James Rooney is telling lawmakers that if they build an addition on to the Boston Convention and Exhibition Center, convention groups will come. Now he’s got proof.

Four groups have signed contracts to hold six future events at the Boston convention center, but only if the facility is expanded. A fifth group says it will come to Boston if hotel space is expanded. All told, the events would attract an estimated 131,500 conventioneers to Boston, resulting in 266,467 hotel room nights and $180 million of economic activity, convention officials say.

“These organizations wanted to lock in and be here, and make sure they got the dates they wanted,” says Rooney, the executive director of the Massachusetts Convention Center Authority. “The language in the contracts essentially obligates us to the dates if we do expand, but it gives them plenty of time to relocate their events if we tell them it’s not going to happen.”

The bookings give Rooney a dollars-and-cents argument for expanding the convention facility and a response to critics who say the convention center has failed to deliver economic benefits promised in the past. “There’s a lot of analysis done about what could happen, or what might happen, but they are just that, they’re just projections,” says Rooney. “Many people use the ‘if we build it, they will come’ phrase to describe a set of expectations. Well in this case, I think you can underline and bold the words ‘will come.’”

BIO, the Biotechnology Industry Organization, is coming to Boston this June with more than 15,500 attendees. It is expected to spill out of the convention center and use space at the Seaport World Trade Center, the Hynes Con­vention Center, and the Westin Boston Waterfront.

Robbi Lycett, vice president of conventions for BIO, says even if the annual event grows only a little in the coming years, it will likely run out of space in Boston. But Lycett says she would like to return to Boston, in part because 25 percent of convention attendance comes from the region.

“Boston, especially, is a town that we want to rotate back into regularly because so many companies have their offices there,” says Lycett. “Not only does it help our show attendance, it’s also important to biotech companies across the country and globe to come to Boston regularly.”

BIO signed a contingency contract, pledging to return to Boston in 2018, but only if the expansion is completed by then.

“There’s a lot at stake here in terms of Boston positioning itself as a global leader in biotech. It wouldn’t serve us well to make that claim while at the same time not being able to host that industry’s biggest event,” says Rooney, noting that he could tell similar stories of other events.

Expansion of the convention center is part of a plan dubbed T5, an effort to make Boston a “top 5” convention destination. Rooney says he hopes to receive approval for portions of the project this legislative session, and says he thinks the contingency contracts will help to quantify the case for lawmakers. Current proposals include adding a second ballroom to the convention center and enlarging exhibit space to accommodate events that currently go elsewhere due to the facility’s size.

The Convention Partnership, a group convened to consider expansion, issued a report last year which laid out options for financing the project but did not endorse any specific proposals. CommonWealth reported last year that the state would need to come up with between $78 million and $117 million in new annual revenue to support financing for the BCEC portion of the project. Possible options for raising that revenue include increases in existing taxes on hotel rooms, car rentals, and other tourism-related activities.

The other groups that have signed contingency contracts related to convention expansion include the American Heart Association, for 2017 and 2021; the Ameri­can Society of Microbiology, for 2017; and ASIS Inter­national, an industry organization for security professionals, for 2017 and 2024. The American Psychiatric Associa­tion has pledged to come in 2022 if hotel facilities are expanded.