Type vs degree of a polarized abelian variety

Question

Let $(A,L)$ be a polarized abelian variety. I know that the degree of the polarization is the Euler characteristic of $L$, so that $d = \chi(L) = \dim H^0(A,L)$ since $L$ is ample.

I've read in a lot of papers the sentence

Let $(A,L)$ be a polarized abelian variety of dimension $g$ and of type $(d_1, \dots, d_g)$, etc.

I've seen the formal definition of type in Birkenhake-Lange book, but I cannot relate this definition with the degree of a polarization, although I am pretty sure they are related.

Indeed, when a statement says "type $(1,1,\dots,1,d)$", I think of "degree $d$", but it is just an intuition.

So my question is:

what is exactly a type of an abelian variety? How do we relate type and degree?

Thanks for help!

Note: I have already posted this question on MathOverflow, but maybe this is a better place to post it.