Let’s have a little post-season quiz. Here are two lists of names, and the idea is to match one name in Column A with one name (or blank) in column B. For extra credit explain how and why the names are linked and for extra, extra credit with whom they are linked:

The names are significant and timely because the general managers’ meetings were held in Arizona last week, and this is the beginning of their season. Free agents are waiting to be signed, and trades are waiting to be made.

This signing and trading season, however, is marked by an expansion of a modern title in baseball front offices: president of baseball operations.

That is the title held by the names in Column A, except for La Russa, whose title is chief baseball officer. Those in Column B are general managers, though a baseball executive remarked that the general managers with teams that have presidents of baseball operations are really assistant general managers.

Each team has its own definition of the roles of the two men and how each functions, but the president of baseball operations and chief baseball officer are clearly No. 1 in the hierarchy of baseball operations. Personnel decisions are made jointly, but in instances where there are differences of opinion, the president’s prevails.

Generally, the general manager does the groundwork in discussions with other clubs and with agents. He then clears a signing or a trading decision with the president, having kept him apprised as he progressed in the negotiations.

Before continuing, let’s connect the names in the two columns:

• Hill/Jennings, Marlins
• Silverman with no general manager, Rays
• Friedman/Zaidi, Dodgers
• La Russa/Stewart, Diamondbacks
• Daniels/Daniels, Rangers
• Melvin/Melvin, Brewers
• Epstein/Hoyer, Cubs
• Hart with no general manager, Braves

Hart, long a close friend of John Schuerholz, the Braves’ president and a long-time general manager himself, will add a general manager because he turned down Schuerholz’s offer to be the general manager after Frank Wren was fired.

Tampa Bay is not likely to add a general manager any time soon. When Friedman left the Rays last month to go to Los Angeles, Silverman, the club president, became president of baseball operations and named two directors of baseball operations, Chaim Bloom and Erik Neander, as assistant general managers.

Silverman’s decision to give up his role as team president for the baseball operations job prompted a question: why? It’s a highly unusual move. But the Rays have been a highly unusual operation. It is an organization run not be experienced baseball men but by Wall Street refugees.

“Their leadership has been the three people,” a baseball official said, referring to Silverman, Friedman and owner Stuart Sternberg. “I think Silverman was involved in baseball discussions so it’s a trust thing with Sternberg. I think they make a lot of decisions by committee.”

The Dodgers, whose 2014 payroll ($235 million) tripled the Rays’ payroll ($77 million), lured Friedman west, embellishing his title from executive vice president of baseball operations. Major League Baseball discourages lateral moves so the Dodgers avoided that with Friedman.

The Dodgers, who fired their nine-year general manager, Ned Colletti, despite having won the National League West title the last two years, bulked up in the front office by retaining Colletti as a senior adviser and adding Josh Byrnes as senior vice president of baseball operations.

His new job enables Byrnes to continue his tour of the N.L. West. He has served as general manager of the Arizona Diamondbacks and the San Diego Padres.

Stewart, a former pitcher, coach and agent, is the Diamondbacks’ new general manager, hired by his former manager, La Russa, who came out of retirement six weeks into last season to be Arizona’s chief baseball officer, his first front-office job after 33 years as a manager.

The Epstein-Hoyer tandem was created in 2011 when the Cubs’ new owners, the Ricketts family, set their sights on Epstein, who had one year left as the Red Sox general manager.

A 5-year, $18.5 million contract and a promotion to president of baseball operations accomplished the Cubs’ quest. The Red Sox could have blocked Epstein’s move, but by granting the Cubs permission to deal with Epstein, they clearly showed they were happy to see him leave.

As quickly as Epstein was hired, he named as his general manager Hoyer, with whom he had worked in Boston. Some people suspected tampering, but neither the Red Sox nor the Padres, for whom Hoyer had been general manager, filed a complaint so the commissioner’s office ignored the suspicions.

(The commissioner’s office reportedly is looking into new suspicions about the Cubs allegedly tampering with Joe Maddon to induce him to opt out of his Tampa Bay contract and manage the Cubs.)

