Troop sizes of second game bonus characters

You may have noticed that the troop sizes of commanders which are added by second game bonuses seems to be 400 with some fluctuations. I will give a review of the algorithm that governs the calculations of these troop sizes: Here are the modifiers for all bonus characters From empirical testing we find, that the optimal average troop count to get the maximum amount of troops from your bonus commander on average will be roughly 480 divided by the modifier of your commander. This will result in the commander's troop count being 425 on average.
 * 1) Calculate the average troop size of your non-footsoldier commanders with more than 299 troops
 * 2) Multiply that number with a modifier that is specific to your bonus commander
 * 3) Fluctuate this number randomly by ± 20%
 * 4) After you start the game, all commanders with troop size >500 will have their troop size set to 400
 * 0.5 : Ouka Toki, Takakura Kamei
 * 1.0 : Morita Ai, Elina, Hasuma Kanae, Makutsudou Nobuh, Mouri Teru, Kobayaka Chinu, Kikkawa Kikku, Uesugi Kenshi, Naoe Ai, Daidouji Komatsu, Nanjou Ran
 * 1.5 : Turban, Natsumi Papa, Kurosaki Yamagata Masakage, Baba Shouen, Kousaka Yoshikage, Sanada Tourin, Dokuganryu Masamune, Orime, Noir, Omachi
 * 2.0 : Nogiko
 * Mouri Motanari doesn't have a modifier and his troop size will be set to 500 by default

An example:
Initially we start with only Ranmaru and Niwa being non-footsoldiers with more than 300 troops, having respective troop counts of 350 and 450. As a second game bonus we only choose Morita Ai. She has a modifier of 1.0, so her troop count will be 400 ± 80. This will result in her troop size being 400 on average.

Now we add Natsumi Papa before we add Morita though. Natsumi Papa has a modifier of 1.5, meaning that his troop count will be around 400* 1.5 = 600. This increases our armies average troop count to (350 + 450 + 600) / 3 = 466.66. If we pick Morita now, her troop count will be 467 ± 93. This will result in around 424 troop size on average - clearly an improvement.

Min-maxing for point runs:
Here is a guide on how to pick second game bonus characters for point runs:
 * 1) Select Natsumi Papa.
 * 2) Select the Mouri bonus.
 * 3) Select Morita, Elina, Hasuma and Makutsudou.
 * 4) Temporarily select all remaining house bonuses.
 * 5) Select Ouka Toki and Takakura Kamei.
 * 6) Unselect Uesugi,  Houjou and Dokugangrou.
 * 7) Select the remaining extra characters.