Estimate has its dictionary meaning
Unless a contract re-defines estimate to mean something else, estimate in a contract has its dictionary meaning:
- an approximate calculation or judgement of the value, number, quantity, or extent of something.
Usually, the estimate is based on normal situations and does not account for any special circumstances. In the case of delivery, it considers the normal shipping time based on distance and common handling times. So "3 [business] days" assumes that they get the parcel to the shipper on the next day (1), assume one night for handling, a day for overland transport (2), and one day to be delivered (3). But that expects one or maybe two sorting centers.
But at times things go wrong, and the estimate can't be held - and no, you do not count percentages as you did for the shipper. Carefully read the Terms and Conditions if there is even a claim against the handler.
Examples
Postal Services
From my own experience, I know that parcels can go through about half a dozen before they get to an international shipping center at the airport, and then once landed in Europe may spend up to a week in a container waiting for customs.
But delays also happen because of how automatic sorting happens, and I have seen the belts in action. Assume a small parcel is packaged in such a fashion that it is slippery on the outside and has all its weight on one end. It ends on the tray belt with the weight on the outside, in the first curve shifts over, and slips off the transport belt, ending in the overhead netting. Those nettings are only cleaned out between once a week and once a month, depending on the parcel center's load (and avilability of someone that has the clearing to climb up there), number of parcels ending there, and the expected delay other parcels will experience by having to shut down the whole parcel transport belt just to get those dropped parcels. And that sort of delay is covered in the T&C of USPS/FedEx/UPS/DHL and most other international postal companies.
Sometimes parcels slip onto the wrong ramp and take a few extra detours over other handling centers, which can take about 2-3 days per parcel handling facility, as they need to get re-identified and re-sorted in those other facilities manually. And that also is covered in the T&C.
Other cases of delay happen because the parcel is tagged not handleable by belt and has to be manually handled, usually adding up to 2 business days per sorting center the parcel goes through.
Now, how are estimated delivery times and thus average delays calculated for the postal service? Not per individual parcel but per bunch of parcels. If one out of 1000 parcels took 30 days instead of any other taking 3 days, the estimated time of shipping is 3.027 days. If 1 in 100 is delayed to 30 days (and the other 99 take 3 days), it's 3.27, and if 1 in 10 is delayed to 30 days, it's 5.7 days.
International Shipping
For another example from May 2021, a ship blocked the Suez Canal for one week. Deliveries however were not just delayed by one week. The containers on the ship that blocked the Canal could only be unloaded in late July, more than 100 days late. Compensation was due to the owners of cargo on the ship, under the transport terms and conditions.