Where does the Each Way Win odds divisor come from?

[hudbud]

Trying to get my head around this and hoping someone can help explain. For the each way market where the does the win price divisor for the place part of the bet come from i.e the 1/4 and 1/5 ?

Let's say for a handicap race with 13 runners, the number of places will be 3 and the price divisor of the win odds for the place part will be 1/4. I understand that the divisor "works" but intuitively in my head for an each way market 1/3 makes sense considering there are 3 places. Just pulled this off wiki for the race type breakdown and each way place odds:

• Handicaps of more than 15 runners | odds: 1/4 | places: 4

• Handicaps of 12-15 runners | odds: 1/4 | places: 3

• All other races of more than 7 runners | odds: 1/5 | places: 3

• All other races of 5-7 runners | odds: 1/4 | places: 2

Is there a mathematical explanation anywhere to explain where this comes from or is it just general rules of thumb bookies have landed on with to calculate the place odds in a each way bet?

Does this also mean at say for a Handicap race of 12 runners in comparison to a handicap race of 15 runners, there is more value to be had backing a runner each way with the same odds in the 12 runner race in comparison to the 15 runner race as the place odds are the same?

Thanks