First, most bounties are unneeded - they are simply badly tagged, and no one noticed them, or badly asked, and no one wanted to answer. You need to make sure you ask a good question first - and if you didn't, or needed to edit it, sometimes bounties are used to get attention to the question.
What do you base the decision on? How do you determine how much a good answer is worth to you?
I think this depends on the reason a bounty is being offered.
To give some examples:
- If you have a simple question about a well known system, but no-one is interested in answering, 50 is more than enough - someone will see it, and answer clearly and well. You may want to ask yourself why no-one was interested initially...)
- If you have a complex question that you need someone to invest time into to understand and develop a solution to, you probably want to offer a bounty that is a function of the time needed to answer. 50 points as a base for a clearly written response, then 100-200 points per hour of expected work seems reasonable, up to 3 hours or so. If it needs more time than that, you probably need a consultant, and this isn't the best place to get such an answer. You can try huge bounties, but you won't necessarily get answers to question if you want someone to invest 8 hours to develop a customized solution for you. It also doesn't belong here - it will be of limited use to others.
- If you have a very obscure question on a system or feature few people use, that does not require much time to answer, but requires tremendous expertise, 50 points will probably bring it to the attention of the right people - but a better solution may be to tag it well when you first ask it.
- If it is an obscure system, feature, or area of knowledge, and someone will have to invest significant time to understand the issues involved, then you may need to put in a significant bounty - few people may be interested, and they may not want to spend time on the issue - this is a answerer's market, and you may need to put up some real reputation if you don't see any answers after a bit. If the question is getting comments, but no answers, check that you are asking a good question and are sufficiently clear.
What are your experiences as to the relationship between the bounty amount and the quality of answers?
Very little, once any bounty is offered. Having a bounty gets clearer answers, better written answers, etc. But not as a function of bounty size. If you are looking for great writing, clear documentation, or customized work, you need to be vey clear about the request - not just up the bounty.