The following table shows the likelihood of succeeding at a level appropriate stunt with either a 'related' affinity or a 'spot on' affinity. The first pink section shows the likelihood of success if no affinity is used (this holds true across all levels). The table presumes an average ability modifier of +2. The large table-breaks correlate to how many action points are spent to re-roll results. As a reminder, no re-rolls are allowed if there is not at least a related affinity and you may re-roll one additional time per tier (level 1-4, 5-9, and 10+). This is why the Tier 1 line is blank for the 2 AP section, and similarly for Tier 1 and 2 in the 3 AP section.
This table also introduces an idea not yet presented. Affinities provide a +1 bonus per tier (+1 at 1-4, +2 at 5-9, and +3 at 10+) to the 'spot on' results or ANY re-roll after spending an action point. The math really didn't need it, but I think people might psychologically need it. If we find out later that people don't need it, it will be extremely easy to remove and won't substantively change the math.
Let's focus on the top section of the table in the '0 AP' zone. Throughout play the most common stunts faced will be basic and heroic. What we see is that even untrained heroes have a decent chance to succeed at level appropriate stunts; they can almost always be included and will face reasonable challenges. Trained heroes (spot on) have a much higher rate of success, passing 91% of the time. This 91% is more exciting, in my mind, than a similar mechanic on a straight d20. The equivalent on a straight d20 is a 3+. This is an 8+ on either of 2d20. That tends to feel more satisfying during play.
We also see that a hero with a related affinity can spend an action point to be almost as competent as the spot on hero. Maybe he'll get lucky and not have to spend the AP, but if he is willing to spend it he can be almost as likely to succeed. Because related affinities are construed relatively broadly, a player willing to put in creative effort can regularly achieve this.
One could argue that construing affinities broadly is similar to adding many different skills to a skill challenge such that everyone has something to do. There are two differences. First, that puts all the burden on the GM and we've already established that GMs regularly fall into apathy. They have a lot on their plates, so shifting some of that burden onto the players is a great idea while also empowering the players. Second, when a GM sets something up so the players can succeed it is seen as gimmicky or deus ex machina or some similarly overused term. When a system is set up so players can facilitate the narrative or input creativity, it is seen as a strength of role playing games.
Next, onto the concept of group success rate that I discussed with the 4e skill system.
[Average (65% + 40%)] x [Average (91% + 70%)] = 42%
What this reveals is that as the party increases in level and as the party is willing to commit more resources to a task, the likelihood that the party succeeds at said task increases. Compare this, again, to what happens to 4e skills as you increase. This system grows more inclusive while 4e grew more exclusive. Moreover, although the higher success rates require the expenditure of more resources, you have more resources available to spend. At the same time, those resources could go to powering more diverse and more potent powers, so the tradeoff remains poignant across levels.