There was a standard-sized Bor, and standard-sized barrels, pots, and cups. As we explained in the Daf-Background, a barrel held half of the water in a Bor. A pot held a third of the water in a Bor. A cup held a fourth of the water in the Bor. That just happens to be the sizes of those containers, and consequently the amount that the recipient receives depends on that amount.

Here is what we wrote in the Daf-Background:

3a) [line 9] L'CHAVIS - [give a portion of the water in this pit to so-and-so] for his barrel (half of the water in a standard sized pit will fill a barrel; in our case, the doubt is whether the owner of the pit wanted to give a minimal amount of water to the recipient, or he wanted to give enough to fill up half ("Chelek") of the barrel)

b) [line 10] LI'KEDEIRAH - [give a portion of the water in this pit to so-and-so] for his pot (a third of the water in a standard sized pit will fill a pot; in our case, the doubt is whether the owner of the pit wanted to give a minimal amount of water to the recipient, or he wanted to give enough to fill up half ("Chelek") of the pot)

c) [line 10] LI'TAFI'ACH - [give a portion of the water in this pit to so-and-so] for his pitcher (a fourth of the water in a standard sized pit will fill a pitcher; in our case, the doubt is whether the owner of the pit wanted to give a minimal amount of water to the recipient, or he wanted to give enough to fill up half ("Chelek") of the pitcher)

Y. Shaw