After the introduction of the horse breeding changes, I wanted to try making a max-stat horse. After many hours, I realized the new system, while capable of improving most horses stats, it cannot reach the maximum values.

This video by slicedlime shows the new and improved algorithm on a graph. The graph showcases that max value horses are possible by continuing the graph up to the max values. This implies that two non-max horses can breed to create max-stat horses. After gameplay testing, however, this does not appear to be the case.

Steps to reproduce

1. Summon two near-max-stat horses i.e.

   /summon minecraft:horse ~ ~ ~ {Variant: 0,SaddleItem:{id:saddle,Count:1},Tame:1,Attributes:[{Name:"generic.max_health",Base:29.999f},{Name:"horse.jump_strength",Base:0.999f},{Name:"generic.movement_speed",Base:0.3374999f}]}

2. Breed these two horses
3. Read new horse attributes with

   /data get entity @e[type=minecraft:horse,limit=1,distance=..2] Attributes

4. New horse will realistically never have improved stats over the parents, and will instead have decreased attributes.

Example

Conclusion: There was a small decrease in jump height, a small decrease in movement speed, and a significant decrease in health, coming from two near-perfect horses.