Which candidate has the potential to exert the most influence on this year’s mayoral race? No, it isn’t the billionaire incumbent mayor, Michael Bloomberg. Nor is it the Democratic front-runner, Fernando Ferrer, the former president of the Bronx. It isn’t the Council Speaker, Gifford Miller, despite his fund-raising prowess, nor is it the energetic congressman, Anthony Weiner, who seeks to become the Ed Koch of 2005.

The two candidates who will shape this race are the newest entrants, who some might say have the least chance of success. Win or lose, however, they will have a huge impact.

Among Democrats, the candidacy of C. Virginia Fields, the president of the borough of Manhattan, promises to change the dynamics of the race. That impact will be felt largely by Mr. Ferrer. The presence of a credible African-American candidate in the race precludes a repeat of the “two cities” strategy that Mr. Ferrer, a Latino, employed in 2001. Then he was bolstered by the strong support of his own ethnic constituency, black voters brought on board by the Reverend Al Sharpton, and the organizational skills of one the city’s most potent labor unions, Local 1199 of the Service Employees. Mr. Ferrer won the largest number of votes in the primary election, but fell short of the 40% needed to win outright. This forced a runoff. In the contentious, racially-charged second round, Mr. Ferrer narrowly lost to then-Public Advocate Mark Green.

The Fields candidacy seems to preclude a reprise of the 2001 strategy. This is working on the assumption that the putative candidacy of Council Member Charles Barron will quickly succumb to common sense, and Mr. Barron will stand for certain re-election rather than a kamikaze mayoral effort. But even without his favored candidate in the race, Mr. Sharpton is unlikely to support Mr. Ferrer over Ms. Fields. There is bad blood between Mr. Sharpton and Roberto Ramirez, Mr. Ferrer’s chief strategist. Moreover, there is some evidence that Local 1199 is toying with an endorsement of Mr. Bloomberg, who just hired the union’s political field director, Patrick Brennan, to work on his campaign.

This leaves Mr. Ferrer with one option – expanding his vote among centrist outer-borough blue-collar homeowners. He has been down this path before, prior to his first mayoral foray in 1997. Following the advice of Dick Morris, Mr. Ferrer became, among other things, a supporter of the death penalty in some cases, and an advocate of mandatory school uniforms. When Mr. Morris became embroiled in scandal, Mr. Ferrer dropped him as a consultant and returned to his more predictably liberal form.

This year, Mr. Ferrer seems to be taking a page from his old Dick Morris playbook, with his emphasis on the plight of the middle class. The presence of Ms. Fields as a primary opponent seems to leave him no choice. The question is whether the baggage from 2001, the backing of Mr. Sharpton, and the undermining of Mark Green’s campaign against Mr. Bloomberg will leave Mr. Ferrer unwelcome among the groups he now courts.

The newest entrant in the race is Thomas Ognibene of Queens, the for mer minority leader of the City Council. Mr. Ognibene is a thoughtful conservative Republican whose public career ended due to term limits. He is now at the center of what could become the mayor’s most troublesome problem, a revolt among the small, intrepid band of local Republicans who see their “Republican” mayor as a closet Democrat.

There is good reason for this. Last week’s State of the City Address could have been delivered by any Democrat. And politically, if patronage is the grease by which officeholders ensure that the political machine will run smoothly, the GOP machine has dried up and ground to a halt. Most of Mr. Bloomberg’s appointments have come from Democratic Party ranks and, amazingly, of the first 60 judges appointed by the mayor, not one comes from Republican ranks. In the Bronx, there is resentment that the mayor might have been a bit too aggressive in pulling the rug from under the imprisoned former state senator, Guy Velella, still a popular figure in the only neighborhoods in that borough won by Mr. Bloomberg in the last election.

Of course, it can be argued that the mayor doesn’t need the party machinery. He does, after all, have unlimited financial resources that will dwarf any money Mr. Ognibene could possibly raise, even with the six-to-one match recently put in place by the City Council.

If that is the attitude, then the mayor is in store for a long, hard summer. New York’s Republican grassroots organizations make a statement simply by their enrollment. They are Republicans on principle, and therefore resistant to even the mayor’s deep pockets. One need only go back 35 years when an earlier Republican mayor, John Lindsay, felt the wrath of GOP voters, losing the primary to state Senator John Marchi of Staten Island. Mr. Lindsay was forced to run on the Liberal Party line alone.

Mr. Lindsay ultimately won re-election because he looked better than his Democratic rival, then-comptroller Mario Procaccino. Are any in this year’s Democratic field as weak a candidate as Procaccino? That is the question Mr. Bloomberg must face if he ends up as only the nominee of Lenora Fulani’s Independence Party, with Mr. Ognibene siphoning off votes from him on the Republican and Conservative lines.

What is the best outcome for Mr. Bloomberg? A summer moving to the right, to fend off Mr. Ognibene in the Republican primary? This only makes the mayor’s work more difficult in November, when it is crucial to win the votes of Democrats. Even if Mr. Bloomberg prevails in September, disaffected Republicans will still be able to cast their November ballots for Mr. Ognibene, who is sure to win the Conservative Party nomination.