In the comments a reader pointed to a discussion on his own blog "The Birdist" where he actually tries to answer the rhetorical question in the title of my blog post. So how many rare birds do we actually miss? The Birdist and his interviewee guess that one-third to over one-half of all rare birds are found. I disagree and I would put the percentage much much lower.
Why do I think so few rare birds are found? Well, for one thing, I look at the very small number that are ever refound. The White-crested Elaenia in Texas last January, or the Variegated Flycatcher in Washington this September, or the European Golden-Plover in Maine in October, or the White Wagtail in the Florida Keys last week, etc etc. all share the fact that none of them was seen anywhere else in North America. Maybe a statistician can comment on the hypothetical numbers involved, but if one-half of all rare birds were being found by birders, I would expect a lot of re-finding of these ultra-rarities. It's likely each of these birds wandered slowly and spent time at many other places where they could have been discovered by birders, both before and after their actual discovery. And there must be countless others that are never found.
The Jabiru in Louisiana July 31, 2008 could be the same one that was seen in southern Texas August 10th and 20th. But that is a big, conspicuous species that even a non-birder will notice. In fact, as I understand it, it was found in Louisiana by a local hunter who noticed it and took a few snapshots. It was refound by a birder in Texas on August 10th (if indeed the same bird) but then went missing for 10 days, reappearing on August 20th! Add to that the experience in August 2007 when a Jabiru showed up in Mississippi. Birders were alerted to it by the local farmers, but after a few days that bird vanished and was never seen again, despite intensive searching and the fact that its most likely path back to Central America would have taken it through Louisiana, past Houston and Corpus Christi, and over several hawkwatches. Rare birds being refound at a distant location are the very rare exception to the rule.
Another interesting bit of evidence is what I will call "delayed discovery". There are many examples, as in the 2007 Mississippi Jabiru that was seen by birders only because the landowner was curious and sent out a photo. It turns out the bird may have been in the area for several weeks before that. Or the Least Grebes recently discovered in a park in Boca Raton, Florida. On September 27th self-described "recreational birders" Lee and David Hasse sent an email alerting other birders that "last Sunday" they saw two Least Grebes. This was confirmed by their photos and by "serious birders" the next day. The following day (28th of September) the nest was discovered, and on the next day (29th) the first egg hatched!
The eggs must have been laid about 3 weeks before they hatched, and nest-construction must have started at least a week before that, and probably several weeks for pair formation, etc. So those two grebes must have been at that park for at least 6 weeks, since mid-August. And if the Hasse's weren't there in late September, or hadn't taken the time to report their sighting, would the entire nesting have passed without birders noticing?
So I'll take on the question now: How many rare birds are actually found? At a place like Cape May in the fall, arguably THE most intensively birded location in North America, a Jabiru is almost certain to be seen and identified, I'd say 80 or 90% of the time, and if it sticks around for more than an hour or two the odds go up to near 100%. As we go down the scale of conspicuousness, Fork-tailed Flycatcher is fairly likely to be found (virtually all birders and even a lot of nonbirders would notice one, even from a great distance); Western Tanager is less likely to be found (much less conspicuous - you have to be within a few hundred feet to notice one); Smith's Longspur is even less likely (secretive and nondescript), etc. The odds of finding a Smith's Longspur that only stays for a day are very very low overall (although if it spends that day on the lawn by the Cape May hawkwatch, it's very likely to be found). Staying longer will increase the chances of being found, and so on.
Psychologically, birders at places like Cape May are somewhat more likely to find rare birds simply because, at known vagrant traps, we expect to find rare birds. The same observation that might set a Cape May birder running after a "possible Smith's Longspur" is more likely to be dismissed as "not worth the effort" by a birder in farm fields in upstate New York. And as soon as a historical pattern develops at a location - like Cave Swallows at Cape May in November - the tables turn and birders start actively looking for a specific rare bird.
Back to my point about birds not being refound: if each of these rarities is spending 10 or 20 or 30 days wandering around inside North America, but is only seen once, that's something like a 10% or 5% or 3% chance of being found, and that strikes me as the right range to consider for how many rare birds we actually see.
As a final note, I like to think that this makes me an optimist, since I can always convince myself that the European Golden Plover from Maine is going to show up in my local patch tomorrow, and that there must be loads of rare birds hiding in the next bush.