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Are the your argies levelled up in melee? Because levelled up stats (along with imprinting boosts) does not affect breeding, their stats only really matters the moment the moment they are hatched or tamed. Otherwise, it's pretty much just bad RNG that got you the most.
For example. Lets say you tamed or hatched two argies. The male has 350% melee, and female has 450% melee. The baby has 60-70% (the chance seems unknown, but it's definitely higher) to inherit 450% melee. However, imprinting and levelling does not affect breeding at all, so if you imprinted or levelled that 450% melee argy to have 520% melee, it'll still use 450% as the chance to pass down.
It's generally a good idea to have a screenshot of the freshly tamed or hatched dino before lvling or imprinting it. It'll serve a good record for breeding.
@OP: For each stat, theres a slightly above average chance of the baby getting the higher of the parent's stats. It's something like 65% or 70%, I forget exactly. But it has that chance for every stat...so the baby has that percentage chance of getting the higher of the two stamina stats, that percentage for the higher of the two weight, that percentage for melee, etc.
There's a lot of RNG involved, and it sounds like you've just had some bad random generation there. You will get it eventually though, keep at it. Just be glad you're going for only one stat - when you get deeply into breeding and you have to combine several different stats from multiple parents into one creature, you may have to go through hundreds of babies before you get the perfect combination you're looking for.
EDIT: Good point Panda, that is something to consider too. Only the levels at tame will pass down, not levels pumped by the player after tame, and not imprinting stats.
According to the wiki, assuming it is up to date, the chances of getting the higher stat is 55% (it used to be higher); so the chances of you never seeing the higher stat in 15 offspring is 100 * (0.45^15) % or 0.0006283298708943145751953125%
Those 2 argies are completely un-leveled and 0% imprinted.
Let's say the female has the best melee but the male has the best health
We don't care about the other stats but we still need to get these in synch because the more stats that match in the parents the higher chance we'll get a baby that has the stats we want
I.E. the more stats that don't match in the parents, the more variation will come out in each baby whereas if only one stat is different there's a 50/50 chance the next baby will have the higher stat we want
So we breed these first two dinos until we get more stats in common, although we have to always ensure to keep the vital stats we need, and breed that better dino back to a parent
E.g. the first generation is a male that has the same health as the father and the same weight as the mother. We now have one less stat to worry about
So we breed this new male with the mother and say we now get one that still has the same health as the original father but now has the same weight and oxygen as the mother
We now repeat the process until we get a baby that has all the stats of the mother but the health of the original father
The last step is to produce a female that has all the best stats and then we can always breed a dino that has the best stats of those two original dinos