Prolific Math

Can you prove without direct empirical data that men are polygynous? Let's take a look, shall we?

Let's assume that a hypothetical monogamous couple procreates as often as is physically possible. How many children can they produce?

A human female hits puberty at about age 10-14. They hit menopause in their 50s, in modernity, but a high-stress lifestyle, like the ancestral environment, drives this age much earlier. For convenience, we'll use age fifty. That gives the woman a solid forty years as a baby factory.
The average human woman produces about 400 fertile eggs during her lifetime. However, a human baby takes 9 months to gestate, limiting the actual number of children which she can have. Doing the math, this works out to 50 children a woman can potentially have in her lifetime, plus some change.

Men produce over 500 billion sperm in their lifetime.

One ejaculation contains roughly 40 million sperm, though this varies wildly.

That's approx 12,500 full ejaculations that a man can do in his lifetime.

For a promiscuous man, we'll call each ejaculation a potential child.

So a man can sire perhaps 10,000 children in his lifetime, if he takes maximum advantage of his output.

(The actual number here would be much higher, since if you're active enough, each ejaculate would contain less sperm, but your incidence of pregnancy would be relatively unaffected. Ghengis Khan, for instance, kept a harem of several thousand women and probably exceeded this quota of offspring.)

Further, this type of reproduction is a weakly zero-sum game.

A man who sleeps with multiple females has the opportunity to sleep with the mates of the hypothetical monogamous males. These nighttime fornications can and will produce children. Often, the children will be assumed to be the offspring of the monogamous male partner, even though this is not the case. For every child that is raised in this way, the monogamous male is denied an offspring.

Not only do promiscuous males have the potential to produce multiple orders of magnitude more children than monogamous males, but a significant portion of those children are actually denying the monogamous males a chance to reproduce. This effect is so strong, that, genetic anomalies notwithstanding, the last human ancestor that was genetically predisposed to monogamy probably died out millions of years ago.

Of course, this advantage is not so strong that men will risk their lives or status for it. If polygyny comes with a high enough social penalty, as it does today, many men may indeed chose to live mostly monogamous lives, purely to save their own skins. Left to their own devices, however, men fool around. All of them.