Of the 13 candidates still in the running to be the next leader of the Conservative Party, only a handful have a plausible path to victory on Saturday night.

A few others have an outside chance of pulling off an upset, while the rest are the longest of long shots.

All of the available data suggest that Maxime Bernier, Andrew Scheer and Erin O'Toole have the most realistic paths to victory.

But the 338 equally weighted ridings, 125,000 ballots cast and a preferential ballot where voters can rank all 14 candidates — including Kevin O'Leary, whose withdrawal was too late to have his name struck from the ballot — from first to 10th, are a recipe for uncertainty.

So which paths would lead each of the candidates to the top job?

The longest shots

There is no empirical evidence to suggest that Deepak Obhrai, Rick Peterson, Chris Alexander, Andrew Saxton or Steven Blaney can win the leadership.

Polling of Conservative Party members by Mainstreet/iPolitics gives them each less than one per cent support, their fundraising represents a tiny fraction of all money raised by the leadership contestants, and they have little to no establishment support.

The best hope to emerge from this pack could be Blaney, as his native Quebec could award him an outsized share of points: Each riding is worth 100, regardless of the number of members it has, and Quebec's 78 ridings represent 23 per cent of the points up for grabs.

But a win by any of these candidates would require all of these usually reliable metrics to prove not only worthless, but to be portraying a completely inaccurate portrait of the race that has fooled even the most seasoned party insiders.

In short, their odds are poor.

The social conservatives

The most homogenous bloc of voters in the race belongs to Pierre Lemieux and Brad Trost, candidates who have run unabashedly social conservative campaigns. All indications suggest that a significant proportion of their supporters will rank the other as their second choice.

Lemieux, who has outpolled and outfundraised Trost, is likely to finish ahead and thus benefit from Trost's supporters. But in order to win, Lemieux would need social conservatives to represent an unexpectedly large segment of the party's membership.

A strong finish on the first ballot — putting him as high as second place — along with a strong showing by Trost would allow Lemieux to take a run at the leadership. He would also need significant backing from voters who supported Scheer and Kellie Leitch to have any hope of pulling off an upset.

The moderates

At the opposite end of the party's political spectrum are candidates Lisa Raitt and Michael Chong.

Raitt's weaker fundraising and polling make her a longer shot than Chong. Her path to victory would start with a first ballot putting her in second place, thanks to a surge in support in the Greater Toronto Area and Nova Scotia. She could then scoop up the supporters of Chong, O'Toole and Scheer to beat Bernier.

Chong's path would also require a big first-ballot performance by dominating Canada's biggest cities, allowing him to gain support from Raitt and O'Toole when they drop off the ballot. Chong would struggle to pick up more second-choice support from Scheer than Bernier, but a win would require him to pull off such an unlikely feat.

The wild card

Leitch's path to victory is predicated on having the most motivated supporters in the party. Her campaign has claimed some 30,000 members, which could represent more than 20 per cent of all ballots cast — if they vote.

She would need a number close to that on the first ballot to have a hope of surviving long enough to go head-to-head with Bernier.

Leitch's difficulty is her limited potential to gain support from other candidates. But a big enough first-ballot performance, along with significant gains from candidates like Blaney, Trost and Lemieux, could push her to the final ballot — at which point all bets are off.

But her campaign has been faltering. The last Mainstreet/iPolitics poll put her in fifth place.

The consensus candidates

Aside from Bernier, the most plausible paths to victory belong to O'Toole and Scheer.

The key to an O'Toole victory lies in finishing ahead of Scheer and winning more of his supporters than Bernier. This starts on the first ballot, with strong showings in Ontario, Atlantic Canada and Manitoba.

O'Toole could also overtake Scheer as other candidates are eliminated — particularly Chong and Raitt. If they do better on the first ballot, and if O'Toole then vacuums up a significant proportion of their voters, he could surpass Scheer before the final ballot, putting himself in a decent position to defeat Bernier with the backing of Scheer's voters.

Scheer has more options. Topping 20 per cent on the first ballot and placing within single digits of Bernier would make him the favourite to win, as he has more potential for second-choice support than Bernier.

Big numbers for Lemieux and Trost — combining for some 20 per cent on the first ballot — could also benefit Scheer, boosting him ahead or within spitting distance of Bernier when they are eliminated.

If Scheer makes it to the final ballot and can win 60 per cent of O'Toole's voters, he has an excellent chance of beating Bernier. Less and his odds of victory drop quickly.

The front-runner

Bernier's path to victory has already been mapped out by the available data. The Mainstreet/iPolitics poll puts him north of 30 per cent. He has raised the most money and has the broadest base of supporters.

He also has enough potential for growth that he can hold off a challenge from Scheer or O'Toole, as long their supporters do not consolidate against him.

But there are a few other targets Bernier might like to hit. With his strong support in Quebec, it is conceivable that Bernier could win the leadership with less than 50 per cent of the points in every province but his own. Winning a majority in multiple provinces would be a sign of national support within the party.

Winning before the 13th and final ballot would signal that the party was not overly divided in its choice. In order to do that, however, Bernier will need to beat his forecasted results by a significant margin. Posting a first ballot result well above the 35 per cent mark would make that a possibility — though it still might take 12 ballots to get him there.

The various paths for each of the candidates might diverge by only incremental amounts, but over as many as 13 ballots, that could make all the difference. The road that party members will travel by will be revealed on Saturday.


Live CBC coverage

CBC's live coverage of the Conservative leadership convention begins Friday at 5 p.m. ET on cbcnews.caFacebook and CBC News Network with a special 1-hour Power & Politics with Rosemary Barton. Coverage continues with our CBC News special hosted by Peter Mansbridge at 6 p.m. ET. We'll have streaming video, live updates and analysis at cbcnews.ca/politics.

Saturday's live coverage begins at 4 p.m. ET, with first ballot results expected around 5:30 p.m.


Conservative leadership index, May 26

Methodology

The index is based on four different metrics: endorsements, fundraising, contributors and polls. In tests on 14 recent federal and provincial leadership races in which all party members could vote, the index has replicated the first ballot results with a median error of plus or minus 2.2 points per candidate. A more detailed explanation of the index's methodology can be found here.