Analyzing effectiveness of noncombat skills

Although I've analyzed the combat effectiveness of many combat capabilities in many games, I rarely tried to analyze the effectiveness of noncombat skills. It is never been very tempting to try because the effectiveness clearly depends entirely on how the game master runs his game. However, in analyzing D&D, it occurs to me that it would be possible for me to try something new and perform a numeric analysis to compare noncombat skills with each other and with combat skills. Even though the effectiveness of a noncombat skills is based entirely on the frequency and manner of use, it should be possible to determine in a general way how it is based on those and under what circumstances the skills would be better or worse than combat skills.

My first step was to name categories for 3 types of skill checks.

Critical skill checks are essential for the adventure to continue along a successful path. Success or failure in the skill check is equivalent, at least in a limited way, to success or failure in the adventure. This type of skill check is equivalent to engaging in combat, and failure is equivalent to losing a combat. In either case, failing and encounter you are supposed to succeed in does not necessarily mean automatic failure on the mission, but it is very disruptive and often forces the GM to invent an appropriate way for the adventure to continue. For instance, he would be a critical skill check to disarm a bomb before it explodes and kills everyone.

Critical skill checks have a long history of causing trouble. They are very common in the source material, since in a book or movie you can create a problem that absolutely has to be solved and guarantee that the heroes can solve it. There are 2 key problems in a game. First, the fact that the game is random and you cannot guarantee that the players will succeed. What happens if they fail? You may be able to handle failure in an appropriate way, but it is likely to feel very forced if you have to do it very often. This would tend to mean that the chance of success has to be very high. But if so, how do you at the same time make skill checks seem challenging rather than trivial. Second, a fight that the players have a high chance of winning can be very exciting because it consists of so many independent actions that can succeed or fail, but a single skill check is anti-climactic.

Torg was able to solve both of these problems with the dramatic skill check. D&D’s version of this, the skill challenge, solves the problem of having only a single skill check, but since D&D does not have fate points, it is still not practical to require that you succeed in a skill check so the rules recommend that you do not use critical skill checks.

A major skill check has a substantial effect which gives a significant award or influences your ability to succeed or fail in the rest of the adventure. For instance, you earn an ally, or gain safe passage through dangerous area, or get an extra magic item, or gain a tactical advantage, or defeat a monster without fighting, or earn a significant amount of experience. You would like to succeed, but failing doesn't send you off course. D&D recommends that a skill challenge be a major skill check.

A minor skill check offers a very small, subtle reward. You may gain additional information that may or may not be useful, or make a friend that you could conceivably need in a future adventure, or be able to get to the next encounter more quickly.

What I'm wondering right now is, for a given noncombat skill, how often, in terms of encounters or levels, would you expect to make skill checks of the 3 different types?