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Who are MLB contenders' most indispensable players?

David Price, right, might not be the only Red Sox pitcher -- or player -- whose absence would put a dent in the team's playoff hopes in 2017. Billie Weiss/Boston Red Sox/Getty Images

If you ask most people to name an athlete or a movie star or a president, they will be able to dig into their memories and came up with more than a name or two. Now, if you ask people to name an orthopedic surgeon, unless that person is a doctor or was recently injured, you'll get silence, a blank stare or perhaps a face full of pepper spray.

The exception: a serious baseball fan. Surgeons such as pioneering orthopedist Frank Jobe, James Andrews and Neal ElAttrache are well-known figures in baseball circles.

Why? Because Tommy John surgery has become more commonplace among pitchers today. Even if the result of undergoing the procedure on your elbow is often a lot sunnier than, say, a rotator cuff, it's bad news when a pitcher on your favorite team is making a visit to one of these famous surgeons. You go under the knife in March and your season is over.

Fortune smiled this week on David Price and the Red Sox -- for now -- as Price received the news from Andrews that Tommy John surgery isn't required at this time. Price just needs rest and a bit of care for the sore elbow rather than a knife.

Even with Chris Sale as the new hotness of the Red Sox rotation, losing Price for a season would have had a serious impact on Boston. Sure, the Red Sox have a pretty good sixth option in either Drew Pomeranz or Eduardo Rodriguez. The problem is that even with a healthy Price, those two pitchers were already projected to get a lot of innings. If Price were out, the nasty surprise is that those extra innings weren't likely to be handled by those two, but by other less desirable options such as Henry Owens or Roenis Elias or Brian Johnson or, frighteningly, Kyle Kendrick.

One of the fun things about having a projection system with a Monte Carlo simulation is that you can tinker around with a lot of scenarios. And filling in a little bit of Pomeranz/E-Rod and a little more of Owens/Elias reduces the Red Sox's probability of making the 2017 playoffs by a whopping 24 percentage points (from 83 percent to 59 percent). Just as teams that are expected to be around 80-87 wins get the most value from additional marginal wins, teams that are expected to be around 85-92 wins get hit the hardest from losses. Losing four wins drops the Red Sox back to the AL East pack somewhat, and while they still project as a strong team and the best in the division, there's no truly terrible team in the AL East. Any of the other four would have realistic odds of challenging the Red Sox if things go that way.

So how would that 24-percentage-point loss compare to other top players in baseball? To answer this, for several contenders I repeatedly simulated the 2017 season a million times with the ZiPS projections, in each instance removing a specific star player from his team and then filling in the realistic Plan B's. The loss of David Price would be one of the 10 biggest hits for a team losing a player (the eighth-worst possible loss).

I'm guessing that neither my editor nor the people reading this will let me escape without the rest of the Top 10. (Editor's note: You are correct.) Players are ranked by the change in team playoff percentage points if the team goes without that player for a whole season.

10. Jose Altuve, Houston Astros: Minus-21.2 percent

Both of Houston's star middle infielders make this list for obvious reasons. The Altuve replacement plan is likely similar to Correa's outlined below, some combination of Marwin Gonzalez and an Alex Bregman reshuffle. Altuve is projected as slightly less amazing than Correa, so he gets the lower spot here.

9. Corey Kluber, Cleveland Indians: Minus-22.7 percent

The Indians survived the loss of Carlos Carrasco and Danny Salazar for part of the 2016 season and got to the 10th inning of Game 7 of the World Series, but that doesn't mean those losses weren't an issue. If Cleveland had its full rotation, maybe the Cubs would still be trying to break their curse. Kluber is projected to be Cleveland's best pitcher -- and he's been the most durable in the rotation -- so losing him would be the Indians' biggest hit. They're likely not a 95-win team, so a whole season of Mike Clevinger, Ryan Merritt and maybe some Tim Cooney later on would have divisional consequences.

8. David Price, Boston Red Sox: Minus-24.0 percent We talked about Price above! You're not trying to skip right to the list, are you?

7. Carlos Correa, Houston Astros: Minus-24.8 percent

The Astros aren't without options if something unexpected happens to Correa. You'd probably see a lot more of Gonzalez, whether at short or third if Bregman is moved to shortstop. With Bregman at shortstop, the Astros would have the option of Yulieski Gurriel at third if they wanted to give A.J. Reed another crack at first. But even if the Astros can cobble together a 1.5-ish WAR solution, Correa is so terrific -- an MVP candidate -- that Houston's grip on the AL West in 2017 wouldn't be guaranteed.

6. Madison Bumgarner, San Francisco Giants: Minus-24.8 percent

The Giants have other stars, but Nick Hundley is at least a competent option at catcher if the team lost Buster Posey. And if shortstop Brandon Crawford went down, moving Eduardo Nunez back to short and giving Conor Gillaspie more playing time wouldn't be the end of the world. But losing Bumgarner? That could be the end of the world. The Giants' replacement plan would be more innings for Ty Blach or Matt Cain, and neither is an exciting prospect for San Francisco.

5. Noah Syndergaard, New York Mets: Minus-25.1 percent

Projected for around 84-87 wins depending on the exact assumptions of health and role, the Mets don't have a ton of wiggle room for losing one of their core, especially a starter who has a good shot at being in the Cy Young conversation. Once you get to Seth Lugo and beyond in the depth chart, the team's pitching resembles a list of busted 2012 prospects with names like Rafael Montero and Sean Gilmartin. Zack Wheeler could rescue the Mets in this situation, but after two lost years, they should be taking any contribution he makes as gravy.

4. Francisco Lindor, Cleveland Indians: Minus-25.9 percent

Lindor is as good as Correa, but Cleveland's replacement plan for Lindor would likely be far less enticing. Sure, Jose Ramirez could slide back to shortstop -- he was moved because of Lindor, not because of incompetence -- but the next move, replacing Ramirez at third, would be problematic for Cleveland. Richie Shaffer is probably a stretch defensively at third full time (ZiPS projects him at 0.8 WAR overall as a starting third baseman in Cleveland). Lonnie Chisenhall is a stretch himself, and Giovanny Urshela didn't do enough to rebound his stock from a poor 2015 stint in the majors.

3. Josh Donaldson, Toronto Blue Jays: Minus-26.8 percent

Nobody really has a great Plan B for a seven-WAR player, and the Jays are at that sweet spot where losing those wins would torpedo their odds of taking the division and even a wild card. Using Steve Pearce as a full-season replacement at third is a bit too optimistic, even though the Orioles used him creatively, and in the end the most likely result would be more plate appearances for Darwin Barney or Ryan Goins. It would be nice if Richard Urena blew through the minors and gave the Jays an interesting replacement option in the infield this year, but we shouldn't set our expectations too high (for 2017) for a player who hasn't yet been above high Class A.

2. Chris Sale, Boston Red Sox: Minus-27.1 percent With Sale, there are the same problems as with a David Price loss, with the same solutions. It's just a little more damaging because Sale is projected to be better than Price this year.

1. Mookie Betts, Boston Red Sox: Minus-27.4 percent

Betts is a legitimate MVP candidate, and while he isn't quite the player Mike Trout is, Betts is on a team with more playoff hope that could be cruelly snatched away by some villain brandishing a Snidely Whiplash/Dick Dastardly mustache. (Am I dating myself here? Yes.) The Red Sox have what should be an excellent outfield, and losing their leader would be a big hit that couldn't be replaced well by some combo of Chris Young, Brock Holt and, if the Red Sox were really unfortunate, Rusney Castillo.