There's some good stories and answers here, but I wanted to sum up and see if I could hit the nail on the head:
...what are the specific odds of me falling into each of those
buckets? Does there exist any study of the aggregate outcomes of PIPs
as a tool for effective management?
My impression is that this is the "kiss of death" for my job and I
need to start looking elsewhere immediately. How likely is it that I'm
Summary - this stuff as as unique as the PIP, you, and the company you are working in. It generally takes a lot of time for a manager to run a PIP, so it is a last resort in most cases.
For the most part - a PIP should aim to be clear, measurable, reasonable & appropriate to the job of the person getting it, and measured carefully. It should also be confidential. In short - it should be doing a process that aims at rebuilding the manager's trust that the employee can do their job, and that it can be over with no further blame or career damage.
That said, in my experience, here is how your buckets sort themselves out:
I fail the PIP. I am fired.
A pretty common case. If the performance issue is something the employee just cannot or doesn't want to change - this happens. Often by this point, "doesn't have the skills", "doesn't have the motivation" and "can't for some other reason (like work/life conflict)" - are so blended and entangled and distorted, there is no sorting them out.
It's also a higher risk if you are on a PIP and the company is in the kind of financial condition that leads to a layoff. The bonus in that case is you get a layoff package, and not a termination for cause.
I don't care about the PIP because I decided to quit.
Also a pretty likely case, and I put it in here, because it is so common and distinct from failing the PIP. Depending on the company, quitting may cause less damage than being fired. It certainly saves you and your manager some pain. Not a crazy idea if you get the PIP documentation and realize that what is described here is absolutely not the job you want to be doing, and that you can get a different, probably better for you job somewhere else.
I pass the PIP but am less effective than before.
Unlikely. The only way I can conceive of this is the company is asking you do to stuff that is important to how the company sees your effectiveness, and detrimental to how you see your effectiveness. Examples - following arcane security procedures, doing a truly excessive amount of documentation, obeying other obscure formalities. Back up far enough and squint and someone thought this stuff was really important to the health and well being of the company and it's customers. It may be that it's not your job to agree, but just your job to follow the rules. If you hate that - see the previous section on quitting.
I pass and my productivity is unaffected.
Possible. Also unlikely. If you and your boss are really out of touch with each other on something you've already been doing, that they didn't know you were doing and all is well, PIP was unnecessary, and it's all over.
In practice - I've never had this case occur and I've been involved in a fair number of PIPs. Unless you have a case of the utterly not paying attention boss, or your in a job where what you do is very specialized and your boss had no context for it, so wasn't setting their own expectations properly - it's hard to imagine how you'd get here.
The PIP causes me to "come to Jesus". I am more effective than before
I've actually seen this one happen. Cases where the employee really honestly had no idea of a required aspect of their job, and having it explained in the (usually excruciating) detail that a PIP requires actually clarified the problem and the employee was able to improve with practice, feedback and maybe even some training.
That epiphany is what we all hope for and what the folks who train managers on PIP processes tout as the goal... but in my experience, the first two cases are more likely.
There's a variant on this - which is sort of a mashup of "productivity improved" and "this isn't the job I want now that I understand it" - which is that the employee and manager realize that although the employee could do this job, they really aren't a great fit, and there's actually a better job elsewhere in the company for them. I've seen that happen... but it's still a rarer case. This one gets more complicated and company specific, as the rules around a PIP are usually pretty rigid, and not every company will let an employee in this situation make a transfer. Usually an employee will have to get through the PIP successfully and then make the transfer. If that works, then they end up more effective than they were before because they are now doing a job they enjoy and are well suited to.
Bottom line: The level of damage being on a PIP can do to a career at a company is largely related to the reason for the PIP, how much the theorized performance issue has impacted other members of the team, and to what extent the employee can change the behavior that led to the reasons of the PIP. When trust is broken, it's really hard to rebuild, so the big question is - what trust is broken?