Working With The New COI Formula

[BlackOak2]

First, let me link some important information as well as explain some things about the new formula and how it might differ from the old one.

Since the release of the new format, we were also introduced to a new COI formula. The old one didn't have an upper limit and one could inbreed with each generation and COI would creep upward at fairly regular and expected increases. Now, we have a new formula that handles COI a bit differently.

The old formula read back seven generations from the horse. What this meant was that if any horses appeared more than once in those seven generations, your horse would have a COI value other than 0%. But it also meant the opposite. If you bred a horse with something other than 0% COI to a horse with 0% COI, but the duplicated horse (or horses) in the pedigree fell outside of the new foal's seventh generation, then the new COI should've been 0%.

This new formula is defined by only five generations. However, each of those horses COI in those five generations add to the value of the primary horse's COI value. Basically, if any of your horse's five generational ancestors had a COI value greater than 0%, then you can expect that your primary horse is likely to have a COI value greater than 0%.
Here's larissar's own words on this:

A horse (may) have zero common ancestors in its own 5-generation pedigree, but if any of those ancestors have a COI above 0 then a portion of that ancestors COI will contribute to the new horses own COI.

The new formula that we use is called the Hardimans equation and can be found in detail here.

For a quick review. The formula is:
"Fx is the inbreeding coefficient of the horse in question, Fa is the inbreeding coefficient of the common ancestor, n1 is the number of generations from the sire to the common ancestor, and n2 is the number of generations from the dam to the common ancestor." (see the link for a breakdown and example)

COI currently does nothing in-game except help with some gene setting and possibly plateauing of a bloodline. There are currently NO ill effects written into the code. That said, each one of us really does need to get used to working with COI and working with maintaining a low COI bloodline [at least]. So, what should we be aiming for? Here's the snippet for your answer from larissar out of the chat:

Only thing I would suggest is you put a lot of emphasis on 40% being a hard limit for when COI would have negative effects, and I just want to clarify that this isn't something I have or will specifically program into the game. In fact the number came from an article I read (possibly the one I linked to) on the COI that breeders aim to keep their stock under for best health. Eventually there will be genetics added to the game that can have negative health effects and a high COI will increase the chances of those bad genes being passed on. I just don't want players to think that I'm specifically programming in negative effects at only 40% COI and higher, it's more like a sliding scale. Low is good, high is bad. I hope that makes some sense.

So, if you're edging in on that 40% COI area, you really need to be considering other options on how you can control it. If this is starting to happen without you meaning to, then somewhere in your breeding program, something's falling short. The best way to help control COI is to breed to 0% COI stock. This isn't always possible and even if it is, these horses may have things that you don't want, for instance, you have a line that carries it's HGP in the upper 60k and your only option is an outbreeding with an HGP in the 30k. A single breeding can ruin the HGP work and force you to inbreed some more to get back up there (assuming you're breeding back into your own line). So although at first you don't think COI can be a problem, it can certainly sneak up on you.

Is there an upper limit? Is there a hard number we can see that will stop increasing to help us in COI control? Yes, but there's a caveat here. Larissar answers again:

Behind the scenes the calculation caps at about 200%, but only displays as 100+%. I put a hard cap on the calculation because otherwise we would in fact have horses with COI in the multiple hundreds.

So, an inbred horse may in fact be far, far, far above that 200%, using the new formula, but larissar has done us a huge favor by artificially restricting any number above that. Why is this a 'favor' to us? Because when we want to lower that COI number, even if the horse is maxed out, we'll only ever be starting never more than 200% COI.

So here we are, at the example part of this guide.

First I'll introduce the two Adoption Centre horses I'll be using:
Pacific Dancer

This is the mare. She's a Forest Horse I picked up from the market. Although she has one offspring, this won't interfere with this guide. Her color (if you're interested) is a Brown Pangare.
Kindred Locks

This is the stallion. He's a Belgian I also picked up from the market. He currently has no offspring. His color is a Blue Roan.

How I'll be running this data collection, is the non-branching family tree method. I will keep a colt and a filly (full-siblings) from this pair and breed them together, and so forth until I'm satisfied I have reached that 200% COI mark. Once reached, I will take new Adoption Centre partners and breed each generation out to a new horse until I've reached again that 0% COI mark.

