Victor Baker

@Altti. Again, determining how much variance should be retained is completely subjective.It is fair (also subjective, clearly) to look at individual breeding instead of population breeding, since the debate is about whether the current formula is sufficient to allow for improvements through selective breeding. The question is also whether you should be realistically able to improve along the entire range of qualities (should it be possible to approach a normalized value of 1?) Personally, I think that the formula is already effective (see my own results) and that any improvements in the formula are only warranted if the effort to implemented such improvement is very low. I also think that implementing your alternative system is not an example of such low effort. Anyway, all in all, I think I've made all the points I wanted to make in this thread. Any further back and forth will likely be repetitive, so I'll release you of the burden of replying to my clear nonsense. Still, I hope that you'll keep in mind that there is such a thing as over complicated solutions to minor problems and that any change you suggest should weigh of the costs/benefits from a wider Minecraft perspective.

@Altti. We are making two different points here. I pointed out that, vis-à-vis the current system, using one random variable increases variance. You deduce that, either way, the variance is below that of wild horses. I'd like to ask: so what? It makes perfect sense that the variance would be lower in a system where two-thirds of the weighted average value is fixed. On a different note, I'd like to share my current breeding results to illustrate that breeding, despite popular claims, is rewarding after all. Here are the normalized values of my eight best horses (my entire current stock) after 508 breds:

Normalized Horse*
0.7429
0.7221
0.7221
0.7117
0.7117
0.7155
0.6919
0.7196

*All observed values are rounded down, so these are conservative estimates.

Just to put the breeding mechanics into perspective: You'd have about a one in 150 chance to find a 0.70+ horse in the wild. As for my entire collection, the wild horses you'd have to find would be well over 1000. On my current world, I've explored about 2000 blocks in any direction (excluding a couple of remote locations I've ventured to through nether portals). All in all I've found some 8 horses (two herds, to be exact)... Well, you get the picture.

Edit: I might also mention that my breeding methods are far from efficient horse wise (rather, it's more focused on time/effort efficiency). I usually breed in herds of 4-8 (depending on the quality gap) and about 4 out of 5 horses never make it out of the pen (they fail the health and jump minimum requirements). The other horses get a thorough testing, but everything is done without mods so a certain margin of error remains. The whole process spits out some 20-40 horses per hour.

@Altti Using one random variable instead of the weighted average of three is supposed to result in less variance, how exactly? Using one random variable and fixing the parent's stats, you'll find that the variance actually triples vis-à-vis the current formula.

Here's the result of a quick simulation. I fixed the parents average stat at 0.5, but any other fixed value won't affect the distribution one bit, obviously. The first variable resembles wild horses, the second variable are bred horses under the current system, the third are bred horses under the alternative.

Descriptive Statistics
________________ N Min Max Mean Std.Dev. Variance
Wild_generation 10000 .17 .84 .4994 .09451 .009
bred_0.5__prnts 10000 .39 .62 .5005 .03213 .001
0.5_prnts_1_rnd 10000 .34 .66 .5008 .05561 .003

Edit: tried to align the table somewhat better.

@Allti. I understand your alternative, Im just not a fan I'm afraid. Introducing your system might be well possible, but far from practical. For example, how would already generated horses be treated after introducing this new system? Are their ''U'' values retrievable, or should they be assigned new ones? Oh and the graph illustrating why it is ineffective to use one random variable for the ''New'' statistic, does not add up for me. As I understand it, your argument is that, either way, the foal is the result from 2*3 (parents) + 1 or 3 (wild horse) random variables, hence reducing variance. Yet, if you breed, the parents' stats don't get recalculated: they are set and (usually) known. Therefore, comparing foals variance for an indefinite number of breeds seems out of place. Do correct me if I'm wrong, but, for any one breed, the variance of the foal's stats should be the same, right?

Edit: seems like I accidentally stumbled upon an emoticon

@Jonathan&Allti

Don't you worry about my breeding experience, everything is going just dandy. All I'm trying to do is help figure out a reasonable solution to this barely significant problem. I'm obviously not as well into the material as you guys, but I can tell you one thing: your solutions are likely to be too complicated for mojang to bother with. Anyway, I've been reading some of the previous posts and I've come across something that I've possibly completely misunderstood: In the breeding formula (Pa+Pb+New)/3 , is the ''New'' variable actually calculated using three random variables (i.e. the same way a wild horse in generated)? If so, what is the logic behind that and wouldn't the strong tendency towards the average be offset if the ''New'' variable were to be calculated using only one random variable?

