Ever since the first televised presidential debates in the US more than 60 years ago the received wisdom has been that TV debates are important hurdles, but that they do not shift a lot of votes. However, the first Conservative leadership debate on Friday evening felt as though it could significantly reshape the contest to succeed Boris Johnson. In reality, the Channel 4 debate was an insight into two different arguments. The big one is the race to be Britain’s next prime minister. That battle is mainly between the three frontrunners in the first two rounds of voting this week: Rishi Sunak; Penny Mordaunt; and Liz Truss. In that respect, Sunak clearly had the best of the evening, with Mordaunt failing to justify her strong showing in the early rounds, and Truss struggling to appeal beyond the right wing of the party. Sunak performed well. He showed no nerves, was better informed, more reasoned and more practical than his rivals. He conveyed the seniority of the position he held in government until last week. But he pitched to the general population, not to the Tory party. His attacks on wishful thinking and easy promises, and his refusal to disavow his tax and spending increases will not have gone down well with many of those whose votes will decide the outcome. Mordaunt came into the debate on a roll. She is ahead in the polls among members and she has surged into second place in the first two rounds of voting among MPs. But she failed to justify her billing. She sounded vague and broad brush. She made few memorable points. She looked nervous. If this debate is remembered for anything it could be as the moment when the Mordaunt candidacy hit rough water. She will have to do very much better in the two other debates. The evening was important for Truss. She needed to consolidate her position as the candidate of the right, and to wrest the initiative away from Mordaunt. She did the first – partly by wearing a pussy cat bow blouse of the kind favoured by Margaret Thatcher. But it was Sunak, not Truss, who did the second. Truss gave an insistent performance, repeating herself a lot, but she may benefit from Mordaunt’s failure to seize her moment. If Truss gets into the final two, she may yet be the winner. The other large issue of the evening was what it told us more generally about what the post-Johnson Conservative party is going to look like. Here, all five candidates had things to contribute. The best showings, though, belonged to Sunak and to the two outsiders, Kemi Badenoch and Tom Tugendhat. Sunak’s insistence that governments have to make difficult choices was a repudiation of Johnson’s cakeism. Badenoch and Tugendhat were able to speak more freely and were able to sound more authentic as a result. Both of them did their prospects of senior jobs in the next Conservative government no harm at all. The debate was a useful reminder that there is more to the Tory party than Johnson. It is important to remember who this weekend’s three televised debates are aimed at. The audience that matters is not the general one or those in the studio. It is the audience watching at home with votes – the MPs who will reduce the field to the final two over three rounds of voting at Westminster in the week to come, and the up to 200,000 Tory members who will decide which of the final two will succeed Johnson in early September. On the evidence of the first debate, that person will be Sunak. But there is still a long way to go.