Cameron is helping Obama win over voters. I don't know whether it will be Cameron or the hot dog or the basketball match that will gain Obama more credibility. I suspect that to the Americans they probably will be expecting Tony Blair to appear as the British PM so will say,'who's that guy?', when they see Cameron. The hot dog and match will probably make Obama more electable in Ohio.
What does Cameron get out of it? A ride in Air Force One to Ohio from Washington and to be photographed on US home ground with Obama looking like best pals. Big Deal! What matters to us in the UK is that Cameron and Obama sort out Syria and agree on a EU/US trade deal.