I don't know if it's actually realistic, but the BRP version in the Troubleshooters feels right. Much like classic BRP, you get a tick on a skill when you use it in a significant way (you don't necessarily have to succeed, but you can't "climb the tree to get an Agility tick"). At the end of each session, these can be used for Experience checks (roll d100 above your current skill, if you do you increase it by 1d6%), or put toward learning a language or an Ability. Abilities are things you either have or you don't, and usually let you be better at a particular aspect of a skill, or use the skill in different ways, or sometimes have more story-oriented benefits. Gaining a new Ability usually costs 5 ticks, but it can be as low as 3 or as high as 8.
You also gain a number of free improvement ticks at the end of each session – 1 to 4 for most sessions, with an additional 3 at the end of a full adventure for completing it without unnecessary bloodshed. These work the same as the ticks you get for using skills. You can only use one free improvement tick per skill and/or ability, so the most you can get per session is two per skill (plus possibly one more for downtime).
Depending on how long it will be until the next adventure, you will also get 1 to 4 downtime periods (a week gets you 1, a year or more 4, so it's not linear). One of the things you can do in a downtime period is training, which gives you the same effect as an additional tick. You still can't get more than two ticks for any one skill or ability per "debriefing" phase, so if you both got a "use" tick and used a free improvement tick on one skill, you can't train that particular skill any further during downtime.
What I particularly like is the mix of Abilities and Skills. Skills are fairly broad, e.g. Red Tape covers all sorts of law, bureaucracy, negotiating deals, and so on. But on top of that you can have Abilities like Called to the Bar (makes you an actual lawyer, lets you use Red Tape instead of Contacts for certain things, and gives you a bonus to Status checks). I like this because in real life, you both have fields of general knowledge, but also specific things you just know how to do.
Now, the Troubleshooters is a game meant to mimic comics like Tintin or Spirou, and the skill and ability list reflect that. Some of the abilities aren't all that realistic in and of themselves. But I think the structure of the system feels fairly believable, if not actually realistic.
You also gain a number of free improvement ticks at the end of each session – 1 to 4 for most sessions, with an additional 3 at the end of a full adventure for completing it without unnecessary bloodshed. These work the same as the ticks you get for using skills. You can only use one free improvement tick per skill and/or ability, so the most you can get per session is two per skill (plus possibly one more for downtime).
Depending on how long it will be until the next adventure, you will also get 1 to 4 downtime periods (a week gets you 1, a year or more 4, so it's not linear). One of the things you can do in a downtime period is training, which gives you the same effect as an additional tick. You still can't get more than two ticks for any one skill or ability per "debriefing" phase, so if you both got a "use" tick and used a free improvement tick on one skill, you can't train that particular skill any further during downtime.
What I particularly like is the mix of Abilities and Skills. Skills are fairly broad, e.g. Red Tape covers all sorts of law, bureaucracy, negotiating deals, and so on. But on top of that you can have Abilities like Called to the Bar (makes you an actual lawyer, lets you use Red Tape instead of Contacts for certain things, and gives you a bonus to Status checks). I like this because in real life, you both have fields of general knowledge, but also specific things you just know how to do.
Now, the Troubleshooters is a game meant to mimic comics like Tintin or Spirou, and the skill and ability list reflect that. Some of the abilities aren't all that realistic in and of themselves. But I think the structure of the system feels fairly believable, if not actually realistic.