While the previous commenter's numbers are exaggerated, the data from articles like this (and a decade ago, from okcupid), consistently shows stark asymmetry between the dating preferences of men and women - to the disadvantage of men in the "bottom" 50%. Before marrying, most of those 61% of women dated other men, and likely with a strong skew towards the top 20% as claimed.
I finally get a chance to pull this obscure study out of my back pocket. It supports your thesis. I’m short by the way and married for the first time at 28 and the second time at 38 (still married). Short men are never in the top 20%.
Tall men were found to marry sooner in life, but were more at risk for divorce later on, as shorter men had more stable marriages. However, researchers note that the link between short men and stable marriages could be because they chose to marry later (or didn't have the option until later).
Tall men were also more likely to marry women closer to their age, and who were better-educated.
