You literally wrote "all else equal" in your comment.
> pull runner speeds from any distribution
Not true. If I pick a distribution of elite women and non-athlete men, all of the top finishers will be women. You're assuming speeds are normally distributed; they are not.
Where is this data that you're citing here? It doesn't line up with any data I've seen, nor with my extensive experience in amateur racing. Most races are won by the same small group of elite runners. The size of the field is immaterial as the majority of racers have no chance of winning.
Normalizing for population size might make sense if you actually had to beat everyone independently. Fortunately, you're only racing the person in first so everyone else can be safely ignored.
Put another way, if Michael Phelps is racing he's going to win. You can only win by beating him, the rest of the field doesn't matter.
>>You literally wrote "all else equal" in your comment.
That's different from the assumption that all competitors are equally likely to win.
>You're assuming speeds are normally distributed
No. Any distribution will work.
>Where is this data that you're citing here?
I didn't say anything about data. I said your argument has a blatant mathematical flaw. You said "why would it matter" in response to "if 90% of the competitors [are men]". It absolutely matters. Even if you do turn out to be correct about women being worse at this sport, you are only right in the broken clock sense.
>Put another way, if Michael Phelps is racing he's going to win. You can only win by beating him, the rest of the field doesn't matter.
The people who show up to the race are coming out of some distribution. Michael Phelps isn't showing up to every race. The probability that you win the race comes down to how fast you are vs. the max of n samples from the distribution of runners.
The list of the winner of some annual marathon is a really shitty piece of evidence. Out of all the racers and times taken, it gives us data on exactly one of them. It is especially useless to try and breakdown running ability by demographic because it doesn't even tell us how much data we have on each demographic of interest.
If you don't see why just citing the list of marathon winners fails to reject the hypothesis that women and men are about equal at ultra-marathons, then you don't understand what makes for a good data-supported argument.
This is what happens when you don't look at the data and argue from your gut. We don't just learn about one person, timed races release bib data for everyone in that race.
If you're a data nerd and a runner armed with this knowledge, it will have occurred to you to wonder if distance (in time) from the winner is correlated with gender and field size. It is not. Thus, you're proposing that we "normalize" for something which is shown to not have an effect on who wins a race.
You literally wrote "all else equal" in your comment.
> pull runner speeds from any distribution
Not true. If I pick a distribution of elite women and non-athlete men, all of the top finishers will be women. You're assuming speeds are normally distributed; they are not.
Where is this data that you're citing here? It doesn't line up with any data I've seen, nor with my extensive experience in amateur racing. Most races are won by the same small group of elite runners. The size of the field is immaterial as the majority of racers have no chance of winning.
Normalizing for population size might make sense if you actually had to beat everyone independently. Fortunately, you're only racing the person in first so everyone else can be safely ignored.
Put another way, if Michael Phelps is racing he's going to win. You can only win by beating him, the rest of the field doesn't matter.