it's pretty obvious what the answer is.
go to the maintenance calculator on the .gov website.
Here are some examples:
If he earns £80k a year, his weekly income is £1583 per week and he's got 0 other children in his care, (assuming he houses his (1?) child only once per week of less) then he needs to pay £162 per week (at least)
If he gets a £40k bonus then his yearly income is £120k.
so take £120k divide it by 52 and you get a weekly income of £2307, under the same circumstances he'd now need to pay £232 per week (at least)
At the start of the year, your partner and his ex sat down and thought, I'll probably get £80k basic wage, and about a 10k bonus so that's 90k per year and a weekly maintenance amount of £180, he's been paying that, so sure, at the end of the year if he hadn't got a bonus, he'd have over paid by £18 per week. but that's not the case, if he ended up with a £40k bonus then he's underpaid by £52 per week.
You might think that his ex wife made a gamble and lost so tough, but that's not the case, he has a duty to pay maintenance (at least) AT THAT RATE. and if she goes to the CSA she will win this argument, and he'll end up paying even more to use the service.
What I would suggest he does in future is: pay at the rate that he's doing now. (e.g. £180 per week). (guessing he'll get a 10K bonus)
and then at the end of the year he uses his p60 to work out what he was actually paid each week, and puts that number into the calculator.
If it works out he overpaid, then walk away knowing that he did the right thing for his kid, if it works out he underpaid, then figure out by how much, (in this case £52 per week so £2704 for the year) and make a lump sum cash payment to ensure that he makes at least what he'd have to pay if his ex went to the CSA.
If it works out that he was paying more than he has to when his average weekly income is figured out (including the bonus), then tell her that she doesn't "deserve" his bonus, if he's underpaid when earnings over the year are averaged, then she is entitled to some of it.
(you don't need to guess, there is an online calculator)
If he makes contributions to his kids savings, then that's great, but has nothing to do with maintenance.
Basically, your idea that they reached and agreement, that she somehow gambled and lost is wrong.
Providing for your child is not a gamble, it's a requirement, (both legal and moral.)