COPE has been discussed at length on the various Facebook pension advice pages that I am on, when you contracted out of SERPS either you and your employer paid reduced NI, or you paid full NI but some was diverted into your company/works pension either way you paid less into the state system.
Under the old scheme contracting out did not reduce the old basic, you still got that but not the second state pension for the period you were contracted out for, which is why a lot of people may not have realised they had been contracted out as they were receiving the basic state pension they were expecting.
However it does affect the New State Pension for the following reason.
Everyone who had a NI history pre 6th April was given a starting amount, to reach that amount the Government used 2 calculations, what you would have got if the rules had not changed, basic plus SERPS, less time contracted out and other variants such as paying the married woman's stamp, and what you would have got if the new rules has been in place all your working life, flat pension with no SERPS, (therefore no contracting out) and you got the higher of the 2.
Your starting amount could be higher than the NSP in which case you get a protected payment taking you over the NSP, but any NI/credits paid after 6th April 2016 did not increase your pension or if you were contracted out for a longer period it would be lower, therefore any NI/Credits increased that amount until you either reached the NSP amount or you reached state pension age which ever came sooner, if you did not have enough years between your starting amount and your state pension age unless you buy extra NI you would not get the NSP.
Although people say disregard the COPE on a forecast it is a useful thing to know, when people post on our pages saying they have paid 40 odd years but their forecast says they will not get the full NSP unless they pay in more the first thing we say is 35 years is not relevant for anybody with a NI history pre 2016/2017 it can be anything from 28 to 51 years and the second thing we ask is does their forecast show a COPE (Contracted Out Pension Equivalent) if so we can tell them they have a works/company pension that will pay at least the COPE amount.