Pretty sure it's a set cycle, not every game. I haven't tracked it, so what I'm going to say is based on loose observation.
Keep in mind that the players who progress the most are 18 year olds. Improvement lessens gradually as they age. So the only way to track this, I guess, would be to play an 18 year old for 38 games. Also, from what I've seen, there is a hidden improvement attribute. Some progress faster than others, some progress with no playing time at all.
With that in mind, I think it goes Rollover / Before first game / about every ten games (or weeks?). In the case of 18 or 19 year olds, you may even see a bump after signing contracts.