Effects of mining pools paying for stale shares/work Some mining pools pay for stale shares / proofs of work, and others don't.

If a pool pays for stale shares, how does it affect individual miners? What about the pool?

Related: What are stale shares and what can I do to avoid them?
Stale shares have no chance of being a valid block credited to the pool, thus submitting one contributes nothing to the pool. The default behavior, then, should be not to pay for invalid shares. (A comparison with matching the difficulty target is illustrative. A miner has no influence on how many of his shares match the target, and hence it is fair to be rewarded for failed shares; however, he does have an influence on how many of his shares are stale, as these can be a result of latency on his end.)

If a pool decides to pay for stale shares anyway, this must come at the expense of someone else (as the total average reward of a pool with a given number of non-stale shares is fixed). The identity of "someone else" depends on the reward method of the pool.

Methods like PPLNS do not absorb any variance, and the operator can never lose or gain any money (beyond a fixed fee); 100% of any block reward is distributed among miners. If stale shares are counted for the purpose of dispersing rewards, it means the non-stale shares are rewarded less on average. If all miners have the same stale rate, this has no effect whatsoever on their average reward; there's the same total reward to go around, so what they gain in rewards for stale shares they lose in rewards for non-stale shares. If different miners have different stale rates, this benefits miners with many stales at the expense of miners with few, removing any incentive for the miners to minimize their stale rate.

Some methods absorb variance, the most extreme case being PPS; any statistical deviations manifest as a profit or loss for the operator. If the pool offers payment for stale shares, it comes out of the pocket of the operator. If the stale rate is assumed fixed, this amounts to an effective fee slightly below the nominal fee (e.g. if the nominal fee is 3% but the pool pays for 0.5% of stales, the effective fee is ~2.5%). If the stale rate is not fixed, then the pool becomes more attractive for high-stale miners, and relieves them of the need to worry about their stale rate. This is detrimental to economic efficiency, but can be easier psychologically. To maintain a profitable business, the operator will need to carefully balance his nominal fee with the stale rate of his target audience.