General aviation pilot reported causing an NMAC when they turned to avoid other aircraft.

Narrative

I was enroute to ZZZ from ZZZ1. While on a heading of about 160 at approximately 2600 feet; I observed a flight of three aircraft on a heading of approximately 255; on my EFIS screen via ADS-B. I believed they were approximately 3 miles away; when they were actually closer to one mile away. I switched my radios over from the ZZZ1 CTAF to the ZZZ CTAF. I knew there was an event taking place at ZZZ; and I suspected these aircraft were the flight participants; based on their track and proximity to ZZZ. While visually scanning the sky for the other aircraft; I anticipated they would take their normal route; which I was previously familiar with. I could see that our paths were converging; so I altered course to a heading of approximately 190 and began descending. I chose this course due to my anticipation of the aircraft making a southbound turn to follow their normal route. As I continued my visual scan; I finally was able to locate one of the aircraft which was approximately 50 feet above; and 200 feet horizontally away from me; and it was making a southbound turn. I could see that the other aircraft was a Cessna; likely a 172. I got on the radio and told the pilot of the other aircraft that the close call was likely my fault; and apologized to him. I ultimately turned back toward ZZZ and landed without further incident. I do not know who the other pilot was. I debriefed the incident in my head for a few days; and I identified some things I could've done to prevent this incident.I misinterpreted the distance on my ADS-B rings. I believed it was ranged out to a further distance; when in reality; it was zoomed in closer than I thought. Basically the aircraft appeared to be twice as far away in my mind; than they actually were. I should have been more cognizant of my equipment. My visual scan was inadequate. I should've been more focused on scanning outside the plane; and less on the ADS-B screen. I should've altered course much sooner; and to a greater degree. I could've switched frequencies sooner; and communicated on the radio earlier. I waited too long to switch from the ZZZ1 CTAF to the ZZZ CTAF; especially since the two airports are so close. I should have announced my position and intentions on the ZZZ CTAF at the recommended 10 mile distance; not the 8 miles at which I actually had planned on.