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I don't remember having had any foals that passed SBA compare worse that their sire or dam, and have used comparison test and SBA on thousands of horses (mostly stallions, but the mare testing seems to be the same). That doesn't mean it is completely impossible, but it would have to be extremely rare to not show up with the number I have tested.

To the best of my knowledge the comparison test look looks at the hidden breeding ability scores of two horses and compares them. Superior means that the horse tested has a significantly better breeding ability than the one it is tested against (its sire/dam or other comparison horse). About as good as means that the breeding ability ranges from slightly better to slightly worse than the comparison horse. It is possible to have an A papered horse that compares about as good as one with B papers if the A is very low and the B very high. In that case the A papered colt is still slightly better than the B papered, but they are close enough that the comparison test doesn't differentiate.

The paper levels each cover a fairly wide range of breeding ability and comparison test allows you to determine where a horse is within that range. It is possible to have 3 generations of A papered stallions, each of which compares superior to sire, and *Star covers an even wider range.

Yes, higher breeding ability means the likelihood for better foals. However, there is always considerable variability, so not every foal will be better than its parents. So, generally speaking B/Red parents will usually produce foals with higher PT scores and higher breeding ability than C/Yellow ones, but it doesn't always happen. A/Blue parents, on the other hand will produce foals with higher PT scores and breeding ability than C/Yellow ones almost always, and *Star/*Gold parents will always do so. Their foals will mostly be better than those of A/Blue, and usually better than B/Red crossings.

The most definite answer to the question of what it actually means is that breeding ability is a percentage number that, except for Perfect Foundation and Exceptionally Perfect horses, is unknown to the player. The game is intentionally designed to be as variable as real life. Secretariat, an outstanding race horse, never sired a son that was as good as he was. However, his daughters included many that produced outstanding foals.

Perfect Foundations have 100% breeding ability, 100% showing ability (9.9 PT) and are perfectly consistent in their show scores each week. They are papered C/Yellow, but there are many foundation horses whose breeding and showing scores are somewhat less than 100%, and some that are a lot less.

Horses can have breeding ability percentages that are better than their showing percentage and vice versa. I once had a mare whose PT score was something like 2.8. However, she was one of my best foundation brood mares. This was 8 years ago, and Ammit has tightened up the papering levels more than once since them, but the same potential difference between breeding and showing ability is still part of the game.

This unpredictability is, for a lot of us, one of the things that keeps the game fascinating and challenging to play.

P.S. Never, never apologize for asking questions. This is a very complex game, and we have all gone through this period of feeling somewhat lost. I actually watched my daughter play for eight months before I felt confident enough to start my own stable. :D

Higher papered horses, on the whole, produce foals with higher PT babies. A horse's papers are determined by the theoretical showing potential of its foals, and a well-lined *Star stallion is always going to make better show babies than a random C-papered foundation. That's not a slight on the C-papered foundation, it's just the nature of the game, as ideally each subsequent generation is better than the last, and produces better foals than the one that came before it.

SBA is absolutely helpful in that context, as is comparison testing (now available for mares!) which moves you from the realm of "this foal at least approximately as good as its parents but could be worse" to a concrete "this horse is better than that horse," but it's a bit expensive: you look at what's called the AFPT of your mares, the average foal performance test value, and after a couple of foals determine if it's better than their dams. Generally you need three or four foals on the ground to get a really good idea of this, so if you're upgraded and can afford it, using comparison testing on everything will cut down on your breeding stock a lot and make sure everything is an improvement but we've played for years and years and years and years and years without it with no issue.

I'm glad my answers were helpful. It's a complex game, so everyone needs help understanding it when they're starting out. I think I get as much fun out of helping newer players understand the game as I do out of breeding my own horses. :)

Q: Do papers directly reflect the likely/possible PT scores of the horse's foals?
A: Yes.

Q: Does this mean the A papered colt will (statistically speaking, I know there's no guarantees) produce higher PT foals?
A: Yes.

Q: Will his foals grow up to produce higher PT foals than his brother's?
A: Potentially.

Q: What about if the A papered has a significantly lower PT himself than the B? I know everybody keeps saying that PT doesn't reflect breeding ability, but are they connected at all, in either direction? How?
A: A horse's PT score and breeding score are only indirectly related but they do not influence each other at all.

I had a really long post about this (complete with picture!) a forum-version or so back but I'll try and summarize it here.

Every horse in the game has two invisible stats: one for breeding ability, and one for showing ability. Breeding ability is ONLY that horse's ability to produce good foals, and the only thing that we as players can see about that horse specifically are its papers. Papers are hard-tied to a range of breeding ability, as seen in yellow-papered foundations, which are approximately 95% to 100% ability breeders, and red papers, which are (I believe) approximately 101% to 105% ability, and then blue papers, which are another tier above that, and then gold papers, which is everything better than blue. (Mare papers and stallion papers are now directly equal. Yellow = C, Red = B, Blue = A, Gold = Star.) Showing ability is ONLY that horse's showing potential, and is visible on tested horses as the Performance Test score (which is influenced by inconsistency; inconsistent horses get lower PT scores even if their showing ability is the same.)

You can see this really dramatically in foundation creates. Some of them have perfect breeding ability but craptastic showing ability, PT'ing at 1 or less. This is also why so many geldings/spayed mares paper so much worse than their sires and dams: their breeding ability just isn't that great, whether it's compared to their showing ability, or because it's compared to said sires and dams.

When two horses are bred, the game takes their Breeding Ability scores and combines them and does some kind of arcane formula magic on them to produce two scores for the resulting foal: its breeding ability, and its showing ability. This is the only way these scores are related. There's a heavy degree of randomness involved in producing these two numbers. You can breed the same two horses together ten times and every resulting foal will have completely different stats. Sometimes both numbers will be high, sometimes both numbers will be low, sometimes one will be great and one will be poor... within the range of ability those two horses can produce. However, high-end Gold/Stars will always produce better foals than foundations, because their breeding abilities are so much higher. If they weren't, they wouldn't be Gold/Stars.

I ran the math on it once, and it seems that perfect foundation horses produce a range of between 8.9 and 10.4 PT score foals when bred together. It's a pretty wide range; I imagine the breeding potential pool is similarly large. The range changes with each generation. Ideally, you want to see a minimum of a half-point AFPT increase between generations. Thus if you figure the average for perfect foundations is 10, then you want their intact offspring to be producing, at a minimum, 10.5s (on average, that's still between 10 and 11 PT scores, so you rarely want to judge on a single foal.) This is ALSO influenced by breeding one horse with a very high breeding score to one with a very low breeding score; a stallion capable of producing 14s put in a pasture with a bunch of foundation mares will skew the high end of the range, but the mares will skew the low end, so you can get some killer show foals that way but they'll almost never make it through breeding inspection.