There’s a compelling logic behind the idea of Arnold Schwarzenegger as a United States senator. But, as he recognized in a Facebook post saying he wouldn’t be making the race, it’s hard to see how he would get there.

Of course, one Facebook post or statement from Arnold that he’s not running doesn’t end anything. This is a man whose words are not to be trusted when it comes to future candidacies. He told everyone he wasn’t running for governor until the very minute on the Tonight Show that he was.

So let’s look at the case for Schwarzenegger as a senator. He’s a former governor whose celebrity brings him a big microphone; that’s vital, because in the anti-Californian and anti-democratic of the United States Senator, a U.S. Senator from California has to speak with the power of 20 senators, just to counteract the advantage smaller states possess in the chamber.

Arnold comes closest to representing the wide swath of California. He’s liberal on social issues and shares the California conviction of climate change’s centrality as an issue. He’s foreign-born, like more than a quarter of the state. He’s a middle of the roader on political reform and infrastructure. But he’s still a Republican with a pro-business outlook.

All these characteristics would make him the best potential anti-Trump senator California could muster. And opposing Trump – a president who has lied about, slandered and sought to delegitimize California – is the heart of the job right now. His Republican affiliation would help there; it’d be nice to have a Californian with access to the GOP caucus. It also is significant that Schwarzenegger is one of the few political figures more adept at using Twitter than Trump; he’s been repeatedly besting the president in their exchanges.

So why wouldn’t he win? For reasons related to those that would make him an effective Senator.

His governorship was a highly consequential one, because he took on so many difficult issues and had many productive failures. Indeed, he took more risks in a year than Jerry Brown has in a political lifetime. But those failures made him a very unpopular governor at the end of his tenure. He also made some high-profile misstatements and mistakes that would show up in negative ads. His governorship looks less like a political asset than a big hole out of which to dig himself.

There are other questions. How much does his now-permanent separation from Maria Shriver, and the tabloid headlines related to that event, hurt him? (Presumably she wouldn’t be campaigning with him or advising him as she did in office). How much would the institutional GOP work against him, given his many moderate betrayals? Can he still run as an outsider, his preferred pose, after seven years in Sacramento? And would age be an issue? If he ran in 2018, he’d be 71 on Election Day. Californians seem to like older politicians, but younger voters don’t know all that much about him.

And he would be a Republican in a very Democratic state that would take some real convincing before sending a Republican to Washington. Some news report suggests he wants to run as an independent. That might sound good, but would be a mistake. He could call himself an independent, and be explicit that he’d be a nonpartisan and an opponent of President Trump on most issues. But party affiliation matters more than ever in these polarized times. He’d have to list himself as a Republican to have any hope.

The reason: it turns out that the top-two primary system Schwarzenegger backed makes elections tougher for independents and moderates.

Under those rules, Schwarzenegger’s winning a U.S. Senate seat would be real magic. If he ends up getting in, would he have any magic left in his bag of tricks?