I think part of the reason you won't see it via TSP is that sometimes the training can go to FT, ST (things that don't attribute to TSP growth). They can also go into skills you have no intention of training in the long run and you may never see a pop there. I think about 1/6th of the difference can be seen there.
At a certain age too, the training will go into skills that you no longer want to pop (ones that are already at 20), or they will be diminished by elastics in some way. Some explanation might lie there. Maybe there are additional penalties to these 10%'s that we don't know about under the hood. Maybe they are counted at 10% of the raw training value before your trainer and youth trainer increase them.
I also believed gym constituted about 8-10TSP difference at level 3 but not 25 TSP. I think about 10 of the 25TSP can be explained by us simply looking at the distribution of skills, FT/ST, hitting skill caps or elastics. The other 5 TSP may be something about the exact details of the implementation that we do not know about. Or that is my assumption when I got this knowledge.
2x NBBA Champion: S55, S56. 3x USA Cup Champion: S54, S55, S56. WR for longest home streak ever at 11 in Season 47.