Andrew Beyer was the racing columnist for the Washington Post. He invented a measure, named after him, that permits the comparison of horses from race-to-race, track-to-track. The DRF publishes a Beyer Speed Figure for every horse in every race. The inherent speed of the track and the speed of the race, and the speed of the horse are the main components of the number. In the example from the DRF, Farnum Alley ran a 79 and an 80 in the last two races. (The first race, with a 53, reflected his bad start, not his speed.) If all other things were equal (a huge assumption), this horse should regularly outrun a horse with Beyers in the 60's range. Unless his Beyers go up with his next races, he will lose to a horse regularly running Beyers in the 90's and high 80's. Over time, horseplayers, race secretaries and others who see horses often will know how the range of Beyer scores fits with the class of a race, whether a lowly claiming race or a fancy stakes race. The best stakes horses are up around 120 range. The good allowance or low stakes horses usually come in around 100. Bottom level claimers typically run in the 50's and 60's.
The typical use of this measure is to figure out which horses are just not fast enough to win a given race, thereby releasing the handicapper's time and attention to be spent on the other horses. Beyers are less useful for telling the handicapper who will win the next race. There are a couple of reasons for this. First, many other elements determine the race outcome besides the native speed of one horse. (A race with one speed horse in it and weak competition is probably the easiest race of all to handicap, but it does not happen very often. Usually the race secretary sees to that.) Second, Beyer Speed Figures are not determinative of race outcomes because most horses do not run consistently or in the same way, race after race.
Another famous student of horses, Len Ragozin, invented the term "bounce" to describe the cyclical race behavior of horses. Most horses will show a consistency or pattern in their Beyers, and then for some reason, there will be a race with a much lower number. This is a "bounce." Then, maybe there's a layoff, maybe not. The horse starts another set of races, and the Beyer Speed Figures improve. They may even go up higher than before. Then, in one race, there may be another "bounce." Good handicappers say they are able to perceive the cyclical behavior (or not) of any given horse and can judge (more or less) when a bounce is about to take place. This is a sophisticated use of the Beyers Speed Figures. The "Ragozin Sheets" attempt to take this to a much higher level.
It should also be noted that young horses, like Farnum Alley in the example above, have not really carved a niche for themselves, and their Beyer Speed Figures can vary quite a bit before establishing the "norm" for a more mature horse.