Ninety-one players reached agreements Friday, leaving 39 headed toward hearings next month in St. Petersburg, Fla., from among the 146 who filed for arbitration earlier in the week.
Every case settled last year, the first time that happened since arbitration began in 1974.
Scherzer and the Detroit Tigers reached a one-season deal for $15,525,000 that leaves him less than a year from free agency. Davis and the Baltimore Orioles agreed at $10.35 million.
Detroit general manager Dave Dombrowski said Friday the short-term agreement doesn't necessarily preclude a lengthier deal before opening day.
"We still have that desire," he said.
Also, NL Cy Young winner Clayton Kershaw and the Los Angeles Dodgers completed their $215 million, seven-year contract, a record for a pitcher and at $30.7 million the highest average salary in baseball history.
Kershaw and his wife, Ellen, have been discussing how to spend the money, and most of their ideas revolve around charitable interests. The couple supports an orphanage in Africa and two groups that fund afterschool programs for children in Los Angeles and Dallas. They have no children of their own.
"Ellen and I understand the effects we can have on a lot of people with this money," he said. "We realize to whom much is given much is expected and that's what we're going to try and do.
Kershaw gets an $18 million signing bonus, payable in $6 million installments this April 15, July 15 and Sept. 15. He receives salaries of $4 million this year, $30 million next year, $32 million in 2016, $33 million in each of the next two seasons, $32 million in 2019 and $33 million in 2020.
Among the players still in arbitration, Cleveland pitcher Justin Masterson asked for the most at $11.8 million, with the Indians offering $8.05 million. The $3.75 million gap is the largest among the pending cases.
Cincinnati pitcher Homer Bailey had the second-highest request at $11.6 million, with the Reds offering $8.7 million.
Other large numbers were submitted by Atlanta closer Craig Kimbrell ($9 million to the Braves' $6.55 million), Baltimore catcher Matt Wieters ($8.75 million to the Orioles $6.5 million) and Washington pitcher Doug Fister ($8.5 million to the Nationals' $5.75 million).
San Diego pitcher Andrew Cashner has the smallest gap among the remaining players, asking for $125,000 more than the Padres' offer of $2,275,000.
Among the settlements, Washington agreed to a $24 million, two-year deal with pitcher Jordan Zimmermann and a $17.5 million, two-year contract with shortstop Ian Desmond.
A total of 57 players exchanged figures with their clubs, and 18 of them settled later in the day. Forty-one players swapped figures last winter.
AP Sports Writers Beth Harris and Noah Trister contributed to this report.