WASHINGTON - Ted Cruz, an underdog going into Wisconsin a month ago, woke up Wednesday morning with 36 of the 42 delegates that were up for grabs in the Badger State, handing front-runner Donald Trump the most significant defeat of the 2016 campaign outside Texas.

While Cruz's lopsided victory emboldened his campaign and galvanized the #NeverTrump movement, a Houston Chronicle analysis shows he remains a mathematical long shot to win the GOP nomination outright.

Looking ahead to New York and several other Eastern states more favorable to Trump, the new delegate math is headed into uncharted territory.

If there is any consensus among analysts across the political spectrum, it is that both Cruz and Trump are likely to fall short of the 1,237 delegates needed to clinch the nomination ahead of the July convention, setting up a rare free-for-all on the floor of the convention hall in Cleveland.

RELATED: Growing chance of contested convention puts added focus on delegates

The Chronicle analyzed best-case scenarios for Cruz in the remaining primary states and found that the Texas senator stood little chance of narrowing Trump's lead to fewer than 200 delegates. Most experts who reviewed the analysis said even that would be a highly optimistic scenario for the Cruz campaign.

The Chronicle calculated predictions for Cruz’s most optimistic scenarios in remaining primary vote, in an attempt to weigh his chances of overtaking Trump before the GOP convention in July. Even an unlikely series of best-case scenarios for Cruz wouldn’t get him there, the Chronicle found. Experts reviewed the calculations and agreed. Explore the data to view current delegate counts and predictions through June.

"It's clear that Trump is unlikely to get 1,237, but also that Cruz probably has a ceiling that is under 1000," said Mark Jones, a political scientist at Rice University's Baker Institute.

After recent victories in Utah, Colorado and North Dakota, Wisconsin served as an exclamation point in what Cruz termed a "turning point" in the nominating battle.

Added to delegates still being selected in Colorado and Wyoming - which award them through a complicated system of party caucuses and conventions - Cruz said Tuesday that he has been able to cut into Trump's lead by some 100 delegates.

In Wisconsin's primary, Cruz thrashed Trump 48 percent to 35 percent and limited the Manhattan real estate mogul to just 6 delegates, far fewer than his most pessimistic projections. Ohio Gov. John Kasich, who got 14 percent of the vote, won no delegates.

RELATED: With Wisconsin win, Cruz keeps the GOP race alive

Despite the setback, Trump still holds a commanding lead in the race, with 743 delegates to 517 for Cruz. To secure the nomination, Cruz would have to win 720 more delegates - about 82 percent of the 882 delegates yet to be claimed in 16 states between now and June 7, when voters in delegate-rich California and four other states hold the final primaries. In other words, Cruz would need to score Wisconsin-sized blowouts the rest of the way.

Current delegate counts by state.

Trump's path is a little easier, but still a steep climb. He has to win 494, or about 56 percent, of the remaining delegates.

The road ahead

To finish even within 200 delegates of Trump, the Chronicle gave Cruz what many experts called "undue credit." The calculation assumes he splits New York's 95 delegates with Trump later this month, while a Real Clear Politics aggregation of four New York polls gives Trump a massive 32 point lead.

The Chronicle analysis also goes against most polls in assuming Cruz wins in states like Pennsylvania, Delaware, Rhode Island and Indiana. And the Chronicle gave Cruz a marginal statewide victory in California - the nation's biggest cache of Republican delegates - which experts and polls suggested is unlikely.

It also excluded Kasich, who likely will take marginal numbers of delegates from both Trump and Cruz.

Geoffrey Skelley, an election analyst at the University of Virginia Center for Politics, estimated that Cruz could not get closer than about 220 delegates behind Trump, even in a best-case scenario for the Texas senator. Skelley expects Trump to sweep the Northeastern states and claim as many as 80 of New York's 95 delegates.

Most of the remaining states have "winner-takes-most" rules that award candidates a greater share of the delegate haul than a purely proportional scheme. Neither Cruz nor Trump, however, consistently has been winning delegates at the clip each now needs to reach the magic number of 1,237 delgates.

Two states loom particularly large in the coming month. First comes Trump's home turf of New York on April 19. While the billionaire developer is heavily favored, he would need to win more than 50 percent of the vote to claim all of the Empire State's delegates. Recent polls have him hovering just above that mark.

Cruz, in an early foray into the Bronx on Wednesday, followed by another stop near Albany on Thursday, clearly is diving into New York with the aim of picking off delegates in targeted congressional districts - and denying Trump the winner-take-all margin.

Trump also leads in Pennsylvania, which votes April 26 along with four other coastal states. Pennsylvania throws a monkey wrench into the process by awarding 54 of its 71 delegates through direct elections in which individual delegates' names appear on district ballots, to be elected separately from a presidential preference vote.

'In the eye of the beholder'

In his Tuesday victory speech in Milwaukee, Cruz vowed to win the majority of the delegates needed to win the Republican nomination, but added a critical caveat: "either before Cleveland, or at the convention in Cleveland."

Most analysts say his best shot is a contested convention, where his campaign's superior organization might wrest away delegates who are formally pledged to Trump but personally loyal to Cruz.

"This fight will go to convention," said Jordan Berry, an Austin-based GOP strategist who supported Cruz in his 2012 Senate bid. "And Ted will win at that convention."

RELATED: Looking past Wisconsin, Cruz strategizes a contested convention

Cruz's come-from-behind strategy, emerging through the tedious process of wooing individual delegates in local party gatherings, is based on state party rules that allow delegates to make their own voting decisions after the first or second round of convention balloting.

It is precisely that prospect that has turned the focus of the GOP race to the behind-the-scenes battle for delegates on both sides.

The closer Cruz can get to Trump in the delegate race before the convention in July, analysts say, the better his chances are of turning the party machinery against the maverick outsider and winning the GOP nomination.

Brandon Rottinghaus, a political scientist at the University of Houston, said the Republican Party could justify electing Cruz as an alternate to the front-runner "if and only if Cruz is close to Trump's delegate count."

However, there is no widely accepted definition for "close." Matt Mackowiak, a GOP strategist in Austin, said the term is "a little bit in the eye of the beholder."

Luke Macias, a Republican strategist in Texas, said Cruz would be a legitimate alternative no matter how far back he lagged in delegates. It is no secret that many leaders are anxious to use a contested convention to prevent Trump from becoming the party's standard-bearer.

The Cruz camp and the Super PACs that support him emphasize the existing party rules requiring a majority of the delegates to win the nomination, no matter how many ballots it takes.