What is a realistic size and population for a predator that eats humans?

its favored prey is humans

despite how much some of us brag about humans being the apex of evolution, we make for a very poor prey: when raised free ranging we are very lean, and fat, energy rich tissues are the most prized tissues for carnivores feasting on their preys. Compare the fat content of a seal with a surfer, and you understand why often sharks bite and drop.

On top of that, we have this nasty habit of hunting into extinction any predator who feels too eager in having this weird two legged tofu sample on their menu.

That said, solitary predators, like most felids, need to be larger than their preys to have decent chances of overpowering them. Compare tigers with wolves: wolves, being able to rely on group hunt, can afford being smaller.

Big cats (tigers, mountain lions, panthers, cougars, lions...) are your reference here for a ballpark reference on the body size. Anything smaller than them would have a hard time in efficiently overpowering an adult. Population size-wise, still look at them.

What I said about the nasty habit we have also becomes the weak point of your setting: a true human like population would quickly act to hunt down the predator population, while for a population without that trait I would argue that it cannot be classified as human. Grazing herbivores do what you want, not hunter gatherers.

As L.Dutch has said, it hardly matters how big these predators get unless they're so tough and heavily armoured that hunter-gatherer humans basically have no chance at all of killing them.

Humans are very good at hunting things, no matter their size. These predators would need to be so heavily armoured that a spear or an arrow could do no damage, and even setting a spear against their charge would result in a broken spear. The predators would have to be awfully suspicious of poisons too, otherwise they might eat a poisoned prey and die.

However, assuming that these predators are able to usually survive any attempts by their prey to reduce their numbers, the populations of predators and prey are mathematically related, according to the Lotka-Volterra equations:

$\frac{dx}{dt}=\alpha x - \beta xy$

$\frac{dy}{dt}=-\gamma y+\delta xy$

Where:

• $x$ is the population density of prey (for example, the number of rabbits per square kilometre);
• $y$ is the population density of some predator (for example, the number of foxes per square kilometre);
• $\frac{dy}{dt}$ and $\frac{dx}{dt}$ represent the instantaneous growth rates of the two populations;
• $t$ represents time;
• The prey's parameters, $α$ and $β$, describe, respectively, the maximum prey per capita growth rate, and the effect of the presence of predators on the prey death rate.
• The predator's parameters, $γ$, $δ$, respectively describe the predator's per capita death rate, and the effect of the presence of prey on the predator's growth rate.

All these variables are positive real numbers.

For warm-blooded predators and prey, this typically works out to the prey having a biomass around 100 times that of the predators, while for cold-blooded predators, the prey might have a biomass of around 10 times that of the predators. As the wikipedia article shows, the population changes of the predators is similar to but lags that of the prey populations somewhat.

So, knowing this, you should be able to calculate the relative populations of hunter-gatherer humans and these mythical predators. Just be sure to assign reasonable values to the variables.