Foal stats (health points, speed and jump strength) doesn't seem to ever exceed all stats of the parental horses.

If you breed two exceptional, high-stat horses, it rarely happens that the foal will have slightly better stats than its parents, so far, in 4 years of breeding tests, this only ever occurs in one single stat, if you take 2 high level stat parents to breed with.

This happens because a third horse with stats varying in range from the lowest to the highest is added into the equation.

While this is very useful for Donkeys and low-stat horses, this makes it apparently close to impossible to breed out a high-stat foal that can surpass its high-stat parents in all categories.

In the comments of this bugpost are many suggestions how to improve on the breeding formula, a comparably simple approach would be to go by real life, where high-stat parental mobs produce also high-stat offspring (e.g. see high-priced bulls/milk cows, but also horses, keyphrase: "selective breeding"/"artificial selection").

If the "ominous third horse" as random factor shall remain in the formula, it could be adjusted in that way that high-stat parents could also have a high-stat "ominous third horse" being used for the equation, basically a higher range that excludes the very lowest stats, but still includes slightly worse/lower stats than the parental horses, to account for the possibility of a negative mutation like in real life.

Similarly then for low stat parental horses, here excluding the highest stats, but the range being still slightly above the parents' stats to account for positive mutations like in real life ("evolutionary/genetical improvement", "natural selection").

As a result of this issue, it's basically not really worth it to breed regular horses.

You are usually better off hunting wild/naturally spawned horses and hope for one with higher stats than those you've already obtained or bred.

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Old bugpost with additional information:

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I have noticed after extensive testing that foal stats do not exceed spawned horse stats. As a result the only way to obtain a horse with exceptional stats is for it to be caught in the wild/spawned. After multiple breedings I was not able to reproduce or produce a foal with stats better than the best stat parents, while the foal can be born with stats slightly better than one, it was never able to be as good or better than both parents.

Two horses I had spawned from eggs both had exceeded stats in run speed and hp/jump ability, foals from these parents never matched or exceeded their stats. (on spreadsheet refer to column 17-10, all breedings after 17 involve offspring from these two parents being crossbred with other breeds with favoured stats)

I thought this would be worth noting as a possible bug as many are under the impression that breeding is supposed to have a chance that the foal born is to be as good or better than the parent. This is obviously not the case and may be a cause for review.

Please refer to the attached spreadsheet of breeding results.

Additional notes:

Speed was measured on a Redstone track that is 40 blocks in length which takes a normal player 10 seconds to complete at the current running speed in the latest snapshot.

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Edit 27/05/2013

As suggested in comments I did another round of tests, this time by breeding horses with identical data, the following data in test 2.xlsx reveal there is the possibility of a foal being born with matching stats and on a very rare chance be slightly better, the chance for better stats was higher with jumping ability, speed has a much lower chance to be on par and a higher chance to be worse, and hp is a medium chance to get matching stats, but very low to get better.

It is confirmed that likeliness of stats is increased if two horses match, however this poses the problem that you would need to rely on data-mining in order to ensure you are breeding matching horses to improve horse stats and would be impossible to manage in multiplayer games unless a mod was made to reveal horse statistics. This would still cause the issue that spawned horses may always be better as people would give up breeding due to horse stats not improving when the breeding pair stats do not match.

I removed personal studies within the game due to speed inconsistencies which happen when mounting/dismounting and leading (refer MC-16421 ) and have left the hard numbers extracted from NBTExplorer on the spreadsheet.

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Edit 19/07/2013

Attached a new image of breeding results as of 1.6.2 with colour coding to show how the current breeding methodology is working.