At the start of the synod of the Old Catholic diocese on Thursday, Ring said, according to the speech manuscript, that he had always assumed that it could not have been any different in the Old Catholic Church than in other churches.
He sometimes hears the "naive thesis" in his church that there is no abuse there because Old Catholic priests are allowed to marry.
"Our Protestant brothers and sisters reassured themselves with this thesis - until their ForuM study was on the table," says Ring.
He knows of two cases in his diocese since the Second World War. There have also been two allegations of abuse against clergy during his time in office.
Ring is sceptical about a separate abuse study for the Old Catholic diocese, "because I don't believe that we will gain any knowledge that goes beyond the current findings, namely that it was no different here".
He does not expect any significant new findings that could be relevant for prevention.
The first case involved a priest who was sentenced to probation in the 1950s. There are also reports of assaults on altar boys.
The second case concerns a former vicar who was sentenced to prison in 1950 for "unnatural fornication".
The youngest victim is said to have been ten or eleven years old. The criminal judgement lists a total of six victims.
Following his arrest, the priest's licence to exercise spiritual functions was withdrawn. He had also left the ministry of the Old Catholic Church.
Secularisation also affects Old Catholics
In his report, the bishop went on to discuss the handling of secularisation.
In the Old Catholic Church, too, church ties are weakening. Ring also sees no great potential for the Old Catholic Church among those who have left the Roman Catholic and Protestant churches: "Most of those who leave have long since lost God, if they were ever able to do anything with it at all."
Instead, it is important for his church to accompany people on their journey of life and faith. "In doing so, we have to accept that we are often enough 'only' partners in stages of life," said the bishop.
The Synod of the Diocese of Old Catholics is the highest decision-making body of the Old Catholic Church in Germany.
It was meeting from Thursday to Sunday in Mainz.
One of the items on the agenda was the discussion of Old Catholic identity and how to deal with church members who are members of a secured right-wing extremist party or organisation. One motion proposed withdrawing the passive synodal rights of such members.
The Old Catholic Church in Germany was founded in the 1870s in opposition to the resolutions of the First Vatican Council (1869-1870) on infallibility and the primacy of the Pope's jurisdiction.
The German diocese has just under 16,000 members in 60 parishes.
Matthias Ring has headed the diocese as its tenth bishop since 2009.
The church order of the Old Catholic Church is episcopal-synodal: the bishop elected by the synod leads the church together with a synodal council made up of clergy and laity.