Thanks to all of you for your thoughts on the horse. I've been breeding all weekend, but Checkmate hasn't given me anything decent yet. Mostly horses with awful stats and one filly that looked decent stat-wise but prefers to cross the finish line last, in game as well as in CK. So Checkmate is still the best one in trials (IF he isn't having a bad day

) with one filly from other lines that mostly comes in second, but manages to beat him sometimes. I just retired her and will match them together to see what happens

BUT....
I still don't really get it. While trying to add some Battling Qualities I got this guy:

I did compare his stats to Checkmate and I think he should be at least a tiny bit better on the track, but he isn't. Not at all. In a trialling field of 7-8 good horses he's only just mediocre (both, ingame and CK), always finishing in the midfield.
But he does have a better Cruising Burst and a lot more Battling Qualities. All other traits are almost the same. Only Battle Heart here has not a full realized potential. I don't know if it's visible on the picture, but the bar is not completely dark green, there is about 1% light green still.
Also Accelaration is a little bit less than Checkmate's, but therefore his Speed is 100% and he's got a bit more Stamina.
And now comes the funny thing... (or maybe it's a common "problem" and I just didn't stumble over it yet)
.... in a larger field he doesn't leave the midfield, not once in 10 trials. But if I trial just my best three horses and him, he wins 8 out of 10 races. Are there invisible traits at work here?