The recent study said a Sodo arena would generate three times more tax revenue than a renovated KeyArena. But “opportunity cost” was not factored in, which favored the Sodo proposal, and the study omitted up to $72 million in leasehold excise taxes the KeyArena project could pay.

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A study released last month by a University of Washington professor had a can’t-miss conclusion: A new sports arena in the Sodo District would bring Seattle three times more tax revenue than a renovated KeyArena.

Chris Hansen and his Sodo arena group paid $16,000 for the “Seattle Arena Public Finance Analysis” study by UW Evans School of Public Policy and Governance professor Justin Marlowe and three graduate students. Sodo arena backers trumpeted the 3-to-1 advantage.

But a review by The Seattle Times found a high potential for fluctuation in the study — including use of raw property and sales-tax data without deeper “opportunity cost” context, an approach two sports economists say favors the Sodo group’s proposal.

Opportunity cost by definition is the loss of possible gains from other alternatives when one option is chosen.

Also, the study omitted up to $72 million in leasehold excise taxes the KeyArena project could pay “in lieu of property tax” under state law while basing other calculations — with limited factual basis — off the assumption a Sodo arena would land an NBA team four years sooner.

Marlowe said in an interview his study made assumptions — amid the city’s private, ongoing KeyArena negotiations with the L.A.-based Oak View Group. Altering some of those assumptions, he added, could result in KeyArena generating more tax revenue than the Sodo project: A big reason Marlowe made his study model public was so people can input various numbers, gauge their impact and further the arena debate.

Up to now, though, the study’s claimed 3-to-1 advantage for the Sodo site — a gap Marlowe pegs at $68 million — has garnered the most attention.

“I get why everyone is focused on that number,” Marlowe said. “But again, the second part is the really important part. What if what’s on the table changes? Then you get different numbers.”

The study wasn’t necessarily wrong — just narrowly focused, with a tight, one-month turnaround deadline that forced assumptions almost certain to change.

Marlowe said the Hansen group approached him in May, remembering his work for King County on a Sodo arena Memorandum of Understanding in 2012. Marlowe asked the Evans School to administer the study because he felt it was a learning opportunity for students, and he needed help to do it quickly.

“They made it clear that getting it done sooner rather than later was good,” Marlowe said of the Sodo group.

But Holy Cross University economics professor Victor Matheson said the study’s lack of “opportunity cost” consideration skewed the results in the Sodo group’s favor.

“The assumption is made that if you don’t build an arena at the Sodo site, that the site will always remain vacant and there will never ever be any economic activity that ever occurs there,” Matheson said. “They’re assuming that if you don’t build this arena there, it will be impossible to generate either retail sales tax or property tax from any other type of development that goes in there.”

Under current zoning, Hansen could build an office complex or other commercial entities if his arena proposal isn’t approved.

Matheson said a more in-context study would have applied only the difference in tax revenues between such alternative Sodo projects and an arena. That smaller “net” difference would significantly reduce — if not eliminate — the Hansen group’s 3-to-1 advantage over the KeyArena proposal.

Andrew Zimbalist, a sports economist at Smith College and pioneer in exploring stadium and arena financing, agreed that gauging tax-generation potential requires examining opportunity cost.

“The point of looking at opportunity cost is there are options, choices that you make,” Zimbalist said. “And you want to allocate your resources in the most favorable way that has the best return. So you look at current uses, alternative uses and the plan that’s in hand, and you compare all of them. That’s the only way.”

Marlowe said the study was meant to gauge only raw tax flows, not opportunity-cost variables.

“As we say right at the beginning, this is not a benefit-cost analysis,” Marlowe said. “If we had wanted to talk about opportunity cost, we would have had to look at all types of opportunity cost. Not just related to land use, but opportunity costs around what’s the value of additional traffic mitigation or any other number of factors.”

Marlowe agreed that opportunity cost matters.

“That’s exactly the sort of question some of the policy makers involved here should be asking,” he said.

In fact, opportunity cost has largely driven Seattle’s arena debate — specifically, the public liability at Key­Arena if a Sodo arena were built. The Seattle City Council paid for a 2015 alternative-use study by the AECOM architectural firm, which concluded it would cost the city $150 million to repurpose KeyArena into a secondary facility that might break even financially. The city has used that to justify OVG’s proposed $564 million, privately funded renovation.

The Marlowe study notes that OVG would not pay property tax on city-owned KeyArena. But it omits part of the state’s leasehold excise tax collected “in lieu” of property tax.

The law says OVG can be taxed 12.84 percent not only on annual KeyArena rent, but its $564 million construction upgrades. That upgrades tax amounts to $72 million payable over OVG’s 35-year lease — with the city’s share at $23 million, or about $657,000 annually.

The Marlowe study shows OVG paying the city only $80,000 in annual leasehold excise tax for rent alone. But with the upgrades provision, OVG could pay eight times that amount.

It’s similar to a California law charging the San Francisco Giants millions in annual property tax for “possessory interest” in operating AT&T Park on free public land.

Here’s the rub, though: Nobody knows how much leasehold excise tax OVG would pay.

Anna Gill, a spokesperson for the state’s revenue department, wrote via email that in general the tax is on “the value of the improvements amortized over the life of the contract (lease)” but added that OVG’s bill would depend on negotiations with the city.

The law allows 12.84 percent tax on the $564 million renovation, but it could be negotiated lower and added to the annual KeyArena rent OVG would pay. State tax officials must approve that final rent amount to ensure it’s at high enough market value.

Marlowe said his study didn’t mention the improvements part of the tax because of the unknown element and that “undoubtedly, there are any number of different ways that these negotiations could unfold.”

A draft agreement between OVG and the city is expected Sept. 12.

Marlowe tried contacting the city without success for specific figures. The Seattle Times did as well but was told none will be released during negotiations.

Marlowe could have waited until the draft agreement becomes public for a more precise analysis. But Marlowe said Hansen’s group wanted the July turnaround, and so did he.

“Personally, I thought … it was important for this information to be out there for the public to consume.”

The Sodo group’s July 10 release of the study coincided with the first Select Committee on Civic Arenas meeting co-chaired by city council members Debora Juarez and Bruce Harrell. The council will decide which arena project to continue with.

Marlowe’s study also assumes a Sodo arena gaining an NBA franchise four years before KeyArena would, basing it off NBA reports and statements by pundits and the notion that a “shovel ready” site would attract the league sooner.

But NBA commissioner Adam Silver told The Seattle Times in April 2016 that a “shovel ready” Sodo site would not hasten expansion. More recently, Silver said expansion was “inevitable” and that Seattle would be on a short list, but he did not retract previous statements about it being years away.

Smith College economist Zimbalist said if the Sodo group proves it can get NBA or NHL teams before Key­Arena, that would be worth considering because “over and above any property or sales-tax generation, the very fact that you can have an NHL or an NBA team, or both, has a social value.”

But the NBA’s return remains another unknown.

Still, the other part of the study’s objective — getting financial topics discussed in public — has succeeded.

“The fact that we’re having a detailed discussion about a spread sheet means that our approach is on to something,” Marlowe said, chuckling. “I mean, that was the whole idea.”