If you are the travel manager for a large enterprise which books a vast amount of travel, statistical information can allow you to save a lot of money.

For any one flight on any given day, there is no real methodology. Perhaps it is a flight which routinely has its lower fare buckets (without AP requirements) open until close to flight time, but on your chosen date there is a school trip with 30 passengers. Perhaps they will cancel.

UA (as well as other carriers) spends an astronomical amount of money on RM/IM software and human analysis because pricing goes straight to the bottom line. You can't match it.