While Delta this week gave its employees bonuses averaging about $13,000, that encompasses both a very lucrative contractual bonus for pilots and a considerably thinner one for some groups with different deals.

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There are very few companies in America with a profit-sharing plan as generous as that of Delta Air Lines, which this week paid out $1.1 billion in annual bonuses to employees — a quarter of the airline’s net profit last year.

Yet the way the payout was distributed has still managed to anger a large group of Delta workers.

When the Seattle Times reported — accurately — that the average bonus paid on Tuesday came to $13,000, more than a half dozen outraged Delta workers called or wrote to say they’d received nothing close to that amount, and that their bonus was way less than last year’s.

“We all feel cheated,” wrote one flight attendant, who asked not to be identified for fear of company retaliation. “It should be even across the board.”

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Indeed there were big differences in the payouts among different worker groups, and not only because some have higher salaries than others.

Delta said flight attendants and ground crew got a bonus of 10.3 percent of their annual pay. For many, that meant payouts ranging from $3,000 to $6,000.

A second flight attendant said her bonus was only $2,300, “less than half what I got last year.”

A member of the ground crew who works only part time said he got a bonus of $1,500.

In contrast, the pilots’ union said that under its contract, Delta’s 13,000 pilots got a profit-sharing bonus of 17.8 percent of annual pay.

An extensive database of airline salaries maintained by analysts at the Massachusetts Institute of Technology indicates that the average salary for Delta pilots in 2016 was about $230,000, which means their average profit-sharing bonus topped $40,000.

The pilots, represented by the Air Line Pilots Association (ALPA), along with the much smaller number of flight dispatchers, are the only groups of unionized workers at Delta. The better terms in the pilots’ profit-sharing plan were part of a new contract negotiated in December.

That contract included a 30 percent pay raise over four years. Crucially, it also retained the more generous profit-sharing formula from previous years, with the payout from a pool of money equal to 10 percent of adjusted pre-tax profits up to $2.5 billion and 20 percent above $2.5 billion.

The dispatchers too retained the same proft-sharing formula.

Non-union workers at Delta got a 25 percent base pay increase in stages over two years.

But at the same time, Delta cut their slice of the profit-sharing formula significantly for the future: This year, their profit-sharing pool was equal to 10 percent of adjusted pre-tax profits.

The result was that the profit-sharing bonus for many non-union workers this year was less than half what it was in 2015.

“I’m not blaming the pilots. They were able to negotiate it into their contract,” the first flight attendant said. “We didn’t get a choice, being non-union.”

Information in this article, originally published Feb. 16, 2017, was updated Feb. 17, 2017. The previous version of this story did not include the information about average wages for Delta pilots.