This information is previously contained in several articles in this website. I have condensed the information to make it easier for the reader to find each category. This list has been updated after the 2018 state tournament.
Portsmouth Trojans Composite State Ranking
State Appearances: 3rd
Number of State Tournament Games Played: 3rd
Number of Decades Making the State Tournament: 2nd
Number of State Tournament Games Won: Tied for 4th*
Number of State Championship Games Played: Tied for 5th
Number of Final 4 Wins: Tied for 5th
Number of State Championships Won: Tied for 6th
These rankings include over 800 high schools in Ohio.
Including that Portsmouth is the 8th winningest program of all time, to go along with the above info, one could easily make a case for the Trojans being a top 5 program all time, with only 1 category having PHS ranked lower than 5th.