As the title suggests, I'm a little confused on breeding. What stats go into how well a horse will produce? What makes a good match?
I've realized that it is not as simple as just breeding a WWW stallion to any mare and getting a better foal.
Also does training impact breeding? I've seen some mentions on people needing to prove the horse?

Please dumb it down for me! My account is only about a week old so I am veryyy new to all the lingo.

There are a lot of quite informative informations found in the game help section of the game and in the guides forum.

Breeding here depends on the ratings of the parents and there is an unknown random factor swining into every breeding... a bit like in real life.

So not every EEExEEE will give you automatically an EEE rated foal - but maybe they breed down to a PPP or PEP/PEE combo rating or even to a S.

But maybe you are very lucky and random factor swings on your side and gives you an EWE / EWW or the top WWW rating. But this is quite seldom, obviousely.

Maybe you want to look at this very old blog post. It is from 2015 - but it is technically still working like this: https://horseeden.com/blog.php?id=18024&b=22

Top breeders are using weeking training rates to match their breedings. This is the super dumbed down version because I don't do this yet. I'm still kind of scattershot breeding. They will put all horses in training and record their training ratings.

Example:

WK4:1 2 2 2 2 2
WK5: 2 2 2 2 2 2
WK6: 2 2 2 2 2 2
WK7: 2 2 2 2 2 3
WK8: 3 3 3 3 3 3
WK9: 3 3 3 3 3 3
WK10: 3 3 3 3 3 3
WK11: 3 4 3 4 4 4
WK12: 4 4 4 4 4 4 [end]
This stud

So I believe this horse would be considered low in Movement and Heart, so you would want a mare who is high in Movement and Heart to even it out (she also needs her weekly training recorded like this so you know her stats). This guy isn't a great example because he's up pretty even almost the whole way.

The WK4 = the week of training (week 4, first few weeks don't matter)

The numbers are how many training bars that horse is up that week (the brown/green stacked bars in the training)

Now... if you want to take the easier route while you are building up your barn, you can spray and pray like me :) I look at their bloodlines. If all their family members have good stats, I want to breed them. For example, the stud has all Ws in his pedigree, I want to breed to him. If he's a WWW with EWE x EEE parents, I'm not breeding to him. Same goes for my mares now that my stable is getting bigger. If she doesn't have well rated parents and/or doesn't produce EEE+, she's gone.