Not sure how to identify who holds what but my understanding is as we head into expiry there will an imbalance between ITM puts and calls, obviously as the market rallies over the weeks into expiry an excess of ITM calls will accumulate, depending on who holds what the selling off of these calls into expiry will force the MM's to hedge by selling the underlying, this creates a down force. Opposite with puts during a downturn.
Sorry rushed reply and based on hearsay, may be correct/may not, but I hope it makes sense.