what's going on here is a probability calculation i think. ...............
probability of exercise increases, of course, as one moves the strikes closer to market price of the underlying. The rate of increase is a curved line, not a straight. My question is, do any of the greeks describe this progression ?
for want of a better term i've been calling probability-of-exercise the jam factor
Maybe you're asking a question a notch or more above this, but let's start with the basics for anyone else that may be reading and are not aware of it. This probability-of-exercise is the delta(s). The rate of change of Delta is Gamma. I understand the natural inquisitiveness of traders but it's almost a moot point to attempt to read too much into it since things change daily and therefore your calculations would also necessarily change upon each incoming tick, every day. It would be a fruitless exercise to the bottom line unless your intent was to form a mid-to-heavy options pairing strategy upon strategy which I will admit we do often, but not for the reasons of being able to calculate a greek or a probability. For us at that point is purely hard P&L decisions.
The very nature of Delta and the Black-Scholes formula is as we know nothing but a calculation based on the Gaussian Distribution (with some practical modification over time) and so right out of the gate is a known flaw with respect to the reality of stock price movement.
The question becomes now one of asking ourselves how much error are we willingly letting ourselves be fooled by so as to make ourselves comfortable in our trade decisions. For us that answer is none at all. We recognize and appreciate the difference between hard numbers we can rely on and the other mental gymnastics we do to simply appease our psyche.
I suppose one could work out the curved nature of all the Greeks using the formula, but again it's been done for you by your broker so the question in my mind other than a personal satisfaction and increase knowledge, is why would you want to?