outside running wrote:
mortyd wrote:
It's not as ridiculous as you think if you look at the top finishers. The top five finishers in the 2020 OTM race were very tightly grouped around the average height:
That's about what you'd find on average picking 5 random men from the USA, fairly "tightly grouped around average height".
That is actually not at all what I would expect to find (as opposed to the previous poster who said I "struggle with statistics"--math is actually my strength). Don't worry, statistics as a subject in general is not intuitive at all. We have to crunch the numbers and not rely on our gut. Let's do some math.
Note that the first five finishers were all within 2 inches of the mean. The first assumption that everyone has already made is that the height of the marathon runner is normally distributed and mirrors the general population. The average height in the United States is 69 inches with a standard deviation of 3 inches. Graph that and then calculate what the area under the curve is within 2 inches of the mean. It turns out the probability that a runner finishing the race is within two inches of the mean height is 49.5%. It is essentially a coin toss per runner whether they will be within that tight range or not. You would expect to see a runner that is more than two inches taller or more than two inches shorter 50.5% of the time.
So the first runner that crosses in that range is 49.5%. Ok, I believe that is possible. The second runner that crosses is also in that range. Ok, the probability is .495*.495=24.5%. Interesting, but still possible if it is random coin flips. The probability of a third runner crossing in that range is: .495*.495*.495=12%. The fourth runner is .495*.495*.495*.495=6%. The fifth runner is .495*.495*.495*.495*.495=2.97%.
So the probability that the first five runners would be within two inches of the mean height is only 3%. That is not what we would expect when picking people from random in the general population. It leads me to believe that something other than chance is going on.
Again, I don't have all the data. I'm not saying we should draw any final conclusions from the math above. It makes me want to ask more questions and get more data to investigate further. I suspect that you don't have all the data either, so don't make definitive statements about things you can't prove without the full, complete data. Again, be kind and thoughtful and respectful. Don't rush to judgement and grab the pitchforks. I'm just asking thought-provoking questions about what I see.