Bad luck can affect pools just like it can affect solo mining.  Back in the summer I was mining litecoin on a pool, the estimate was that the pool should have been finding ~2 blocks per day.  That pool hit a VERY bad run, it went 6 days without finding a block, pool hashrate and difficulty stayed roughly consistent the whole time.  And then when it finally got a block, it got orphaned... ouch. talk about a kick in the teeth.  Then 2 more days to the next block, then it resumed a neutral luck pattern again.  I actually switched pools after the second day of nothing, but I kept watching it.


It re-enforces what I always say: It doesn't matter what method of mining you choose.  If you average out your mining over a long enough period of time, the total amount you earn will be about the same.  The only thing that changes is the payout, either small amounts throughout the period, or a large lump sum at the end.  
How long is long enough for it to average out?  Well... that could be a long time depending on your hashrate vs the total network hashrate.  It's not necessarily the time to your first solo block, it takes more time than that to average out.
The rule of thumb that I've heard stated, and I tend to agree with, is that if you can solo mine at least 1 block per day, then it makes sense to go solo.  Less than 1 block per day, then you're better off on a pool.  I can't think of any scenario that would necessitate someone needing more than 1 payout per day.