Ok I try to cover the main points. There are some very good guides about matching and training in the guide-section of the forum. You can also search for specific blogs about culling, matching or training via "search blogs" --> scroll down to the bottom of the page and search by tag.
When matching you're trying to even out your mare's weaknesses by matching her with a stud that's strong where your mare is weak. To determin where your mare is weak in, you need to set her training to all disciplines. That way she'll gain training bars in all six traits. After each week of training you note down the traits she gained a training bar in. It might look a little like this:
wk4: 112221
wk5: 122222
There are several ways players track training, as long as you know what it means, any system is fine. In the system above, each number is equivalent to a training bar of one of the six training traits. So after four weeks of training the horse has 1 training bar in mv, 1 in int, 2 in hrt, scp and spd and 1 in str. In rare cases horses trained all discipline gain a training bar after three weeks of training, so make sure to take a look at your foals from early on. To determin which traits are strong or weak you use the training weeks. Any trait gaining a bar week 3, 7 and 11 is very strong. Any trait gaining a bar week 4, 8 and 12 is strong. Any trait not up a training bar week 5, 9 and 13 is weak so those are the traits you need to even out when matching. So the example training I gave above: The horse was up a training bar in hrt, scp and spd by week 4: so that's are his/her strengths, but it hadn't gained a bar in mv by week 5 so it's weak in mv. So when matching that horse, I need to find a horse strong in mv that can be a little weak in hrt or scp or spd because my horse makes up for it.
What good training looks like is dependable on the horse's gender and rating. The lower the rating the longer the horse takes to gain training bars. Geldings train faster than stallions and mares.
With a PEE+ rated horse I expect them to have all bars up week 5 and 9. I don't care much about week 4 it's an indication, nothing more. The longer you train a horse the clearer you see it's true potential. Some exceptional week 4s have had very bad week 8s and other horses with average week 4s and 8s have had very good week 12s. I usually track training until week 16 to have a good idea how strong my horses are. By week 16 they usually have a foal to show for as well. Production in my oppinion is a far better indication of how strong a horse is than training. Training to me is an indication and a tool to choose good matches.
I hope I've been of some help. Feel free to pm me if you have questions :)
Spring Showers
