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1.7^2 is 2.89, so wouldn't your numbers change to 29% instead of 37%?You’re technically correct, however, it also works the other way, because having 17% more units is not a 17% improvement, it’s a 37% improvement, because you not only have 17% more HP you also have 17% more attack damage. Having more units is exponentially more effective than having better units for this reason.
This means if you do the math you can calculate how many Knights you will want to make for the Cavalier upgrade to be worth it. However, it depends on the situation.
It should be noted that both FU Knights and FU Cavalier in Imperial age kill Arbalests in 4 strikes, so the attack doesn’t matter, the only thing that matters in that particular comparison is the HP difference, and Cavalier only have +20 HP so it’s not a massive deal and the Cavalier upgrade in this case only ends up being worth it after you have 62 Knights, because it’s always better to have 5 more Knights than to have the Cavalier upgrade _until you already have 62 Knights_. 63 Cavalier is better than 68 Knights, 64 Cavalier is better than 69 Knights, etc. But 30 Knights are better than 25 Cavalier.
Against other Cavalier though, it’s different. Both the attack and the HP matter. It’s 16 hits compared to 11 hits for Knights against Cavalier. This means that the upgrade is worth it after 24 Knights. Otherwise, adding 5 more Knights is better. Test it out in the scenario editor; 29 Knights vs 24 Cavalier. It should be a pretty even result. Prove me wrong! I probably messed up the math somewhere.
Against Halberdiers, the HP doesn’t matter, both FU Knights and FU Cavaliers die in 4 hits from Halberdiers. So the attack damage is all that matters. The Cavalier upgrade is only better than 5 more Knights in this case after you have 52 Knights.
Basically, my point is that if you are only going to make a small amount of the knight line, there is no need to get the Cavalier upgrade, because it’s better to invest the 300 food and 300 gold into more kts. However, obviously if you are going for the kt line as your main army, the Cavalier upgrade is definitely worth it, especially in team games where you are focusing more on population efficiency than cost efficiency (and in that case usually the Paladin upgrade comes in).
Also thank you guys for all of your responses
It's true that Knights upgrades are prioritized as follows usually: +4 armor, then cavalier. Personally if I'd give a general rule (given no pala or only weak cavalier) I'd only upgrade cavalier if I had about 15 knights on the field.