There's more to it like services, friends, history/loyalty, all playing an influencing role to a different amount depending on who the consumer is.Honestly, the recipe is quite simple and is based on 3 basics : price, power, games.
You can also try to find success with innovative features, but it's more risky. One example is the Wii.
Another important factor is brand popularity.
As for Iroboto's mathematical model, I don't think one can be created. I don't think the metrics align - for example, there's no way to know how successful a game will be despite several decades of reference materials. If Sony were to set out to make a GTA type game, it could be a huge success, or it could fail horribly and lose crazy money. If such a model were possible, the console companies would be pursuing something along those lines to help with decision making, I guess. And in that regards, Sony has looked at the numbers for their hardware and software and decided exclusives make enough of a difference to be a priority. At the same time, MS looked at their data and decided exclusives weren't. Some would correlate PS4's better sales with PS4's different library (it's about the only real difference at this point), though mathematically it's not enough data to prove correlation. For the general onlookers like myself, a history of platform exclusives and game diversity for PS and PS's market leading sales, plus Nintendo's exclusives and Nintendo's ability to sell hardware that can fail in a lot of other criteria, is enough of an indicator that exclusives are not just a value-add but a significant decider. I also agree with you that if the 3rd party libraries covered all the bases and provided enough diversity and quality, that wouldn't matter, but it seems the first-party contributions manage to fill a void or raise a bar and continue to be a way to bolster a platform.
Going forwards, the value of exclusives versus the value of a persistent, ongoing, cross-device library may become quite the deciding factor above all else - we just don't know at this point. I do wish MS would make more of the future-proofing of their library rather than just leave it implied and for the concept to grow organically.