Birding is a funny old game, ever trudged your local patch everyday, week in and week out and then you miss a day - what happens... somebody finds the bird of the year. This is hypothetical of course but birding does tend to throw up some odd happenings, mathematicians would probably explain it all away with probabilities and scientific formula.
How about the simple rule of thumb, if you have find a good bird then you are more likely to find another one shortly after or if you find a particularly difficult to identify rarity then you are much more likely to be able to identify that bird the second time around and therefore go looking for that species at suitable times and places and thus end up finding a 2nd or even a 3rd - I know birders on their 4th self found Blyth's Reed Warbler or the guy who found both Grey-tailed Tattlers in the UK- coincidence or fate ?
Heard the one about the birders on St Agnes a few years ago - they spend all week there, on the last morning they flush and briefly see and hear an interesting pipit - whilst trying to refind it they stumble over a Semi-palmated Sandpiper. They leave Agnes and arrive just in time for the Scillonian to depart back to Cornwall. One of the party legs it to the sightings board in the middle of Hugh Town and quickly sribbles the Semi-P up before catching the Scillonian. As they get on the Scillonian off gets a birder who immediately goes to the sightings board. He reads the latest message Semi-palmated PLOVER (note the mistake and now he thinks he is faced with a 3rd record for Britain). Off he dashes to St Agnes where he discovers the Plover is in fact a Sandpiper and not quite so interesting... whilst walking away from the plover he flushes a pipit with a distinctive call, having just got back from American he immediately knows its a Buff-bellied Pipit
and not only that but it shows fantastically well, a mega find (of the earlier bird) , but ... was it coincidence or fate !
Another aspect that runs through all of this is SKILL, which would probably be explained away by the mathematicians as 'experience meeting opportunity'. Whatever it is, most field birders have it to some degree but a few have it in abundance - we all know who these people are and their records silently scream it from the pages of the BB annual rarity report. If you have ever been in the presence of these birders then you will remember it like your first Siberian Thrush - they ooze quality !