How do I improve this timsort algorithm in python?

Question

I am trying to implement a timsort algorithm in Python. I was wondering how I could implement the following into my algorithm:

1. Binary insertion sort instead of regular insertion sort.
2. Galloping while merging Here is my current code:

def calcMinRun(n):
    r = 0
    while n >= 32:
        r |= n & 1
        n >>= 1
    return n + r

def insertion(arr, left, right):
    for i in range(left + 1, right + 1):
        j = i
        while j > left and arr[j] < arr[j - 1]:
            arr[j], arr[j - 1] = arr[j - 1], arr[j]
            j -= 1

def timSort(arr):
    n = len(arr)
    minRun = calcMinRun(n)
    for start in range(0, n, minRun):
        end = min(start + minRun - 1, n - 1)
        insertion(arr, start, end)
    size = minRun
    while size < n:
        for left in range(0, n, 2 * size):
            mid = min(n - 1, left + size - 1)
            right = min((left + 2 * size - 1), (n - 1))
            if mid < right:
                merge(arr, left, mid, right)
        size = 2 * size
    return arr

def merge(arr, start, mid, end):
    start2 = mid + 1
    if arr[mid] <= arr[start2]:
        return
    while start <= mid and start2 <= end:
        if arr[start] <= arr[start2]:
            start += 1
        else:
            value = arr[start2]
            index = start2
            while index != start:
                arr[index] = arr[index - 1]
                index -= 1
            arr[start] = value
            start += 1
            mid += 1
            start2 += 1

Any help would be appreciated!