In his big speech to the state Democratic convention last week, Gov. Cuomo rattled off a slew of statistics meant to show that things are looking up in New York on his watch.

“The proof is in the numbers,” he declared.

But the numbers he cites don’t always prove what he wants them to.

A case in point:

“Unemployment in upstate New York, which has been a problem for decades, just had the largest one-year drop in unemployment in recorded history — period,” he said, to hearty applause from the party faithful.

He was referring to a report from the state Labor Department showing that the jobless rate for 52 upstate counties plunged to 5.7% in April, from 7.4% the year before.

But the data behind those numbers are not so sunny as Cuomo implied.

The unemployment rate is based on monthly surveys gathering two key pieces of information — how many people have jobs and how many people are searching for jobs. By that measure, the upstate unemployment rate did drop in the past year — but not because lots of people from Buffalo to Albany found jobs. It dropped because fewer people were looking.

The Labor Department’s count of upstaters with jobs over the year was essentially flat at 3.1 million. But the size of the labor force — which is people with jobs plus people looking for jobs — fell by 69,000.

Some of those people retired or moved away. Others just gave up hope of finding a paycheck.

Had those people stayed in the hunt, the unemployment rate would have risen slightly over the past 12 months, to 7.5%.

Nationwide, the unemployment rate also dropped during that period, from 7.5% to 6.3%. But the size of the labor force held steady, meaning the trend reflected a real increase in employment.

For Cuomo to offer the upstate number as evidence of a surge was “extremely misleading,” said fiscal watchdog E.J. McMahon of the Empire Center for New York State Policy. “It’s accurate only if you ignore what’s driving it.”

But Cuomo is not the only politician who’s looking at the jobless rate through rose-colored glasses.

Accepting the GOP nod to challenge Cuomo, Westchester Executive Rob Astorino said his home county “has one of the lowest unemployment rates in New York.”

As McMahon points out, that statistic, too, is driven more by a shrinking labor force than by an increase in employment.

The reality is that New York has two economies — with downstate doing quite well even as upstate is languishing.

If the NYC metropolitan region were its own state, it’s 7.1% growth in private-sector jobs over the previous three years would rank seventh in the nation, according to McMahon. But the 1.5% growth rate in the counties north of Newburgh would be dead last.

Add them up and New York State during the Cuomo years sits in the middle of the pack at 21st — with job growth a percentage point lower than the national average.

Which brings us to another questionable statistic, as quoted in state-sponsored TV ads — that New York is “No. 2 in the nation in new private-sector job creation.”

The Cuomo administration bases that claim on its own state-by-state analysis of jobs lost and regained since the Great Recession of 2008 and 2009. As of March, New York has seen a net increase of 238,000 jobs — more than any state than other than Texas.

But remember that New York is the third-largest state — so it naturally would have a large number of jobs, even if its economy were only so-so.

The more relevant measure is the rate of growth — by which, as we’ve already seen, New York comes out below average.

The truth is that New York’s economy has chronically lagged the rest of the country’s for decades. And some factors contributing to that reality — including the upstate New York’s infamously harsh and snowy winters — are beyond the control of any elected official to change.

What governors should focus on — and be judged by — is not short-term trends but long-term efforts to correct the ship’s course.

So give Cuomo due credit for capping property taxes and keeping a lid on state spending.

And fault him, if you like, for failing to authorize well-regulated natural gas drilling or extending business-unfriendly taxes that were due to expire.

But take his statistical claims with a grain of salt.

© 2014 New York Daily News