For kicks and giggles, here's the stats of both.
Mare
HGP 32566 - no color
Speed: 18
Strength: 48
Stamina: 32
Movement: 39
Tempo: 28
Agility: 29
Balance: 26
Stallion
HGP 30725 - Red Movement
Speed: 14
Strength: 43
Stamina: 29
Movement: 28
Tempo: 17
Agility: 36
Balance: 17

I won't be keeping track of the stats of the foals here, but I'll make note of each of them in the horse's notes. So for those that are interested, you can see them there. Also, I won't be favoring HGP or stats of the foals, for the most part, when I get a gender, I won't be replacing it. However, if one gender keeps popping and I'm having trouble with getting the other one, I may favor a better stat foal over the very first one.

First Generation (0% COI, no inbreeding)
Huckleberry Couch and Missing Charger

Second Generation (first inbreeding)
25% COI
My Plenty Trail and Angelic Tune

Third Generation
37.5% COI
Oak Virtue and Hypnotized Mirror

Fourth Generation
50% COI
Neon Daydream and Blushing Willow

Fifth Generation
62.5% COI
Marine Flicker and Chimney Pepper

Sixth Generation
75% COI
Voiceless Racer and Out My Magnet

Seventh Generation
87.5% COI
Iron Cupcake and Broken Executive

Eighth Generation
99.61% COI
Jack Frosts Idea and Path Daredevil

Ninth Generation
100+% COI
Opulent Rogue and Doodle Mistress

*Note, from here on out, since we've breached the +100% COI and it appears that the COI builds about 25% every other generation, we'll head right to the 25th generation to ensure that we 'Max Out' at that 200% COI mark. That should give us, give or take about 6 extra generations to help confirm we're at that mark.

Tenth Generation
100+% COI
Gambling Galaxy and Toward Jester

Eleventh Generation
100+% COI
Red Chuckle and The Wicked Union

Twelfth Generation
100+% COI
Reverse The Dawn and Starstruck Sorrow

Thirteenth Generation
100+% COI
Faraway Remedy and Evermore Kryptonite

Fourteenth Generation
100+% COI
Chocolate Patchwork and A Frozen Evening

Fifteenth Generation
100+% COI
Gardenia Sapphire and Dashing Humour

Sixteenth Generation
100+% COI
Ivy and Loud Conquistador

Seventeenth Generation
100+% COI
Arctic Prayer and Tardy Peacock

Eighteenth Generation
100+% COI
Grand Darling and Doomed But It's True

Nineteenth Generation
100+% COI
An Ordinary Oak and Forgotten Mystery

Twentieth Generation
100+% COI
Cute Little Orchestra & Peppered Invitation

Twenty First Generation
100+% COI
The Silver Pixie & Orange Gambler

Twenty Second Generation
100+% COI
Revolutionary Toy & Snow Premonition

Twenty Third Generation
100+% COI
Egyptian Duchess & Romances Crescent

Twenty Fourth Generation
100+% COI
Splendid Maker & Estranged From Frog

Twenty Fifth Generation
100+% COI
Dabbling Crescent & My Rhythm Clyde

Final foal born to move to the next phase: Braided Hero

Now that I've gotten out enough generations, here I'll start the AC horse breeding phase. To remind you, each generation, I'll purchase a NEW AC horse and use that horse to breed a foal to the current line. So every foal will have ONE AC parent and one from this original line. We'll see just how many generations it takes to get back down to certain thresholds. First threshold will be a visible COI threshold, which just means that we'll see a movement in the 100+% COI.

First AC horse: Any Rust
Resulting foal: The Limited Crane
COI: 96.88%

So, in just one generation, we've already dropped to that very first threshold 'visible COI'. Could this be because that 200% maximum wasn't reached? Well, I checked with the only ones that can say for certain.

This horse you linked is maxed out at 200% COI.

On the Braided Hero.

Conclusion is that it only takes ONE generation to a 0% COI horse to bring the COI back down to readable status. The next threshold is at or under 50% COI.

Second AC horse: Purple Haze
Resulting foal: Ramblin' Thundercloud
COI: 47.66%

Again, we've reached the second threshold in a single breeding. When breeding out to a 0% COI parent, the COI is more than cut in half. Our next threshold will be 25%, if our schedule still holds, we should be under this one with the very next breeding.

Third AC horse: An Ordinary Sparrow
Resulting foal: Soaring Castle
COI: 23.44%

Another threshold! Great! As long as the companion parent has a 0% COI, getting it back under control is a bit of a cakewalk. Theoretically (by other players experiences), this next set of thresholds is supposed to be more difficult to get through, so we'll see.
Our next threshold will be 10%.

Fourth AC horse: Rosey
Resulting foal: Oak Wings
COI: 11.52%

Fifth AC horse: Societies Me
Resulting foal: Cowboy Deception
COI: 5.66%

This time, it took two breedings to drop below that 10% threshold. But we also made it below 5%, almost. So let's try for the final threshold and see how many additional breedings it'll take to get back to 0%.

