[edited 12 and 14 Jan, 2008, adding comments about the index]
I've been thinking about redpolls more, and had another, more careful, look at Troy's 1985 paper, which is filled with interesting observations and some serious "food for thought".
First of all, Troy identified redpoll specimens using a character index, which is a well-established method of objectively sorting out variation when there are no obvious discontinuities. I don't know why I never thought of this before, because the character index is probably the best way to classify redpolls, and it can certainly be used in the field.
I've done a series of sketches (below) showing the range of coloration of undertail coverts, flanks, and rump. I have tried to match Troy's published reference photos. You need to see each feature well enough to match it to a number, then you can add up a total score - a sort of "paleness index". Troy simply divided the range of scores into thirds: the darkest third he called Common, the palest third Hoary, and the middle third he left unidentified. This is arbitrary, but at least it's somewhat objective. Numerically, a male (pink breast) with a score from 14 to 18 was called a Hoary in Troy's paper, a score from 3 to 7 would be Common, and from 8 to 13 intermediate. For females and immatures (no pink) it only took a score of 11 or higher to qualify as a Hoary, since no female-type scored higher than 13, and a score of 3 to 6 indicated a Common; leaving 7 to 10 intermediate (I'm using the straight numbers, Troy adjusted so that the lowest score was 1).
Important: Since I have sketched my own character index, even though it is based on photos in Troy, it will give different results, and the biases of different observers will inevitably skew the results, so we can't expect Troy's numbers to work universally with my index. Also, remember that redpolls become significantly darker as their feathers wear, and Troy's study was done in summer when birds would be at their darkest. In mid-winter we should expect all the redpolls to be a little paler, and it might be necessary to adjust the index a bit.
[12 Jan - Ron Pittaway on ID-Frontiers has emphasized the seasonal changes in redpoll plumage and questioned the value of this index, but I think the darker appearance of redpolls in worn summer plumage would come almost entirely from the upperparts. The streaking features being scored by this index should not change very much. That would be easy to test with specimens. In the meantime I think the index is still a very useful tool for objectively comparing redpolls, but of course we still need to work out what the index numbers mean.
14 Jan - And another caution about using the index: Declan Troy commented that he never intended the index to identify species, only to provide a measure of variation in plumage. Then by dividing the whole range into thirds he could test pale, dark, and intermediate groups for differences in size.]
I hope this index will provide a starting point for discussion, and I encourage people to try it out, comment, and suggest revisions.
1) The most interesting observation in the whole paper, I think, is the fact that all redpolls from study sites in the taiga (boreal forest) were dark (low-scoring) Common-types. No intermediate or Hoary-types were found at those sites. At tundra sites most redpolls were either intermediate or Hoary, with small and variable numbers of dark birds scored as Commons. Troy found no location with exclusively pale Hoary-type birds, although a couple of far-northern sites were close to that (and in those cases it's possible that his method of simply dividing the scores into thirds was too conservative, and maybe all those intermediate birds are good Hoaries). Places like Churchill, Manitoba, with a mixture of forest and tundra habitats, show the entire range of plumage, while places farther away from the forest had a higher proportion of Hoary-types.
So, based on this, one way to look at the redpoll situation would be to name a consistently dark, southern, forest population (Common) and a paler, northern, tundra population (Hoary). In this arrangement, any redpoll paler than a typical Common could be assumed to have a tundra origin and one could make an argument for calling them all Hoary. This may seem like an extreme suggestion, but it is less extreme, and more defensible, than the current status quo, in which the Hoary name is reserved for only the very whitest individuals, and ambiguous pale birds are casually and confidently (and falsely) called "pale Commons".
One of the contradictions I have been trying to resolve in this discussion is my observation that a lot of the Hoary-type redpolls I have seen at places like Barrow and Gambell, Alaska, would not be pale enough to satisfy most observers as Hoary in the lower 48. There do seem to be true intermediate redpolls, so I don't really advocate calling all the pale birds Hoary, but calling them "pale Commons" is even worse, and simply reflects a narrow southern bias.
2) Note: There is the possibility of subtle regional variations within North America, but this has not been studied. Complex regional variations from Iceland across northern Europe makes the situation much more complicated there.
3) The three characters used by Troy - streaking on undertail coverts, rump, and flanks - are all related, so combining all three is probably not much more powerful than using a single one. Adding independent features to the identification process - especially back color and pattern - might significantly increase the separation of two species. I haven't put up an index for back color yet because it is more subjective than the three streaking features, but I'll work on that and other potential features to add. Anyone using the index should also look at back color, back pattern, fluffiness of forehead, paleness of neck sides, and perhaps other things to supplement the streakiness score.
4) Like other studies, Troy found no real difference in bill length. Actually, he did find a significant but very small difference in female bill length (premaxilla length), the difference between males of the pale and dark types was not significant. So there is a slight tendency for pale Hoary-types to have shorter bills, but it should not be emphasized as a field mark (compare the short-billed and long-billed Hoary-types in my previous post). I would compare it to the difference in bill size between Thayer's and Iceland Gulls: we get the impression that there is a difference between the two populations as a whole, but it is so small and there is so much overlap that it has very little value for identifying an individual bird. The fluffiness of feathering around the base of the bill is probably a better feature to focus on, but that is also variable, and can be tricky to assess depending on angle of view and the bird's attitude.
5) Also very interesting... At his only study site east of Hudson Bay - Fort Chimo on the northern coast of Quebec - Troy found consistently dark Common-types, averaging just slightly paler than the birds of interior Alaska but none as pale as Hoary-type. Since this is about as far north as one can get in Quebec, this suggests that pale Hoary-types may be scarce or absent east of Hudson Bay, and that the pale redpolls appearing in the east may come from farther to the northwest. Just north of Quebec, on Baffin Island, the larger Hornemann's (Greenland) Hoary Redpoll nests. So I wonder what the status of Hoary Redpoll is in mainland Canada east of Hudson Bay?
Troy, D. M. 1985. A Phenetic Analysis of the Redpolls Carduelis flammea flammea and C. hornemanni exilipes. Auk 102:82-96. pdf here