Who Was Osborne Reynolds? What Was He Modeling?
In my research I came across the work of Osborne Reynolds, a 19th century English physicist and engineer whose area of interest was “turbulence” (fluid mechanics). In 1883 Reynolds, by experimenting with pipes of varying sizes, was able to come up with a number, (now known as the “Reynolds number”) that tells engineers when a fluid system will reach turbulence.
The Reynolds number is calculated by multiplying together several variables including the diameter of the pipe, the velocity of flow, the mass of the fluid, and the fluid’s viscosity. Reynolds showed that when that magic number is reached, the flow through the pipe becomes turbulent (i.e. becomes erratic).
So, what does this have to do with horse racing? Plenty. Especially if you are a modeler. Suppose you are modeling 6 furlong races at Hollywood Park for 3 factors:
| The Model | EP | SP | Class |
| race 1 | 1 | 2 | 2 |
| race 2 | 2 | 1 | 3 |
| race 3 | 3 | 1 | 1 |
| race 4 | 3 | 4 | 1 |
| race 5 | 2 | 3 | 1 |
| race 6 | 4 | 1 | 1 |
| race 7 | 1 | 1 | 1 |
| race 8 | 1 | 1 | 5 |
| Sum | 17 | 14 | 15 |
| Worst | 4 | 4 | 5 |
How would you interpret this model? This is the kind of model that one would call “loose.” There is no single factor that can be used to eliminate down to a playable number of horses, though when we sum the columns we can come up with “something.”
Let’s create some “Reynolds number” columns for each 2-factor combination. Thus, the EPxSP for race 4 is 12 because 3 x 4 =12 (i.e. EP x SP = EPxSP).
| The Model | EP | SP | Class | EPxSP | EPxCl | SPxCL |
| race 1 | 1 | 2 | 2 | 2 | 2 | 4 |
| race 2 | 2 | 1 | 3 | 2 | 6 | 3 |
| race 3 | 3 | 1 | 1 | 3 | 3 | 1 |
| race 4 | 3 | 4 | 1 | 12 | 3 | 4 |
| race 5 | 2 | 3 | 1 | 6 | 2 | 3 |
| race 6 | 4 | 1 | 1 | 4 | 4 | 1 |
| race 7 | 1 | 1 | 1 | 1 | 1 | 1 |
| race 8 | 1 | 1 | 5 | 1 | 5 | 5 |
| Sum | 17 | 14 | 15 | 31 | 26 | 22 |
| Worst | 4 | 4 | 5 | 12 | 6 | 5 |
Now when we look at the worst, it makes more sense. SP x CL is certainly the most powerful column, as no winner has had an SPxCL Reynolds of worse than 5! It also explains why, if class is so important, a horse with a Class rank of 5 could win (race 8). He made it up by having 1’s in both of the other two columns!
If we were to describe the profile of a winner in these 8 races, we could say:
1. Must have a 4 or less in EP.
2. Must have a 4 or less in SP.
3. Must have an SPxCL of 5 or less.
4. Must have an EpxSP of 6 or less.
| The Race | EP | SP | Class | EpxSP | EpxCl | SPxCl | Elim |
| Horse #1 | 1 | 3 | 3 | 3 | 3 | 9 | X |
| Horse #2 | 3 | 2 | 2 | 6 | 6 | 4 | |
| Horse #3 | 2 | 4 | 4 | 8 | 8 | 16 | X |
| Horse #4 | 4 | 5 | 1 | 20 | 4 | 5 | X |
| Horse #5 | 5 | 1 | 5 | 5 | 25 | 5 | X |
Applying rule #1 eliminates #5, leaving: #1 #2 #3 #4 (not enough EP)
Applying rule #2 eliminates #4, leaving: #1 #2 #3 (not enough SP)
Applying rule #3 eliminates #1 & #3, leaving: #2 (not enough SP and CL in combination)
The Reynolds number will also help when you have a model that is a little more obvious. Let’s add one more column: EpxSPxCL.
| The Model | EP | SP | Class | EPxSP | EPxCl | SPxCL | EPxSPxCL |
| race 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| race 2 | 2 | 1 | 3 | 2 | 6 | 3 | 6 |
| race 3 | 3 | 1 | 1 | 3 | 3 | 1 | 3 |
| race 4 | 3 | 4 | 1 | 12 | 3 | 4 | 12 |
| race 5 | 2 | 3 | 1 | 6 | 2 | 3 | 6 |
| race 6 | 4 | 1 | 1 | 4 | 4 | 1 | 4 |
| race 7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| race 8 | 1 | 1 | 5 | 1 | 5 | 5 | 5 |
| Sum | 17 | 14 | 15 | 31 | 26 | 22 | |
| Worst | 4 | 4 | 5 | 12 | 6 | 5 | 12 |
The rules for this race are:
1. Must have 3 or less in SP
2. Must have 3 or less in CL.
3. Must have 4 or less in SPxCL.
4. Must have 8 or less in EpxSPxCL.
| The Race | EP | SP | Class | EPxSP | EPxCl | SPxCL | EPxSPxCL | Elim |
| horse #1 | 1 | 1 | 3 | 1 | 3 | 3 | 3 | |
| horse #2 | 3 | 2 | 2 | 6 | 6 | 4 | 12 | x |
| horse #3 | 2 | 4 | 4 | 8 | 8 | 16 | 32 | x |
| horse #4 | 4 | 5 | 1 | 20 | 4 | 5 | 20 | x |
| horse #5 | 5 | 3 | 5 | 15 | 25 | 15 | 75 | x |
Once again, with conventional modeling we would not have been able to eliminate as many horses. The first two steps would have easily gotten us down to two, but the model clearly says that a horse must have enough of everything (i.e. EPxSPxCL) to qualify.
Think about that minimum in rule #4. How does a horse get 8 or less?
| 1 x 1 x 1=1 | 1 x 1 x 4=4 | 1 x 2 x 3=6 |
| 1 x 1 x 2=2 | 1 x 2 x 2=4 | 1 x 2 x 4=8 |
| 1 x 1 x 3=3 | 1 x 1 x 5=5 | 2 x 2 x 2=8 |
Let’s work up a set of descriptions.
– If a horse has 2 or more 1’s, he’s in.
– If he has only a single 1, he must have no worse than 2 x 3 in the other two slots.
– If he has no 1’s, he must be all 2’s.
– All other horses are out!
We’ll revisit Osborne Reynolds and his contributions to handicapping at a later time.
Joe Garchinsky says
Please explain what EP, Sp, and Class are and how they are determined.
Joe G.
Dave Schwartz says
“EP” stands for “Early Pace.” Essentially, it is the speed or velocity rating to the 2nd call (i.e. 4f marker in a 6f race).
“SP” stands for “Sustained Pace.” Essentially, it is EP+SR, double-weighted on the “SR.”
“SR” stands for “Stretch Run” and represents the speed or velocity from the EP call to the finish line (i.e. the last 2f in a 6f race).
“Class” is a more complex formula. It is comprised of Earnings-per-Start (EPS), Average Purse Value (APV) and a consistency rating.
All of these are, of course, irrelevant to the discussion above. The rating columns could be anything.