While 1 is a completely valid point for hunter-gatherer tribes or an all-out-war, it is quite irrelevant if we talk about professional soldiers. A standing army with full-time soldiers comprise only a small fraction of the population, because it has to be supported by a lot of farmers and other jobs. So it shouldn't really make a difference if this 2-3% of the workforce is male or female.

And even with predominantly melee warfare (so mainly spears) I've yet to see convincing numbers about men consistently outperforming women in a complex task like fighting, where coordination, morale, group cohesion, dexterity play a bigger role than raw peak-strength.

For 3: You don't even have to go mechanized. Even fighting from horseback is already a discipline where better technique and better coordination with the animal easily outperforms stamina and strength.

@Falco a small standing army is far from the norm through much of history. Even if that argument was valid - I'm not convinced - a society isn't going to want to switch to a completely different mode of operation once matters turn to all out war. For your other two points - even if valid, there is much more to soldiering than the tiny amount of time spent actually fighting, and many of the tasks require considerable physical strength eg constructing fortifications and carrying heavy loads. The group cohesion you mention relies on everyone literally pulling their weight.

I think many societies operated like this a small professional core (later often nobles or knights) and depending on the situation a varying number of rather untrained farmers with weapons. The military elite of such a society could as well be mostly female, while the call-to-arms to defend your homes could reach more males than females.

Regarding "pulling their weight" - modern studies suggest females may actually possess superior stamina, endurance and resilience to males. This is why women often run on par in very long-distance runs and similar activities. For typical army activities endurance could very well be more important than strength.

@Falco this is mostly at the ultra-endurance level, as in a double marathon. At a somewhat shorter level of endurance (marathons, tour de france) the men still dominate very much.

@Falco you are entitled to your opinion. There are definitely outliers in capability at both ends of the bell curve - a few years ago I was beaten in an ultra by over an hour by a woman celebrating her 60th birthday, which made her a decade older than me. There are also certain military roles, as explored by Keith Morrison in his answer, that can be filled better by smaller individuals. However, the fact is that the average size and strength of human females is significantly less than that of human males, which puts most of them at a disadvantage in the field where raw strength matters.

Exactly - I'm not contesting this. What I'm contesting is if raw strength matters enough in a military like e.g. the Roman Army to make a mixed gender army actually perform measurably worse in war.

"violent, risk-taking (aka stupid) ones" -- Does evidence support that risk-taking is correlated with lower intelligence?

@Falco Would the Olympic Games convince you? Sport fencing isn't a mixed-gender event. Nor is any regulated sparring competition in any martial art anywhere, for that matter. Sure, a skilled woman can often beat a less skilled man, but sheer strength and mass is always an advantage.

@Falco The load that infantry carry routinely in combat areas is between 60 to 100 pounds. These heavy loads contribute to chronic pain suffered by male soldiers. Your average women is signifcantly weaker than your average man.

@Falco Modern studies suggest... What modern studies? Give me a paper with a name. I'll give you one, War and Gender by Joshua S. Goldstein. A very small percentage of women are as physically capable as a significantly larger percentage of men. Depending on where you set the bar it can range from an army that is 85% men and 15% men (Taking 50% of the population) or that is 99% men and 1% women (Taking on the population of people who are 2 standard deviations higher performance than the average man)

@WayneConrad I was being slightly tongue-in-cheek and was thinking of adding that I enlisted (with parental permission) at the age of 17, with most of my fellow enlistees also being male and, with hindsight, lacking in wisdom if not intelligence.

@WayneConrad In a common use, "stupid" refers not to a degree of brute computational capacity, but more to an attitude, or state of mind. (See stupidity.net for such a definition: story 2, page 24.)

@Michael Yes, especially if its consistently the most warlike women who are dying in combat instead of having warlike children.

I doubt you actually need better firearms, so long as the weapon designs you are using can sufficiently level the playing field. In this regard, a way to re-cock a crossbow that provides a large enough mechanical advantage may be competitive.

If you have to consider "total war", you need to think of the ratio of front-line troops versus the logistics personnel, the people working to produce the arms, ammunition (and everything else) the troops are using, the industrial net supporting that, and finally the people working the farms that feed everyone. If you look at both world wars, the ratio looks pretty good, and it doesn't matter too much who you put on the front line. However, if the war then drags on into attrition, and you keep having to replace those troops, it becomes a problem again.

@Graham the olympic games (like most sporting events) have a long selection bias in favor of males. E.G. the male top athletes are usually selected from a much wider group of males trying to be successful in sports. On the other hand fencing is a good example of body/muscle mass not having a significant impact. There are no weight-groups in fencing and the fencing champions are usually not the largest fencers - in fact articles who looked at this came to the conclusion "there is no correlation between size and success in fencing

@Questor I was referring to this article from the Uinversity of alaska. But they don't give an original source. uaf.edu/news/women-may-have-advantage-in-the-long-run.php

@Questor My understanding is this: The load which a soldier needs to carry is usually as much as the average soldier can carry reliably and sustainably without reducing his combat effectiveness too much. So if women can in fact carry less, the army would reduce the overall weight of stuff they need to carry and this would probably be the disadvantage of a mixed gender army, they having less stuff (or lighter weight armor)

The big gap in reasoning I'm still missing is how these small differences in raw strength, body size etc. actually translate into reduced combat effectiveness and on what scale. If a mixed gender army would e.g. be 3% less effective than an all male army, this difference would be completely irrelevant and not even measurable in a medieval setting, because other factors would be dominating the equation when comparing armies between different countries.