I have a working hypothesis that if a long-running bubble show doesn't cross that threshold and meet its "expectation", it has a higher chance of being canceled. In fact, my research here would actually explain the renewal of Bones and the cancelations of Castle and Nashville. Take a look:
Bones
A18-49 rating when renewed: 1.14
C3 expectation according to my research: 1.06
Castle
A18-49 rating: 1.09
C3 expectation according to my research: 1.57
Nashville
A18-49 rating: 0.94
C3 expectation according to my research: 1.24
It may also explain the renewal of Grimm. Take a look:
A18-49 rating when renewed: 0.92
C3 expectation according to my research: 1.04 (see explanation below for why a 0.92 A18-49 rating most likely means at least a 1.04 in C3)
It may even explain Sleepy Hollow's renewal. While disappointing on Thursday, Sleepy Hollow retained a good portion of its audience on Friday and cleared that 0.65 C3 number that it would need if the ad rates set were completely correlated with the ratings. The formula, unfortunately, does not predict the cancelations of Undateable and The Mysteries of Laura, though it does predict the cancelation of The Good Wife and renewals of the CBS Friday 9-11pm duo. It may or may not explain iZombie's renewal, which at the time had an A18-49 number about 0.15 away from the C3 "expectation number". So it basically depends on how much it rose in C3, though then again I have a theory that The CW is simply in the business of getting all their shows to 70 episodes regardless of ratings. In the case of Undateable and Laura, the #1 explanation I can think of is that the ad rates were so low that even reaching that threshold wouldn't be enough for it to be seen as enough of a moneymaker for NBC. So far, these two are the exceptions.Also, remember that C3 numbers are higher than A18-49 numbers. Very few C3 ratings are available to the public, but judging by premiere week, most shows will rise about a tenth or two. It's not that much of a stretch to say that Grimm, with a 0.92 A18-49 rating, cleared the 1.04 C3 rating threshold. However, it more than likely was not enough for Castle or Nashville to cross that threshold. I will admit that media coverage and the general consensus that they would be renewed was part of my equation in making Castle and Nashville likely renewals; but if I had taken a chance and stuck by this little research of mine, I would have had two correct predictions. Ditto with Bones.
Freshmen Shows and Hits
Don't expect to use the freshmen show advertising rates for anything other than entertainment purposes. For example, The Catch was renewed even though its supposed threshold was over a 2.0. In ABC's defense, they had no real way of knowing what they should expect out of the show. Also, if a show isn't seen to be in danger of cancelation for any reason (i.e. SHIELD, Scandal, etc), this does not apply. Maybe advertisers were disappointed, but it wouldn't be canceled just because of that. This works best for shows that have low ratings but aren't going to be saved for a reason like being a season away from syndication, making $3 million/episode in syndication (looking at you Elementary), or something else of that sort.
Of course, L+SD ratings aren't everything these days, but they do still tell a lot. Could it be coincidence? Maybe. But as shown in past articles, it's pretty darn accurate with the shows I tested it on. If you recall, I used the research on Chuck, Parenthood, Parks and Recreation, Private Practice, 30 Rock, and Revenge, to see if the troubled veterans would squeak out another season. It nailed every prediction except for the final season renewal of 30 Rock. But who knows, maybe awards and critical recognition were too much for NBC to truly consider the show to be in danger of cancelation in its penultimate season.
To conclude, I think more research is needed, but I definitely think I am on to something. As long as you know when to consider a show a true bubble show (as opposed to one obviously staying alive for extraneous reasons), this research could truly be telling.