The Miami Marlins, where Jeffrey Loria is very much a hands-firmly-on owner, are in the second stage of their new tandem.

Hill, an African-American, was an assistant general manager with Larry Beinfest as general manager when other clubs began showing interest in Hill. Loria didn’t want to lose him so in 2007 he elevated Beinfest to president of baseball operations and made Hill general manager.

I was doing a study of minority hiring for decision-making positions around that time, and I was about to add Hill to the list when a member of the Montreal organization alerted me to the reality of the situation. Hill was general manager in name only; Beinfest was the decision-maker.

Now that Beinfest has been fired and Hill has replaced him, Hill presumably is the decision-maker, though no matter who holds the title, Loria makes the decision. In the team’s current contract negotiations with Giancarlo Stanton, the face of the team and its No. 1 player, no one but Loria will make the signing decision.

The other three presidents of baseball operations attained their titles in the last couple of years, and their teams don’t have separate general managers. All three men retained their g.m. titles when they were promoted to president of baseball operations: Milwaukee’s Melvin in May 2012, the Rangers’ Daniels March 2013 and Washington’s Rizzo last August.

The Melvin and Rizzo appointments were straightforward. The Daniels development contained far more intrigue and controversy.

Daniels had been the Texas general manager and Nolan Ryan, the Hall of Fame pitcher, had been president and chief executive officer. But in March 2013 the co-owners, Ray Davis and Bob Simpson, decided, without explanation, to make front-office changes. They promoted Daniels to president of baseball operations and stripped Ryan of the president half of his title.

Not surprisingly, Ryan subsequently relinquished his remaining title and left the Rangers, eventually migrating to the Houston Astros, with whom he pitched for nine years and where his son Reid was president of business operations.

Ryan had recruited Davis and Simpson, Texas oil billionaires, to buy the Rangers in 2010, but they apparently grew disenchanted with the attention Ryan was receiving as the face of the team and acted to induce him to leave.

They apparently have no such problem with Daniels, a New York City native, who at the age of 28 in 2005 was the youngest general manager in major league history.

Tal Smith was in his 70s and had had decades of front-office experience when he became the first president of baseball operations in the mid-1990s with the Houston Astros. Andy MacPhail was the second, with the Baltimore Orioles, in 2007.

Smith was the Astros’ general manager when John McMullen, a limited partner in George Steinbrenner’s New York Yankees ownership, bought the Astros in 1979. Less than 18 months later, McMullen fired the fan-favorite Smith over their disagreement with Smith’s lifestyle.

When McMullen sold the team in 1992, he extracted a promise from the new owner, Drayton McLane Jr., not to hire Smith. McLane, however, was not a knowledgeable baseball man, needed help to revitalize the Astros and brought Smith back.

“I came back to the Astros in November ‘94 as president,” Smith said in a telephone interview last week. “Drayton decided to split baseball and business operations, and I became president of baseball operations.

“When I came back at the end of ‘94 Bob Watson was the general manager. Gerry Hunsicker succeeded him. I was not doing day-to-day g.m. duties. I was advising Drayton. Day-to-day supervision of scouting and player development was under the general manager. He had dual reporting responsibilities to me and Drayton.

“I was Drayton’s sounding board. I was his sounding board for baseball and long-range planning. I was his adviser on key negotiations. Day-to-day and contact with other g.m.’s was Watson’s responsibility. Drayton had little knowledge of baseball. He needed someone to rely on for baseball decisions.”

Smith remained as president of baseball operations until Jim Crane bought the Astros in November 2011. Tim Purpura and Ed Wade served as general managers under Smith after Watson and Hunsicker.

MacPhail was not the Orioles’ general manager for two reasons. He had served as president of the Cubs, and Peter Angelos, the Orioles’ owner, hated the title. He still does. Dan Duquette, who currently performs the duties of a general manager, is called executive vice president of baseball operations. The Orioles do not have a president of baseball operations.