Small aircraft Flight Instructor reported observing a near miss between two aircraft in the traffic pattern at a non-towered airport in VMC. Aircraft Z improperly entered the pattern; causing Aircraft Y to immediately maneuver away to avoid the aircraft.

Narrative

Day 0 beginning approximately XA:05; while in the pattern at ZZZ flying Aircraft X with a pre-solo private pilot student; I heard and observed the following: NMAC Aircraft Y and Aircraft Z. The pattern was busy with four aircraft in left-closed traffic along with a couple of itinerant arrivals. There were several aircraft awaiting departure. I was on downwind; approximately 1 1/2 miles behind Aircraft Y when this began. I observed the targets - Aircraft Y; downwind and Aircraft Z; base - on ADS-B; converging; and with 100 ft. separation. I looked up to see Aircraft Y take evasive action.After the incident; I looked up Aircraft Z's flight track data and noted he made a continuous descent from cruise altitude onto the base leg and final. A perfect set-up with a low-wing above and a high-wing beneath. This pilot's lack of situational awareness; improper radio procedures - never stated type aircraft - and total disregard for proper pattern entry at a non-towered airport could have resulted in a mid-air collision.