WASHINGTON — Officially, President Barack Obama and British Prime Minister David Cameron are just going to Dayton to watch a college basketball game. No politics is the official White House line.

But nearly eight months before the presidential election, it may be hard to convince anyone that Obama’s high-profile trip Tuesday to a crucial electoral state doesn’t involve at least a tiny measure of politics.

“Everything the president does this year is political,’’ said Robert T. Bennett, former chairman of the Ohio Republican Party.

Mary Anne Sharkey, a nonpartisan political consultant who grew up in Dayton, said, “Coming to Dayton is a good move on his part,’’ pointing that the November election will be “Ohio, Ohio, Ohio. He’s got to have Ohio. The race comes through Ohio. It always does.’’

“It certainly will help him in the Dayton area,’’ Sharkey said. “They tend to remember things like a presidential visit.’’

Obama and Cameron will fly into Dayton on Tuesday to watch a NCAA First Four game at the 13,000-seat University of Dayton Arena. The Dayton event is the first round of the college basketball tournament called March Madness.

Obama loves hoops so much he’s appeared on ESPN to talk about the brackets. He is a passionate fan of the Chicago Bulls and is known for playing pick-up games.

Both Democrats and Republicans said Obama can only help himself in Ohio by appearing in an arena surrounded by thousands of basketball fans. (Unless, of course, his visit causes endless traffic tie-ups). Combined with the visit to Ohio this week by Vice President Joe Biden, it’s yet another sign that Obama intends to vigorously contest Ohio. Romney narrowly won the March Republican primary.

“It is not unaccustomed for the out party to find politics in everything the in- party’s president is doing in an election year,’’ said J. Kenneth Blackwell, the former GOP state treasurer. “So my saying there is some politics involved in this is a ‘dog bites man’ story.’’

The reason Ohio is critical is obvious. No Republican has ever won the White House without carrying Ohio and the last Democrat to win the presidency while losing Ohio was John F. Kennedy in 1960.

Obama won the state four years ago against Republican presidential nominee John McCain. But Obama also carried Virginia, Florida, North Carolina and Indiana — states that normally trend toward the Republican nominee. If Obama loses those four states in November, Ohio and its 18 electoral votes become even more crucial.

“Ohio is always important,’’ said former Republican congressman David Hobson of Springfield. “It’s particularly important because (Obama) is not going to get Florida.’’

It will be back to business on Wednesday when Obama hosts a state dinner for Cameron, the first Conservative prime minister since John Major in 1997.