What will Dodgers and Angels do in free-agent market?

The absurdity of baseball’s year-round calendar was abundantly clear Tuesday, when almost a million people jammed the streets of Kansas City for the parade and rally that celebrated the Royals’ World Series championship.

The masses waved at all their Royals heroes — including infielder Ben Zobrist and pitchers Johnny Cueto, Ryan Madson and Chris Young, who technically were no longer members of the Royals.

Free agency starts on the day after the World Series ends. Zobrist, Cueto, Madson and Young are among 157 free agents, a pool large enough for every team to sign five players, with some left over, and there are more free agents to come as teams continue to make personnel decisions.

Free agents can sign as soon as 9:01 p.m. Pacific time Friday. Baseball’s general managers — and presidents of baseball operations — meet next week in Florida, the unofficial start to the Hot Stove League.

A look at some possible off-season moves involving Dodgers and Angels:

Who will sign Zack Greinke?

Greinke is the rare free agent who will have as many questions for a team as the team will have for him. He’ll want to know about your plans to win now and win later, and he might know almost as much about your farm system as you do. When he met with the Dodgers, he mentioned how he liked their first-round draft pick that year, an infielder named Corey Seager.

Greinke is a terrific athlete, a strong fielder — and a good hitter who likes to take his cuts, which gives National League teams an edge. As favorites, we’ll go with the Chicago Cubs, who have an unrivaled collection of young talent among position players, plus Jake Arrieta and Jon Lester to share the pitching spotlight. Other teams that might interest him: the St. Louis Cardinals, Washington Nationals, San Francisco Giants and Boston Red Sox.

The wild cards: the Arizona Diamondbacks, where Paul Goldschmidt and A.J. Pollock arguably are better position players than anyone the Dodgers have to offer, and the Miami Marlins, now managed by Don Mattingly. Greinke lives in Florida, but he probably is too smart to buy any pledges of long-term stability and success offered by mercurial owner Jeffrey Loria.

Could Greinke stay in L.A.?

Absolutely. Greinke, 32, liked playing for the Dodgers, and opting out of his contract simply allows him to negotiate with 30 teams instead of one. That said, the Dodgers declined to discuss an extension with him last winter.

The Dodgers remain wary of committing long term to players into their late 30s, not so much because of the money — it would be disingenuous of a team with an $8-billion television contract to complain about $50 million at the end of Greinke’s contract — but because suitable replacements are usually not available when a star player breaks down in the middle of a season.

What about Greinke’s elbow?

The Angels had some concerns about Greinke’s elbow and did not seriously try to retain him after the 2012 season, when Greinke signed with the Dodgers and the Angels spent the money on Josh Hamilton. Greinke missed time during spring training in 2013 and 2015 so he could tend to his elbow, and a sore elbow delayed one of his 2014 starts by two days.

Nonetheless, in his three years with the Dodgers, he pitched 602 innings. None of his three career stints on the disabled list were the result of an arm injury: He got treatment for a social anxiety disorder, fractured a rib playing pickup basketball, and suffered a broken collarbone when Carlos Quentin charged the mound and threw him to the ground.

If the Dodgers don’t get Greinke, then what?

The free-agent market is flush with starting pitchers, and the Dodgers probably should sign one even if they bring back Greinke. Their rotation right now is Clayton Kershaw and Alex Wood, with hope for the rehabilitation of Hyun-Jin Ryu and Brandon McCarthy and the development of Julio Urias and Jose DeLeon. That’s a lot of hope for one season.

The head of the free-agent class, aside from Greinke: David Price, followed by Cueto and Jordan Zimmermann. The options beyond are solid and plentiful: Brett Anderson, Bartolo Colon, Marco Estrada, Doug Fister, Yovani Gallardo, J.A. Happ, Scott Kazmir, John Lackey, Mike Leake, Jeff Samardzija and Chris Young. At the trade deadline, when the Dodgers needed one top-flight starter, the team instead opted for two lesser starters, Wood and Mat Latos.

The Dodgers might be able to get, say, Gallardo and Estrada for the same money as Greinke or Price. They said the issue in not trading for Price, Cueto or Cole Hamels at the deadline was a reluctance to surrender top prospects, and no prospects are required to sign free agents.

Which pitcher should the Dodgers seek?

Right-handed reliever Darren O’Day, 33, has pitched 68 games in each of the last three years, and 69 the year before that, with these earned-run averages: 2.28, 2.18, 1.70 and 1.52.

He could secure the eighth inning — no one has done that for the Dodgers since Brian Wilson did for two months in 2013 — and his sidearm delivery would be a nice change of pace between the power arms of Chris Hatcher and closer Kenley Jansen. The Dodgers finally could take the ball from Kershaw in the seventh inning without holding their breath.

What about the Angels?

They should be interested in all the best pitchers. Their current rotation is the opposite of the Dodgers’ rotation: nice depth, no ace. But the Angels’ list of needs is so long — an ace, a second baseman, a third baseman, a left fielder, a catcher — that spending the kind of money necessary to get the likes of Price or Greinke might preclude an upgrade in other areas.

The Angels have in-house options, if unproven ones, at every position but left field. That position happens to be stacked in the free-agent market, with Yoenis Cespedes, Jason Heyward and Justin Upton as headline options. The best fit for the Angels might be Alex Gordon, a spectacular defensive player. A run saved is just as good as a run scored, and an outfield of Gordon, Trout and Kole Calhoun would be a huge help to fly-ball pitchers Andrew Heaney, Hector Santiago and Jered Weaver.

Gordon bats left-handed. Someone ought to, in order to balance the right-handed Mike Trout, Albert Pujols and C.J. Cron. It sounds a bit rich that a left fielder who has never hit 25 home runs and has a career batting average of .269 could command $20 million a season, but that’s where the market might go for Gordon. The greatest risk in a free-agent signing for the Angels might be forfeiting the first-round draft pick they desperately need to rebuild a farm system lacking in position player prospects.

bill.shaikin@latimes.com

Twitter: @BillShaikin

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