How can I quantify the number of swaps required for insertion sort? Based on the Wikipedia implementation of insertion sort:

Given an input array $A$:

for i ← 1 to length(A)
    j ← i
    while j &gt; 0 and A[j-1] &gt; A[j]
        swap A[j] and A[j-1]
        j ← j - 1


is there a way to quantify how many swaps are needed to sort the input list? It's $O(n^2)$, but I want a more precise bound. A perfectly sorted array clearly needs no swaps (so insertion sort is $\Omega(n)$), while a completely reversed array requires something on the order of $n^2$ swaps, but how do we quantify the number of swaps?
It is a classic exercise to relate the running time of insertion sort to the number of inversions in the input. An inversion is a pair of indices $i &lt; j$ such that $A[i] &gt; A[j]$. The number of comparisons made by insertion sort when there are $I$ inversions is always between $I$ and $I+n-1$.