How can I make a Lego heroica scale gladiator arena?
Let's assume that the Heroica figures are exactly half the scale of the normal LEGO minifigure.  That would be roughly 1:100.  At that scale, 1 meter would be roughly 0.75 studs long or the height of a standard LEGO brick.

Now let's convert the Coliseum dimensions:


Height: 50 meters  ~ 50 bricks high
Length: 189 meters ~ 142 studs
Width: 156 meters ~ 117 studs


To calculate the real dimensions of this LEGO construction, let's remember that a brick is 9.6mm high and the distance for 1 stud is 8mm (= 1 stud radius + the distance between two studs).

Using these values we get:


Height: 50 bricks = 480mm (~18.9 inches)
Length: 142 studs = 1136mm (~44.7 inches)@
Width: 117 studs = 936mm (~36.9 inches)@


@Those two distances are calculated by multiplying 6.4mm with the number of studs, and then adding 1.6mm for the last little bit of beam left after the last stud.