As long as the parents have 0+ blup, the gp should always increase. Skills and gp both have an element of randomness to them, so if you birth multiple foals some will have higher gp and/or skills than others - even from the same parents. Inborn skills seem to be a lot more random than gp, so if you're trying to breed the best you can (both gp and ibs wise) you'll need to sire multiple foals and pick the best for whatever your goals are Remember, the ones with highest gp wont necessarily have the highest ibs, so pick wisely!

I feel like I haven't explained much, but have just sort of laid down my experience with breeding foals. Someone else may have a more technical answer for you!

This is not answering your question, rather, pointing out an unfortunate turn of phrase...

Selle Francais denotes the French Saddle horse in this game, with the word Selle a direct translation of Saddle.

However the word 'Selles' has a completely different translation, which I won't expand upon here, except that I suggest you Google: Selles French, to see for yourself...

Back to your question...

The difference in skills that you describe is mostly attributable to the inborn skills calculation. Yes, there is a little variance in GP of foals but for the large discrepancies that you describe, then this is due to IBS.

Howrse does not divulge its calculations... however there have been many bright minded folk playing this game over the years. The general consensus is that for +100 BLUP parents, the resultant foals will have IBS of 20% of parents average GP, with a variance of 0.8%.

So the range can be from 19.2% to 20.8% - e.g. for a pair of +100 BLUP parents with an average GP of 10,000, any foals born could have IBS from 1920 to 2080, a spread of 160.
If tears were used, this range would be x1.5... so in above example: 2880 - 3120, a spread of 240.

The higher the average GP, the bigger the possible variance...