@Allti

From a mod post:
"The algorithm should be simple, both for performance and so they can understand it, and therefore tweak it as desired.
It should be possible for children to be both better and worse than their parents.
But children should probably be similar to their parents, rather than weighted towards average values.
They're probably not expecting players to breed horses hundreds to times to get decent results.
Most players aren't going to have any way of getting hard numbers about their horses' stats, and will have to rely on their perceptions."

It seems that being able to notice stat difference is a preferable outcome to changing the formula. Furthermore, since this bug report does not technically describe a bug in the first place, offering suggestions for changing the method is appropriate here. Rounding would be so enormously easy compared to your suggestion, and beneficial to breeders that don't use mods and breeders in general.

I want to revisit the idea of rounding the statistics. If the statistics were to be rounded (the actual values, that is), then it could benefit the breeding process in two major ways: First, horses are noticeably different from (or equal to) each other. This means we don't need mods to be effective breeders (yes having to resort to mods is a bad thing) and we also don't need to be jumping over enderportals and cacti while splashing our horses with potions. Second, the probability of breeding better offspring increases at every level. Also, the probability of breeding equally good offspring increases.

Breeding example with two identical horses:

with rounding to multiples of 1

80 80 0-100 odds of improving stats --> 0.185^3 + 0.185^2*0.03*3 +0.185*0.03^2*3
80 80 0-100
80 80 0-100

= 0.006331625 + 0.00308025 + 0.0004995 = 0.009911375

Chance of equal stats 0.03^3 = 0.000027
Equal or better= 0.009938375

with rounding to multiples of 2

80 80 0-100 odds of improving stats --> 0.17^3 + 0.17^2*0.06*3 +0.17*0.06^2*3
80 80 0-100
80 80 0-100

= 0.004913 + 0.005202 + 0.001836 = 0.011951

Chance of equal stats 0.06^3 = 0.000216
Equal or better= 0.012167

with rounding to multiples of 10

80 80 0-100 odds of improving stats --> 0.05^3 + 0.05^2*0.3*3 +0.05*0.3^2*3
80 80 0-100
80 80 0-100

= 0.000125 + 0.00225 + 0.0135 = 0.015875

Chance of equal stats = 0.027

Equal or better = 0.027+ 0.015875 = 0.042875

without rounding

80 80 0-100 odds of improving stats --> 0.2^3 + 0.2^2*0.03*3 +0.185*0.03^2*3 = 0.008
80 80 0-100
80 80 0-100

odds of improving any of the stats by at least 1 --> 0.18^3 + 0.18^2*0.02*3 + 0.18*0.02^2*3

= 0.005832 + 0.001944 + 0.000216 = 0.007992

Chance of equal stats: n/a

-

The odds improve as the chance to retain the parent's statistics increases. New horses will be more significantly better or worse compared to the current system. With rounding to multiples of 10 (just for illustration purposes), breeding two 80% horses gives a 1.6% chance of producing a foal that is at least 83.33%. The larger the multiple becomes though, the larger the gap between breedable values and the perfect ones. Perfection can then only be achieved by finding the perfect stats in the wild. Still, breeding should become more rewarding and less tedious if the statistics were rounded.

And for all this, the ''old'' formula does not need to be changed.

@ Patrick I hadn't thought about potions of leaping, I stand corrected! Oh and carpets only get you so far as they need to be placed on a full block. Anyway, I guess that makes measurements accurate to the point that rounding is not really needed.
@ Jonathan You've inspired me to think of another way to measure jump height, and I think I've come up with something pretty neat.

@Altti
Well it's really not though. In vanilla, there's only the jump-over-obstacle method to determine jumping height. The most precise reading involves jumping over snow layers, which are 0.125 in height. If minecraft were to let players have an accurate measurement without having to resort to mods, rounding the jump height would be a way to do it. Also, if calculating the correponding values is too much, then just disconnect the gravity for upward movement all together.

@Allti

Seems to me that your formula has become measurably more complicated than the ''old'' one, but perhaps I'm just ignorant. Still, don't expect mojang to fix this problem if it can't be done so with just a few lines of code. As for the jumping height/strength difference: then round jump strength statistic to the nearest statistic that corresponds with a 0.125 multiple of jump height. Is that a better resolution?

