Erik Skau

@unknown: Good point, playing around with that idea I agree with you now. So I am now completely behind supporting your method of:
offspringStat = randomParentStat+noise.
Are there any other ideas floating around though?

I completely agree with the mathematical niceness of handling the edge cases like you two are considering, but I am not convinced it is necessary. (And worry it is likely to scare away the Mojang Programmers? I do not know how much math they like?)
Consider the example:
Let the scale of stats be 0-10, and choose a bell curve with std dev 0.5, a pretty large standard deviation in my mind. Half the time the stat will change by more than ~0.3. A quarter of the time it will change by more than ~0.6. This seems reasonable to me?
If your horse is 9, then ~2.5% of offspring would be perfect. If we consider all three traits being 9, then the offspring will be perfect ~0.0015%.
If your horse is 9.5, then ~15% perfect. All three traits being 9.5, perfect offspring in all three ~0.3%.
If your horse is 10, then 50% perfect. With three traits 12.5% will come out perfect.
So to get a perfect horse it seems like it would still take a bit of work without limiting gains near the top.

So sure, by not dealing with the edge cut off, a perfect horse is attainable, but depending on the kind of standard deviation that Mojang wants and if they are ok with people getting perfect horses, it may not be necessary? So I am a fan of this approach as a first attempt:

offpsringStat = min( max( randomParentStat + random, minHorseStat), maxHorseStat); //random is from some bell curve type distribution with mean=0, and std deviation of about 1/10th-1/20th of the horseStat range.

If it doesn't work out in testing because it's too easy to get a perfect horse, or they don't want perfect to be attainable, then try the more complicated thing.

I wonder if this thread is so long that everyone from Mojang stopped reading?

@unknown Your method seems like a very elegant mathematical solution (didn't actually run through the algorithm, but I think I got the intuition), but probably not very appealing from a programming perspective, as well as it is not as readable as code. I think I would prefer something simpler such as:
offspringStat = min( max( (Pa+Pb)/2+random, minimumHorseStat), maximumHorseStat); //random comes from some distribution with expected value of 0. Probably Gaussian-ish.
Your idea nicely addresses and fixes the problems that occur with this method when both parent horses are an extreme case. But I think that practically either one would suffice and that very few players would be able to distinguish between the two, especially not until they had very good horses anyway, which is when the differences between the two methods would manifest themselves. I could be wrong about this, I think the easiest way to find out would be just to implement both and test them seeing if there is any real difference from the players perspective.

@unknown I also thought about your method, and I would be quite satisfied with it as well. My only complaint with it would be that it does not necessarily mean good game progression, but this is really just my preference. To demonstrate this let me give an example.
ParentA is good at running/jumping but has crappy health. ParentB has good health but really bad at running/jumping. The offspring could either be perfect, or flawed in one or more aspects.
In the case of perfect, then the player has achieved the ideal horse after 1 breeding instance, not very rewarding in my mind.
In the case of flawed, the horse will be really bad at one or more of those things, in my mind making the horse not fun, and not really a step up from either parent.
If on the other hand things were averaged, the first case of a perfect offspring is not possible, and the second case would be a more well rounded horse rather than a horse extremely flawed in one or more aspects, which I think makes better for game progression.
But again, I like your method too, and would be quite happy if it was implemented.

Any word from anyone on the Mojang team about this? Is this all moot because they are already working on some fix?

I just made an account to follow/vote on this issue. I hope it gets resolved soon. (I do not know the ranges of horse stats, so I make up numbers to convey concept.)

If horse breeding in fact works as offspring stat=(Pa+Pb+Random)/3, where the random number is from some set distribution like [1,2] (the distribution Pa and Pb came from), then this does make horse breeding relatively worthless. If Pa and Pb are both very good, then the Random will almost never be as good, and so will most likely make the offspring more average. Breeding in this system will "always" bring things to average.

I propose the relatively easy fix of offspring stat=(Pa+Pb+Random)/2, where the random number is from a distribution like [-1,1] (centered around 0). Notice the divisor is 2. With this method the expected value of an offspring will be the average of the two parents, 1/2 of the time the offspring will be better/worse at a given trait, and 1/8 of the time the offspring will be better/worse at all 3 traits. Also, this should be pretty similar to how selective breeding works in real life.

Hope this gets resolved soon.