The Democratic presidential field is suddenly shrinking.

Michael Avenatti, a candidate mainly in his own mind, has decided not to run.

The Stormy Daniels lawyer who became intoxicated by his cable news stardom cited his family, but obviously his arrest on suspicion of domestic violence downgraded his chances from far-fetched to nonexistent.

And Deval Patrick, the former Massachusetts governor, has told associates that he won't be a candidate despite encouragement from the Obama inner circle, according to Politico.

That leaves roughly 572 Democrats still eyeing the White House.

In light of yesterday's emotional funeral for George H.W. Bush — attended by Donald Trump, Barack Obama, Bill Clinton, Jimmy Carter and the chief eulogist, George W. — it seems an apt moment to reflect on what makes a good president and the art of winning the office.

If Trump, a real estate developer, is an unlikely president, so was Carter, a peanut farmer who camped out in Iowa and somehow caught the post-Watergate wave. So was Obama, a community organizer and freshman senator who had to break a racial barrier.

Bush 41 was the ultimate establishment figure — ex-senator's son, congressman, ambassador, party chairman, CIA chief, vice president, — but would not have won had he not unleashed Lee Atwater to run a very aggressive campaign.

The Democratic field can be grouped several ways, but the greatest divide is between the aging old guard and a younger generation of contenders.

Joe Biden, who had already been a senator for eight years when Bush became vice president, recently declared himself the most qualified person in the field (as well as an admitted "gaffe machine"). He has the stature of a former VP and an ability to talk to blue-collar voters, but his past presidential campaigns were disasters.

Some pundits see Bernie Sanders as the automatic front-runner given his strong showing last time. But it's just as likely that his moment has passed, that he was the beneficiary of anti-Hillary sentiment, and he remains weak with black voters.

Elizabeth Warren is in this group too, even though she hasn't been in Washington nearly as long. She seems to get under Trump's skin and could siphon some of Bernie's populist support, but her campaign skills are suspect.

Then there are the senators. Sherrod Brown could make inroads in Ohio and the Midwest. Kirsten Gillibrand has street cred for saying Bill Clinton should have resigned but alienated some elements of the party who like the Clintons, who had helped her. Kamala Harris has a built-in African-American constituency. So does Cory Booker, who tried to drum up a Spartacus moment during the Kavanaugh hearings, but seems more second-tier. So does Amy Klobuchar: likable, little-known and possibly suffering from Minnesota Nice.

Beto O'Rourke, who recently met with Obama, gets his own category. He has the kind of charisma that gets the media swooning and raised truckloads of money in his 3-point loss to Ted Cruz. Sure, it's Texas, but it's still not easy to see a losing Senate candidate pulling a Lincoln and winning the White House two years later.

There are many other names — Eric Garcetti. Julian Castro, John Hickenlooper — who may be accomplished people but still feel like long shots, and perennial presidential tease Mike Bloomberg.

The media, it's clear to me, will play a key filtering role with such an unwieldy field. Not because of their predictions; they blew it with both Trump and Obama. Not based on whether journalists like the candidates, although that can be a peripheral factor.

No, the key question is who gets the ink and airtime necessary for a viable candidacy. That can change — contenders who get hot can move from the kiddie table to the main stage — but coverage is like oxygen. (Even negative coverage, in Trump's case.) You can't survive without it.

Even Jeb Bush, who raised $100 million and made plenty of mistakes, couldn't overcome the Trump spotlight.

Ultimately Democratic voters have to decide how liberal their candidate should be and whether he or she should be as hyper-aggressive as Trump or a milder, contrasting personality.

The media, unlike what we saw yesterday at the Washington National Cathedral, were never particularly kind to George Herbert Walker Bush. But his example reminds us that when it comes to White House wannabes, character counts.