Thanks impart to Newton, we can calculate the gravitational force between large objects (like planets) with a formula.
F = G (m1*m2)/r^2.
Because we are referencing the same masses (the moon and the Earth), M1 and M2, we can assign any value to them (greater than 1). Because G is constant, we can assign any value to it (less than 1). (Checkout the Newton website for why we need values greater or less than 1.) Let’s make it easy and set M1 and M2 each equal to 1, and set G equal to 0.1.
The “lunar apogee” is when the moon is furthest from the Earth, and the “lunar perigee” is when the moon is closest to the earth. Respectively each is 254k miles and 220k miles.
Lunar apogee F: F = 0.1(1*1)/254k^2 = 1.55^-12
Lunar perigee F: F = 0.1(1*1)/220k^2 = 2.06^-12
Difference in apogee/perigee = 2.06/1.55 -1 = 32.9%
Because the moon orbit is elliptical, the 32.9% is the lower bound for the in difference in gravitational pulling strength of the apogee vs. perigee (if the orbit was exactly circular, then the difference in apogee vs. perigee would be exactly32.9%). Hence, the perigee pulls "on average" an additional gravitational force greater than 15% on the Earth (think of it like +32.9%/2), and +15% in my opinion is relevant (had it been much lower like 1%, then I would have concluded the Super Moon was irrelevant to the Japanese quake).
With a little math and a degree of faith that an additional +15% moon-gravitational force is relevant, we can conclude that the "Super Moon" helped create the earthquake in Japan.