I think I can make some tentative statements about the $1 TOA based on all the information I have. We are told there were three print runs. These are best considered as orders from the Emporium, and even then these were delivered in batches. The first run had no selvedge text, the second had text and logo, as did the third. However that run had the falling man icon in the logo rotated 180 degrees so that he is falling compared to other icons. Bath perforations only apply to some stamps from the first print run, and the four ‘new’ sports only appear with the third run.
Often selvedge is left attached to stamps, but is limited help. The absence of text in the four corner stamps (including the splash sport in top left) of a sheet places the stamp as part of the first print run (A, B, C, and D on the image). Text or logo means second or third print run, but only two will allow them to be assigned to one of these runs by the presence of the falling man icon in the logo (E and F).

Between batches delivered to the shop, different print settings, different printing machines and different printing companies were used. This was in order to improve speed of printing, improve print resolution and to reduce costs. This has resulted in small shade variations during the lifetime of the stamps, and different patterns at high magnification of both dot resolution and colour registration caused by different settings, machines used and direction of sheet printing

I can put forward a tentative and simplified version of the print runs and batches, showing how there is are overlaps of printing runs and delivery runs, print runs and perforating, and so on, but first off you can narrow down which of the print runs certain stamps come from.

Print run	First		Second	Third
Logo icon	None
Margin text	None		yes on end stamps	yes on end stamps
Perfs	Bath	Wincanton

But then taking into consideration the fact that the ‘new’ sports only appeared on the third run, then it is possible to match ‘old’ sports and common stamps to those. In fact the third run was delivered in two batches, early in 2004 and again in the summer. This is borne out by there being two shades for the ‘new’ sports. So now, if you have sufficient spares of course, you can have examples of all new and old sport plus a common for both of those two deliveries.

The Weathervane, Falling Man 2 Birds, Falling Man 1 Bird
and Bigger Splash sports in matching mid green shade
and a more yellowish shade

Then most likely any original Splash sport with marginal text is from the second print run, and any without from the first print run. Now you can match shades of the original Falling Man stamps and commons to these. Any other stamps with marginal text or logo, that are not accounted for as a third print run stamp, will likely be second print run too. You may be able to match first print run shades too using any stamps with a side margin that is missing text. There is quite a range of shades out there, so it’s highly unlikely any of us will get a complete set of both sports and a common for each shade. But live long enough and you complete some of them!