The +1 armour effect of each upgrade appears to be misreporting by the game. Testing by
SMZ,
Carl,
Lusted and
Foz implies that armour upgrades work as expected, in that each upgrade provides the reported type of armour (padded, light mail etc). The upgraded armour stat does not appear to be correctly reported, but the unit is still as resistant to missile fire as you would expect from a unit with that type of armour. Here is
Lusted's summary of what armour stat corresponds (roughly) to each armour type:
Level 0: Flesh - 0
Level 1: Padded/leather - 3/4
Level 2: Light Mail - 5
Level 3: Heavy Mail - 7
Level 4: Partial Plate - 8/9
Level 5: Full Plate -9/10
Level 6: Advanced Plate - 10/11
The implication is that the lowest type of armoury is a great bargain - raising the armour stat of your initially unarmoured troops by around 3-4 points.
Discussion and original research here:
https://forums.totalwar.org/vb/showthread.php?t=79784
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