Sixth AC Horse: My Thyme
Resulting foal: Turquoise Sunlight
COI: 2.78%

Seventh AC Horse: Starlit Holiday
Resulting foal: Charismatic Lollipop
COI: 1.37%

Eighth AC Horse: Forest Heaven
Resulting foal: Limited Flame
COI: 0.67%

Ninth AC Horse: Thoughtful Enigma
Resulting foal: Unusual Poem
COI: 0.33%

Tenth AC Horse: Breathtaking Blossom
Resulting foal: Tattered Duke
COI: 0.16%

Eleventh AC Horse: Waters
Resulting foal: Lady's Thy Gusto
COI: 0.08%

Twelfth AC Horse: Inky Trail
Resulting foal: Winners Risk
COI: 0.04%

Thirteenth AC Horse: Salt Kicks
Resulting foal: Velvet Triangle
COI: 0.02%

Fourteenth AC Horse: Hot Shot
Resulting foal: Sophisticated Truce
COI: 0.01%

Fifteenth AC Horse: Ruby Fire
Resulting foal: Modest Enigma
COI: 0.01%

Sixteenth AC Horse: Caramel Mix
Resulting foal: Bright Seeker
COI: 0%

So, that was like pulling teeth... just a little. For the remaining >5% COI, it took an additional 11 horses before 0% COI was achieved. Overall, it took a total of 16 0% COI horses to get back to 0% COI. 16 generations.

What can we take out of this? That to get to 0% COI from 200% COI (our hard cap), it's a bit of a hike. But if your aim is a little higher, for instance, under 25% COI, it'll only be three generations. Even for under 10% COI, five generations will do it.

So as long as you have a few 0% COI's sitting around, you'll be good to go, to help control your COI. All that said, they're not a dime-a-dozen around here. Plus, breeding to AC stock will certainly tank your HGP easily.
Controlling COI otherwise may be fruitful or difficult, depending on how high the outside COI stock is. I would still suggest you aim to control COI while building a new breed, rather than aiming for 0% COI without some breeding partners.
I would suggest to help control your herd's COI while maintaining your herd's success, that you keep a horse from your own bloodline that's back more than five generations before use within your herd. This may mean that you'll have a rather defunct horse, compared to what you have 'currently', but you won't be trashing your current line's overall with an AC 0% COI style horse. By keeping a rolling holdover every three to five generations, you will help to control your COI instead of explode it into unacceptable areas.

Eventually, COI will become something that will negatively effect our horses. According to admin, at about the 40 percentile, we will have possibly significant issues. So aiming to keep COI well under that mark will limit the affects we might see.

If you've worked with controlling COI under the new formula and you'd like to share your experiences and the methods you used, please comment below.

[RoyalCrownAcres]

You are so wonderful for putting this together! I've been trying to slowly introduce new stock into my vanner program and this will definitely help me figure out how to work towards lowering my COI while breeding up my new line.

[Argent]

COI currently does nothing in-game except help with some gene setting and possibly plateauing of a bloodline. There are currently NO ill effects written into the code. That said, each one of us really does need to get used to working with COI and working with maintaining a low COI bloodline [at least]. So, what should we be aiming for? Here's the snippet for your answer from larissar out of the chat:

COI is not setting any of the genes or causing plateaus to bloodlines. It isn’t -doing- anything, it’s just the calculation of how related the pedigree is.

[BlackOak2]

COI currently does nothing in-game except help with some gene setting and possibly plateauing of a bloodline. There are currently NO ill effects written into the code. That said, each one of us really does need to get used to working with COI and working with maintaining a low COI bloodline [at least]. So, what should we be aiming for? Here's the snippet for your answer from larissar out of the chat:

COI is not setting any of the genes or causing plateaus to bloodlines. It isn’t -doing- anything, it’s just the calculation of how related the pedigree is.

It can aid in 'setting' genes if you want to get more of one particular gene 'into your herd'. And I've had it cause a plateau in my own bloodline as well as many other people have experienced this. By maintaining a high COI, you start to produce carbon copy horses and it CAN cause a lack of good upward, or also downward movement by breeding out all of the upper and lower limits. Meaning both upward and also downward movements can be a lot slower to progress.

And yes, it is a 'calculation of how related the pedigree is', but it can also help define how many of certain genes are in your line or aren't.

One last thing. I didn't say it sets genes or causes plateaus. I said it can HELP set genes and POSSIBLY plateau a bloodline. These are uses-of and things to watch out for.

[Argent]

Can this be pinned