It depends. (Of course.) The short answer is: Not only don't we know, we can't know. The long answer uses the word "however" a lot.
Shared hosting has a well-earned reputation for volatility, due to the fact that you are sharing resources with other people and neither you nor we know from moment to moment what they or the visitors to their site are going to do. However, the most common causes of downtime for member sites are specific to the particular site affected (misconfigured DNS, an expired domain, runaway scripts, letting your prepaid account run out of funds, etc).
We find that when people ask us about uptime, they are expecting us to give them a magic number with a certain quantity of nines in it that represents what fraction of the time our service is available. However, our service is sufficiently varied and complex that offering such a number would be disingenuous, especially since we host a large number of sites and they don't all move in lock-step; one person's downtime might not affect someone else.
It would be very easy (and blatantly dishonest) for us to pick an arbitrary metric that would allow us to claim 100% uptime, or any number of nines we want. But, likewise, for any sufficiently large cluster of computers, something somewhere is always offline for maintenance, so we could probably make an argument for 0% uptime. (Though we won't.) Sites move back and forth, servers go up and down, and most of it happens without any visible effect. Even when a production server crashes (which does happen from time to time) it typically affects only a relatively small percentage over our members' sites, and usually only for a few minutes.
Our clustered approach does provide resiliency against many (but not all) types of hardware and load problems that cause downtimes at providers where your site is 100% dependent on the availability of a specific server. However, we do develop and maintain our own clustering software, so occasionally something incredibly weird may happen here that never would have or could have happened anywhere else. Such events are rare, but not without precedent.
Sites hosted at NearlyFreeSpeech.NET are probably slightly more likely to be "collateral damage" of a denial-of-service attack targeting some other controversial site hosted here than at other hosting companies that are less flexible in terms of hosted content. However, the flip side is that you are probably better protected against most such attacks due to our extensive experience with them, leading to (most likely) a very small net difference in the chance of being affected by that type of downtime.
All in all, our overall service availability is probably above average to very good when compared to other shared hosting providers. However, "overall availability" is meaningless to someone who's affected by something that doesn't affect everyone. Each person's view of our service availability can and will vary widely based on their personal experience as well as their personal criteria for what constitutes "availability."
We do monitor all of our systems and services continuously from multiple offsite locations and respond to problems detected as quickly as possible, 24x365.