The question of the amounts of bond needed for each level for various Servants came up in another thread and I thought I would poke at the numbers for a bit. Namely, they’re not constant, so why do the amounts of bond differ between Servants? So far, my best answer is that it’s probably a statement about Servant personalities, and doesn’t seem to have anything to do with any hard stats otherwise.
I looked at 4* Sabers, which is a decently sized list that restricts the number of variables involved, and then added some 4* Lancers and 3* Sabers (and Jason), and a 4* Caster for a Cavalry class.
There are a couple of common bond growth types.
One is a very flat progression: 3k, 6.125k, 6.125k, 6.125k, 6.125k to level 5, then 262.5k, 290k, 300.5k, 309.5k, 315k. This holds for Suzuka Gozen, Nero Claudius, and Siegfried. After an initial fairly easy “getting to know you” phase, your relationship develops steadily as long as you spend time together. Of course, for everyone it’s the case that after the basic bond is established, the deeper relationship takes much more work but for these Servants it’s still just steady going. A very workaday sort of relationship.
Some grow linearly, then a bit quadratically: 2k, 3k, 4k, 5k, 6k, then 210k, 230k, 270k, 350k, 400k. These sorts of Servants strike me as high initial gregarity: Diarmuid Saber, Altria Lily, Qin Liangyu. It’s easy to hang out with them at first, but harder to make things deeper.
Other Servants are very spiky. Salter’s first 5 are 4.5k, 20k(!), 2.5k, 2.5k, 10.5k. Is she tsundere, resisting at first but then easily acquiescing to a deeper bond until hesitation the crucial step? Her back half is the same way: a comparatively low 160k followed by a wall at 365k, then a rather lower 315k, 310k, then 350k. Lancelot Saber uses the same numbers and Nitocris behaves similarly. Perhaps these Servants are touchy about certain subjects. Yagyu Munenori behaves similarly but at an even greater extreme, very standoffish in general: 5k, 15k, 10k, 2, 18k, followed by 150k before 400k (usually a capstone level), 300k, 280k, 370k, the highest total among 4* Sabers.
Then there is Raikou Lancer: 3.5, 8.5, 7, 6, 2.5, followed by 272.5, 330, 310, 290, 286. A unique pattern. A pattern which, if one graphs it, looks decidedly like… two… mounds…