Grumman AA1B pilot was made aware post flight that they were involved in an NMAC when entering the traffic pattern at a non-towered airport.

Narrative

I approached ZZZ from the southwest; landing on Runway XX. I stated my intention to land on Runway XX on CTAF; but I mistakenly stated that I would enter the left downwind on the 45. Another pilot; a flight of two aerobic airplanes questioned my call. I clarified that I would overfly the runway at midfield at pattern altitude and join the downwind leg for Runway XX. Aside from the flight of two aerobatic airplanes; I heard a call from a Cessna that was 3 miles out. The flight of two aerobatic airplanes' lead aircraft pilot was very active on CTAF explaining in great detail how they were approaching the airport for landing and how they would break and circle to land. I was trying to understand their position and intentions as I overflew ZZZ. I announced on CTAF that I was at midfield and would be joining the left downwind for Runway XX. I did not hear any responses.I turned left to join the left downwind and landed normally. While I was tying down my airplane; the Lead Pilot from the flight of two aerobatic airplanes drove up and introduced himself. He informed me that I had been party to a near miss on the downwind leg. I apparently cut off another airplane and that airplane descended below my flight path. I never saw another airplane in the pattern. I had my iPad mini running Garmin Pilot in split screen mode with traffic on the right side. I never saw traffic approaching my flight path either on the iPad or visually. I did not properly determine that the downwind leg to my right was clear before I joined the downwind leg. I also allowed the lead pilot in the two aircraft flight distract me with the extensive description of unusual pattern activity. Further; I did not have the traffic screen zoomed in sufficiently to discern converging traffic.To avoid any similar issue in the future; I will do a far better job of visually clearing legs in any pattern for converging traffic and carry out more deliberate clearing turns prior to any substantial heading change. Additionally; I will attempt to avoid allowing radio chatter distract me from building a complete mental picture of my environment.