Which players in baseball are most important for their teams down the stretch? The answer is trickier than simply picking the league's best players, because as we head toward the final quarter of the season, half the teams are practically -- though not mathematically -- eliminated from playoff consideration. Add in a few more heavy playoff favorites -- J.D. Martinez and Mookie Betts could retire tomorrow to operate a food truck and not prevent Boston from reaching the postseason -- and you're looking only at a subset of great players who actually remain playoff-relevant.
For each team's best players, I ran the difference in postseason probability with and without the player in question, with the replacement player coming from whom the organization has on hand rather than a literal replacement-level player. This consideration is more important than it was a few weeks ago because now there is no price a contender can pay to trade for Manny Machado or Noah Syndergaard or J.T. Realmuto.
10. RHP Zack Greinke, Arizona Diamondbacks
Playoff odds impact: Adds 10.6 percent
With the Rockies showing a pulse in the last month or so and the Dodgers not falling back again despite their usual rash of injuries, Arizona's playoff hopes remain up in the air. The team quietly improved with a few moves at the trade deadline, but it still lacks enough minor league depth to fill in any holes. Losing Greinke would put a big dent in Arizona's chances, but at least the Diamondbacks still would have Patrick Corbin, Zack Godley, Robbie Ray and the shockingly decent Clay Buchholz in their rotation.
9. SS/3B Manny Machado, Los Angeles Dodgers
Playoff odds impact: Adds 10.7 percent
Machado is terrific and you might think he should rank higher, but the Dodgers are already well-equipped to handle injuries to their position players, especially after the addition of second baseman Brian Dozier. The Dodgers, of course, would take a hit if they lost Machado, but they have a strong stable of average-ish players hanging around to limit the damage to a 10 percent hit.
8. LHP James Paxton, Seattle Mariners
Playoff odds impact: Adds 10.7 percent
Five years ago, if someone told you that Felix Hernandez would be sent to the bullpen, you might have assumed that the Mariners had the greatest rotation in history if they could afford to banish King Felix. But they don't have the greatest rotation in history, and Paxton remains both their highest upside pitcher and the only one with real ace potential. With team's rotation a weakness, Seattle can't afford to be without him.
7. 3B Matt Chapman, Oakland Athletics
Playoff odds impact: Adds 10.9 percent
Khris Davis may be khrushing home runs, but Chapman is the single best player on the A's, with an OPS north of .850 and a Gold Glove-worthy performance at third. Losing Chapman would very well take the oomph out of Oakland's improbable second-half surge.
6. CF A.J. Pollock, Arizona Diamondbacks
Playoff odds impact: Adds 11.7 percent
Arizona has ample experience with losing Pollock to injury, but it's still something the Diamondbacks would rather avoid. Pollock has hit only .273/.333/.421 since returning from a broken thumb -- a shadow of the .293/.349/.620 line at the time of the injury -- but this offense still needs baseball's second-best fish-surnamed center fielder.
5. LHP Clayton Kershaw, Los Angeles Dodgers
Playoff odds impact: Adds 12.5 percent
The Dodgers have lost Kershaw before and survived, but in past years, Kershaw's absences tended to come while they sat comfortably atop the division. The Dodgers are in a real fight for their playoff lives, and while Kenta Maeda could ably fill in, that could weaken a bullpen reeling from Kenley Jansen's heart condition. And really, Maeda or any other replacement is not Clayton Kershaw.
4. 1B Freddie Freeman, Atlanta Braves
Playoff odds impact: Adds 12.8 percent
Ronald Acuna Jr. and Ozzie Albies might be the new hot names in Hotlanta, but the team's dependable fixture, Freddie Freeman, remains the most crucial Atlanta Brave. While Freeman likely won't ever hit 40 home runs, he is in his third consecutive season with an OPS+ over 150. Freeman's 156 OPS+ since the start of 2016 is the third highest in baseball, behind just J.D. Martinez and Mike Trout, neither of whom the Braves could obtain if any misfortune befell Freeman.
3. 3B Nolan Arenado, Colorado Rockies
Playoff odds impact: Adds 13.0 percent
Rockies position players have combined for 8.3 FanGraphs wins above replacement (fWAR) in 2018. Arenado and shortstop Trevor Story have combined for 8.2 of that total. Arenado is making a strong case for this year's National League MVP award, and if the Rockies were to lose him, Ryan McMahon couldn't compensate for the loss. And knowing the Rockies, they might have a significantly worse replacement in mind than McMahon.
2. RHP Aaron Nola, Philadelphia Phillies
Playoff odds impact: Adds 13.0 percent
Max Scherzer is the NL Cy Young favorite once again, but Nola has improved so much that he is a legitimate ace and a key reason the Phillies' rotation has the third-most WAR in baseball. Losing Nola would be devastating, and with it being August, there's no Jake Arrieta or Cliff Lee to fix the mess his absence would cause.
1. 1B Paul Goldschmidt, Arizona Diamondbacks
Playoff odds impact: Adds 14.7 percent
Back in May, when Goldschmidt hit .144/.252/.278 with only eight RBIs, the team went just 8-19. Luckily for Arizona, that was the first baseman's only bad month, and with Goldschmidt hitting like his normal superstar self, Arizona has gone 57-36, a .613 winning percentage. Now, Goldschmidt isn't really worth 300 points of winning percentage all by himself, but he is the key player for an offense that's simply not very good otherwise.