Caradoc,

for my Beyer-TG comparison I used 100 running lines from the PP's of stakes races which I had handicapped. All the data were part of a matched pair of Beyer and TG ratings given to the same horse for the same race. the 2 sets of data were averaged to get 2 means equivalent to each other. I calculated from the ratio of points assigned for beaten legths at the same distance for both sytems and found that 1 TG point equals 3 Beyer points. Using this ratio brought the TG zero equal to Beyer 101. Any deviations from this point would be counted as a 3 to 1 ratio of Beyers to TG.

For the Timeform - Beyer ratio, I used the Dr. Roman study and a smaller number of my own races to determine that the scale was the same 1/1 ratio for both scales with the only difference being the 15 point higher Timeform standard. Therefore one need only substract 15 from the Timeform rating to get the Beyer. Having done this, in order to get the TG from Timeform, one must first transform the Timeform to Beyer and then convert the Beyer to TG, as given above.
I'm not totally familiar with the methodology used to obtain Timeform ratings except that since European courses vary so much for different races, even at the same track, and the pace can vary so much from race to race that horses are basically compared to their competetors in terms of beaten lengths in the race they ran using the projection method for the most consistent horses that ran an in form race. Jerry could probably give you a more detailed discription of how timeforms are calculated. My personal experience is that they are very skillfully crafted and accurate.

I'm falling asleep as I write this due to the lateness of the hour and hope i was able to answer your questions. If not, feel free to ask me for any further clarification you may need tomorrow.

Good night for now,
Bob