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From the source code on Github, it seems that all trainings do what it says on the description, for ex. the Close Combat one gives 1% boost to the Attack stat with no upper limit.

The Fire training benefits the Bazooka and Gunman, Chemical training benefits the Mercenary and Knifer.

The only training apparently not being used is the Speed boost.

cool... that is very helpful... thanks... I didn't know the fire training and chemical training benefited those troops!

And do you know if the melee bump will affect all the melee from the hobo to the ninja? likewise with the range bump?

Yes to both answers.

Adding that the Weapon training benefits the Rowdy, Sniper and Hitman.

And each level of the Coordination training gives 0.1% power, up to 100% of course. Power is calculated based on your total units supply, and as soon as you get to 253 your power goes down to 99%, but it goes down slowly, at 1000 supply your power is 98%

wow, very interesting on both answers... thank you very much for your informative answers @cfpg!