I played a few seasons with injured-prone players, and I checked over two seasons, and there is no sign whatsoever that there is more 15 games injury than 8 games injury or any other length period. In fact, my data shows that, as expected by the chart, the most common injury scenario for players with less than 600 PAs is 1 day.
I think that the feeling some people have that 15 games injuries are more common to, say, 1 game injuries comes from the fact that the 15-games injury appears on the front office page much more longer. When one of your player is hit with a 15 games injury, for five continous days, every time you click on your front office page, you see that injury, whereas, if you don't look at the day-by-day reports, you might not be even aware that a player of yours was injured for one game.
Also,
don't forget that some players don't even have 3-games injury---they only have REM injuries. These players have an unusual high number of PAs (I don't remember the threshold, but I think it's close to 700 PAs).
Aray,
I've played for four seasons now, and I have never, never seen a player with less than 600 PAs being hit with an injury of more than 3 games.