Details provided about counting relatively large numbers of birds

The eBird help section has an excellent article on counting large flocks, passels, gobs, and masses of birds, and I encourage all eBirders and other birders to read it. This article, however, is about the details provided by eBirders to support their submitted large numbers of birds that the relevant filter flags.

In the above-linked article on the details box, is this sentence:

For entries that are flagged due to a high number, a simple comment on how the number was derived is what we want:  "counted 1x1," "counted by 10s," or "estimate" usually suffice.

I wish to add a corollary to the above. For numbers of a species that flags at a low value, say <10, particularly for numbers <5, the careful eBirder may also want to provide some ID details. That is because such low filter limits are created by one of two aspects of occurrence: 1) The report date is near either the front end or back end of a migration-abundance taper (see Fig 1 here) and higher numbers might actually involve other species (such as Clay-colored or Brewer's sparrows among Chipping Sparrows) and 2) the species is typically found only in low numbers within the relevant filter region.

The main thrust of this article, though, is points about methods of counting, as reported in species comments by eBirders.

Point 1: Many people seem unaware of the general mathematical concept of "Greatest Possible Error." I learned this in math class in either elementary school or high school, and it has stayed with me throughout my life. Relative to this essay's subject matter, this concept of Greatest Possible Error means that if counting by 10s, then one should allow for an error of 5 for each block of 10. Additionally, that Greatest Possible Error can go in either direction, that is a block of 10 might hold as few as 5 or as many as 15.

Example 1: I am counting Red-winged Blackbirds as they come into a marsh to roost for the night. I have decided that the rate of arrival is low enough that I can easily count the birds in blocks of 10. The arriving flock peters out and I have arrived at 270, counting by 10s. However, I see another few birds approaching and realize that there are only 4. Since 4 is smaller than the Greatest Possible Error of my counting by 10s, I do NOT add those four birds in, either as 4 or as another block of 10. Had there been 6 more birds, I would report a total of 280.

Corollary 1a: When counting by 10s, my final total MUST end in a zero. That is, one cannot count by 10s and report 276, for multiple reasons. First, 6 does not equal 10, nor vice-versa. Second, the possible error, particularly the Greatest Possible Error, in the previous 27 blocks of 10 so swamp those measly 6 additional birds that the 6 are irrelevant. Thus, when counting by 25s, the reported total must be a multiple of 25, such as 175, 350, 6000, etc. When counting by 100s, the result must end in at least two zeroes.

Corollary 1b: When dealing with very large numbers, say >9999, the concept of Significant Digits comes into play. Considering all of the possible errors inherent in arriving at a figure of 15,017, there is no good reason to report those last 17 birds. By reporting those 17, one is entering the realm of False Precision.

Point 2: A count is a count is a count. A count is neither conservative nor liberal. If one reports on a count, either by 1s or 5s or 10s or 37s, it is simply a count. It is understood that mistakes are made during counting and that the possible sources of counting mistakes are legion. No modifiers are needed. Additionally, unless one specifies the size of the counting block, a "count," whether "conservative" or not, is assumed to be by 1s, thus is unlikely to end in zero (1-in-10 chance; though see next sentence) and really unlikely to end in two zeroes (1-in-100 chance) . There are caveats about probability when counting, as there is actually a much larger chance than 10% of a count of 1 for a number of reasons, but once one is past those first few birds, those estimates in parentheses, above, are reasonably accurate.

Example 2: In my experience in Colorado, the most difficult flocks to count are large, dense flocks of American White Pelicans. Despite that I have learned over the years that "counts" of such flocks are invariably lower than the number of birds present, I still find it impossible to arrive at an accurate count until the birds spread out or leave in such a manner that I can get a better count. However, unless the situation changes to allow a more-accurate count, I report the number that I counted, knowing full well that it is probably low. I report such, as I can justify that number; I know it to be at least the minimum number of birds present. That probably-low count is NOT a "conservative count," as I counted each apparent separate individual that I could detect. Who knows, my count might be bang on, so, again, it is not a "conservative count," it is simply a count by 1s (or 1x1 -- "one by one" -- in Van Remsen parlance).

Corollary 2: As an eBird reviewer, I have seen many estimates of American White Pelican numbers that were low or crazily low, sometimes accompanied by photos that prove that the estimate was low. This happens frequently in late summer and fall when the species masses in large numbers at particular water bodies on Colorado's plains. In fact, reported counts of American White Pelicans at places such as Jackson Reservoir, Morgan County, can differ by an order of magnitude, that is 10x larger or 1/10 the number (and don't get me started about the illogicality of the phrase "10x smaller") -- on the same day! At approximately the same time!

The take-home message of this essay is that care should be used in counting and in reporting of numbers of birds.