Six, and I saw more of Google than most. I'll leave it at that.
If you are performing well and get poor calibration scores (which aren't secret)
You get a range for your calibration score. Whether your manager tells you the specific number is up to him, and you have no way of knowing whether he's telling the truth. Most Googlers will get Meets Expectations (3.0-3.4) which ranges from the 2nd to 70th percentile. For most, it means "solidly OK, but not yet promotable". 3.5-3.9 is Exceeds (70th-95th percentile) and means "on track for promotion" and 4.0+ is Strongly Exceeds (95+) which means "promotable". Almost never are numbers below 3.0 or above 4.5 used, because sub-3.0 requires PIP/termination proceedings (which are a lot of work for the manager) and 4.5+ makes an employee eligible very large cash bonuses (and, occasionally, double-promotes).
If your manager gives you 3.0's but positive verbal feedback, you'll think you're getting 3.3-3.4 (which is perfectly respectable) but you won't be able to transfer. Except for the first quarter, 3.0 means, "you suck but I'm too busy to deal with the PIP/termination process"; 2.x requires the manager to do a bunch of extra work so 3.0 is understood as the "he's awful but I don't feel like doing anything about it" score.
However, there are managers who give positive verbal feedback and 3.0-3.1 ratings to keep good people captive. You didn't see what I saw. I have data but I'm not allowed to share it because I'm not supposed to have a lot of that stuff myself. It's not most managers who do that shit, but it's a sizable contingent and executives are aware of the problem. They don't do anything about it, in my opinion, because they're afraid that it would sacrifice project expediencies to reduce managerial power.
then that's something to bring up with HR and your manager's manager.
Try this out. In any company. Please, I encourage you to do it. You sound like just a wonderful person and I'd love to see you take a crack at it.
Nah... I'll tell you what happens, not because I give a shit about you, but because other people are reading.
If you go to HR, you get fired. Not "officially terminated" because the company doesn't want the lawsuit risk, but HR and your manager will make it look like (a) no one else in the company wanted you so (b) they can PIP and eventually terminate you. You won't be able to transfer because "you have to solve the problem where you are before you move on" and because there will be feces smeared across your personnel file. This known in HR-speak as "passive firing". With passive firing, the employee is technically permitted transfer but it is made impossible. It's a way to give managers unilateral termination without the lawsuit risk.
If you go to your boss^2, you are similarly fucked, because your boss^2 picked your boss, idiot. Who do you think he'll side with? If you seriously think that a boss^2 is going to take the side of an underling, then please, try to make it happen the next time you are checkmated. If you have a shitty boss, your boss^2 knows and is tolerating him because it's expedient, if wrong.
If you want to jump your boss, you have to go to the boss^3 or higher, and the probability of that working is low because the social distance and credibility gap is high. But you have much better odds with a boss^3 than a boss^2. The boss^2 will tip off your boss and you are fucked; the boss^3 will just say, "Who are you?", and tell you to get back to work.
it's almost impossible to transfer teams before you've spent at least 1.5 years on that team.
At least you admit to that problem. Yes, that is correct.