But don't forget that the little battle scene does have quite a bit of information...
As was asked above, your soldiers dress reflects your techlevel, or rather when you reach certain specific levels you get a new sprite. If several nations are involved you can see all of them on the field with the correct sprite and flags...
But if you look carefully in the picture of the seabattle, you'll see up in the right corner and in the lower left you see a flame of sorts with a number next to it... That means the ships are in the fire phase and the numbers signify the total of techlevel, commander (admiral(s) in this case), other special bonus you might have... While the arrow in the middle between the shields signify who is winning...
Cobos
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If you are not part of the solution you are part of the precipitate.