@Altti Tammi. Are you sure that a completely new system is really necessary? In principle, the current system works, despite the fact that breeding higher quality horses becomes unreasonably difficult at some point. How about leaving the basic system as it is and introduce a small mutation that increases as the parent's stats get higher? That way, things will be kept simple and tweakable for mojang, breeding higher end horses will be doable (by the grace of mojang), and the system would only significantly affect the high end horses. Here's my suggestion for such a sytem:

(pA+pB+pR)/3 + F/(2*pMAX - (pA+pB)) where F is a random error with a small interval around 0. The whole second term is random mutation that is likely to be larger as pA and pB approach their maximum values.

Also, as for being able to track progress in vanilla, I suggest rounding the jump statistic to the nearest 0.125 multiple (a layer of snow). That will enable people to accurately check the horses jump statistic by jumping over obstacles. Speed is already easily recorded with a redstone racing track (the longer the track, the most accurate the statistic) so it really does not need to change. Health also seems pretty straightforward and not in need of a change.

I agree with you that it's not realistic, nor it is of much practical use. Still, some people would like to breed towards perfection. Not being able to see any progress for a couple of thousand of breeds at some point, seems, somehow, kind of mean.

I still think that's it's not realistic to be able to breed your way beyond the 90 percentile without incredible effort / luck. However,I do get the compulsion. I'm not much of a mathematician, but I've been trying to come up with a suitable formula that doesn't over complicate things but still does the trick:

(pA+pB+pR)/3 + F/(2*pMAX - (pA+pB)) where F is a random error with a small interval around 0. The whole second term is random mutation that is likely to be larger as pA and pB approach their maximum values.

It'd be easier to transfer already good stats to new generations of horses, which is not to say that developing new stats would be any easier. You are completely right on that account. The process of breeding would get more difficult as horses get higher stats, as it should. Anyway, I do think a slightly better edge would be a good thing, but it really shouldn't be too easy to get into the 90 percentile.

It's not that fair though. You want a nice and steady increase in stats, but that's not very realistic nor is it challenging. Reducing randomness would make finding horses with one exceptional stat all the more important, but you'd be set if you find all three of them. Even without all three, you could still max out each individual stat through breeding, and breed the results with each other (individual stat breeding is so much easier). Anyway, it quite resembles real breeding if it's set up like this. The current system is also representative, but it is too tedious (as many have complained).

To elaborate: reducing the influence of the random horse will allow for more targeted breeding with less ''noise'', while still being essentially random. It will be harder to breed good horses from mediocre ones, but horses with excellent stats can more steadily transfer those stats to their offspring. As the stats get higher, the impact of the noise gradually increases, but you'll be able to get a lot more out of selective breeding. Actually, perhaps a random weight of 0.5 is too low, but there should be a balance somewhere.

I do get what you're saying. There may be an argument for reducing the random factor altogether. That way, though, breeding below-average horses will be more tedious and you'd pretty much have to search for wild horses with good stats to breed with. I don't think it'd be fair to have it both ways (more influence of random factor when the stats are below average, and less when the stats are above). However, there really is no need for complicated formulas to rebalance the system. Just refactor the impact of the random horse vs. parent horses. Don't remove the randomness of genetics though. So, maybe. a weight of 0.5 for the random horse and 1 for each parent?

Then, perhaps, wild horses need to be rebalanced instead? I suggest to randomize three sets of stats per horse and take the average of that. That is much more likely to produce average wild horses. Though, personally, I like the idea of horses with one extremely good stat. They're just as likely to have have horrible ones and they are probably not decent in all three stats That's where breeding comes in handy.

If the random distribution is truly as such, then I'm inclined to agree with you. However, wouldn't it be easily fixed by fiddling with the distribution of the random factor? For my part, I'd have the probability of each possible value equally distributed. In fact, I assumed this was the case already. Where did the data for those distributions come from?
If equal distribution is too rich for mojang, they could at least soften the bell to rebalance breeding. There is really no need for complicated formulas and selective assignment of genes.

@Altti Tammi

As long as the ''random'' factor isn't biased, Then I see no reason why selective breeding couldn't continue to improve stats. Yes, breeding gets harder the higher your stats are, but that's supposed to be the case. What are these distributions representing precisely? The distribution of the random factor?