Hamming distance in XOR decryption

Question

I've been working on cryptopals 1.6, breaking XOR, and have got it working. I found this answer that explains why hamming distance works, and after some consideration I believe I'm starting to understand it.

One thing that I stumbled on was key size estimation, step 3. I finally found a write-up:

fn score_keysize(keysize, bytes) {
  let block1 = bytes.getblock(size=keysize)
  let block2 = bytes.getblock(offset=keysize, size=keysize)
  let block3 = bytes.getblock(offset=keysize*2, size=keysize)
  let block4 = bytes.getblock(offset=keysize*3, size=keysize)
  let hamming = hamming(a,b) + hamming(b,c) + hamming(c,d)
  return hamming / 3
}

And this works. I tried a variant but didn't even get nearly as good results. Almost all of my attempts, with some variance, got a lower score the larger the key became, this included.

fn score_keysize(keysize, bytes) {
  let block1 = bytes.getblock(size=keysize)
  let block2 = bytes.getblock(offset=keysize, size=keysize)
  let block3 = bytes.getblock(offset=keysize*2, size=keysize)
  let block4 = bytes.getblock(offset=keysize*3, size=keysize)
  let hamming = hamming(a,b) + hamming(c,d)
  return hamming / 2
}

Could someone explain why that's so much worse? Or is it dependent on the text?