Knights upgrades against xbow?

So assuming you scout xbow, in what order should you upgrade your knights? I was trying to do the math and it looks like bloodlines is the least valuable?

Assuming bodkin for the xbows, their attack is 5+2 so I’m measuring success by ability to one shot a knight (my calculation is designed to figure out how many xbows it would take to one shot a knight with perfect accuracy).

Baseline: for a knight with 0 upgrades, it takes 20 xbows to one shot a knight (base armor of 2 means each xbow does 5, 100 hp/5=20)

So your first decision is whether to get bloodlines or the first armor:

+1 armor: 25 (100hp/ 4) Bloodlines: 24 (120hp/5)

Thus assuming you get the +1 armor first, then is it better to go bloodlines or +2?

+2 armor: 34 rounding up (100/3) Bloodlines: 30 (120hp/4)

So my question to reddit is, am I missing something (very possible?). Because it looks like it’s much effective to go armor first then bloodlines if you know you’re facing archer/xbows.

For spears/pikes bloodlines comes first of course. But I’ve just been blindly going bloodlines first without thinking through alternative options