Well ...
It's more complex than that.
Introduce the cost of the army in your equation and it will be different.
Using your postulat the army with a lot of soldier should contribute the most even being inferior to a technological and more efficient army having less soldier.
Use a recent example like desert storm
I (the 90's one

)
Saddam army should have contributed more to a UN mission than the coalition.
But doesn't have Saddam's army been badly beaten ?