100 percent humidity again. THAT, plus my 3 in a row this past weekend (15 mile run Saturday, 13 mile walk Sunday, 4 mile race on Monday) left me tired. So I did a slow, untimed 6.3 (10K) run/walk. Today, it was enough.

Women’s legs and running

Ok, the youngest woman in the photo (calves!) is in her late 50’s. The one with the blonde ponytail is in her early 60’s; the other two are over 70. Yes, all frequently win awards at running races.

So the question: do these ladies get their legs from all of that running, or were these ladies attracted to running because they had the genetic potential to have good legs for running? The answer isn’t that clear, is it.

Yes, I’ll put this as a bonus question on an exam at the appropriate time.

Speaking of statistics: Nate Silver gives a run down of the current state of the election. Clinton is about a 70 percent favorite in many models (including the betting lines) and about 90 percent in the Princeton model (see the NYT model and other models here). If you look at what we are seeing in the polls right now (Trump with a narrow lead in a few of them; the rest showing Clinton with up to a 6-7 point lead), we see that 3-4 point Clinton lead best explains what we are seeing.

Presidential elections in “no incumbent” running years tend to be close (3 times in my lifetime, the popular vote spread was less than 1 point: Kennedy-Nixon, Nixon-Humphrey, Gore-Bush, twice it was 7-8 points: Obama-McCain, Dukakis-Bush).

And this leads me to another topic: conditional probability. This shows up in the famous Montey Hall problem.

Imagine a game: you are shown 3 doors; the prize is behind one door and the other two doors have nothing. Here is the rule: you pick one door. Then the person running the contest *always* shows you a door that does NOT have the prize. Always…and you know that the person running the show WILL do that.

So, should you switch to the door that you did not pick that remained unopened?

Answer: YES. And pigeons are actually better able to figure it out than humans!

Here is the math behind this:

You pick one door: 1/3 is your probability of success. Then you are given the option to choose from the two doors that you did NOT pick…that means if you switch, your probability of success climbs up to 2/3. Remember you only fail if you were right the first time.

Think of it this way: imagine there were 100 doors. You pick. Then you are shown 98 doors where the prize is NOT. Would you switch? Remember your probability of being right on the first choice was 1/100.

Here is where “conditional” comes in: label the doors I, II, III. You pick I. You are shown that it is NOT II.