Who is in the running for the National League MVP Award? The better question might be, "Who isn't?"
While the foremost members of the American League MVP Award field are fairly well established (Michael Trout is having the best Mike Trout season, Jose Ramirez is putting up one of the great seasons by a third baseman in history and Mookie Betts is the central figure of a Red Sox team for the ages) the NL field seems to evolve by the hour. There is a cluster of similarly strong statistical cases on the position player side and even some brewing discussion about pitchers who could contend for the honor.
Six weeks from now, some uber-hot stretch by a particular player on a team sealing an October entry could make all of this moot, but for now, there are legit MVP arguments to be made in many markets. So here's one man's ranking of the NL MVP Award field, with a quick look at each guy's case.
(All stats are through Thursday.)

1.Matt Carpenter, Cardinals
.975 OPS (2nd), 162 OPS+(1st), 157wRC+ (1st), 5.3 bWAR (tied for 1st among position players), 5.0 fWAR (tied for 1st)
You know how many qualified NL players had a lower OPS than Carpenter's .558 mark as of May 15? Just two: Lewis Brinson (.529) and Carpenter's teammate William Fowler (.551), neither of whom (spoiler alert) will be appearing on this list.

So strictly within the context of 2018, this might be the most unlikely MVP Award case of them all. And it also might be the best. As you can see, I'm putting more emphasis on advanced offensive rate stats, but do note that Carp is leading in good old-fashioned dingers (33), too. And if storyline matters to you, he's powered the Cards back into contention in the second half.
Carpenter also makes his own salsa, which should be worth like 0.1 WAR, at least.
2.Freddie Freeman, Braves
.939 OPS (4th), 154 OPS+ (2nd), 150 wRC+ (2nd), 5.2 bWAR (3rd), 5.0 fWAR (tied for 1st)
There is nothing especially unusual about Freeman's 2018. Though his batting average has never been higher (and is tops in the NL) other more meaningful rate stats like OPS, OPS+ and wRC+ are darn near identical to his 2016 and '17 seasons (the latter of which, unfortunately, was truncated due to a broken left wrist).

So it's not news that Freeman is awesome at baseball, but suddenly this season -- as a function of the Braves finally having a contending team around him -- he is a household name and prominent NL MVP Award pick. Though teammate Nick Markakis deserves some down-ballot love and Ronald Acuna Jr.'s importance becomes more pronounced by the day, Freeman probably deserves the top honor as much as anybody right now and can win it if he and Atlanta finish with a flourish.
3.Nolan Arenado, Rockies
.981 OPS (1st), 145 OPS+ (6th), 145 wRC+ (6th), 4.8 bWAR (tied for 4th), 5.0 fWAR (tied for 1st)
Arenado has finished in the top eight of the NL MVP Award voting each of the past three years, but he has never finished higher than fourth. There is a known bias against numbers accrued in Coors Field, and, anyway, Arenado wasn't helped by the fact that the Rockies' lone postseason appearance in his tenure was last year's second Wild Card slot, when his case was complicated by the historic leadoff production of teammate Charlie Blackmon (Arenado finished ahead of Blackmon but received one fewer first-place vote).

This year, Trevor Story's strong year could complicate things, though probably not to the degree that Blackmon did. The bigger issue might be the right shoulder injury Arenado has battled in recent days. But with the Rox deeply embroiled in the NL West race, Arenado is again a worthy candidate.
4.Javier Baez, Cubs
.896 OPS (7th), 130 OPS+ (13th), 132 wRC+ (tied for 13th), 4.8 bWAR (tied for 4th), 4.2 fWAR (tied for 5th)
Baez has been the most valuable everyday player on a first-place Cubs team, and his WAR total helps reflect the value of his defensive versatility and 19 steals.

But Baez has a .325 on-base percentage that drags down his overall offensive profile relative to the rest of the league. The only time in the past 40 years that a position player won the MVP Award with an OBP below .350 was Andre Dawson in 1987. He, too, was a Cub, so maybe there's some cosmic symmetry there, but Baez would still appear to have his work cut out for him if the usual standards are applied here.
5.Paul Goldschmidt, D-backs
.920 OPS (6th), 137 OPS+ (9th), 145 wRC+ (5th), 4.1 bWAR (tied for 6th), 4.2 fWAR (tied for 5th)
Like Carpenter, Goldschmidt has asserted himself with an in-season surge (his OPS bottomed out at .675 on May 22), and he comes with the added pedigree of three prior top-three NL MVP Award finishes. This past year, his case fizzled when he played through a right elbow injury and had a miserable September (.555 OPS). This year, Goldy seems poised for a much more robust finish, and the D-backs could win the NL West.

Maybe Goldschmidt will finally get over the MVP Award hump, though teammate David Peralta might sap some of his vote strength.
6. (tied) Max Scherzer, Nationals; Jacob deGrom, Mets; andAaron Nola, Phillies
Scherzer: 2.19 ERA (2nd), 0.88 WHIP (1st); deGrom: 1.81 ERA (1st), 0.97 WHIP (2nd); Nola: 2.28 ERA (3rd), 1.00 WHIP (3rd)
The stars don't always align for a pitcher to win the MVP Award, but this could be one of those years in the NL.
As you can tell from the length of this list, nobody on the position-player side is up and running away with this thing, and that could continue to be the case down the stretch. Voters are increasingly turning to WAR as a basis for their MVP Award argument, and as of this writing, these three hurlers all outpace every NL position player in bWAR (the same is true of Scherzer and deGrom in fWAR, though Nola is behind some position players -- as well as D-backs lefty Patrick Corbin -- in that FanGraphs calculation).

Therefore (and without getting too deep into the statistical woods here), it is conceivable.
But unlike when Clayton Kershaw won the NL MVP Award in 2014 or Justin Verlander won the AL MVP Award in 2011, the Cy Young Award winner here is not clear-cut (both of those guys were unanimous Cy Young Award winners in those respective seasons). deGrom is outpacing Scherzer in ERA and adjusted ERA, but he has famously won just seven games. Scherzer could notch 20 wins and 300 strikeouts. Nola probably trails both of those guys in the Cy Young Award discussion, and yet, for those who place importance upon October entry, he might actually be more likely to garner MVP Award votes (the Phils don't have a legit MVP Award candidate on the position-player side).

So as if the position-player race for the NL MVP Award weren't confusing enough, here's another layer of complexity. Yes, a pitcher could win this MVP Award, but even if you get to the point where you're comfortable with that notion, you've still got to decide which pitcher. So I'd label it doubtful right now.
9. Lorenzo Cain, Brewers
.814 OPS (25th), 118 OPS+ (tied for 22nd), 123 wRC+ (tied for 19th), 5.3 bWAR (tied for 1st), 4.3 fWAR (4th)
Teammates Jesus Aguilar (.950 OPS, 149 OPS+) and Christian Yelich (.886 OPS, 3.6 fWAR) also have a case here. But Aguilar's WAR is dinged by his defensive positioning, and Yelich is an easy-to-underrate player who is good at pretty much everything but not superlative in any one category.
In the increasingly influential community of nerds (and I use the term lovingly), Cain's case seems to have the most traction. You can see here how he fares in the WAR tallies, and he's among the league leaders in average (.301), on-base percentage (.391) and steals (21), in addition to leading in defensive runs saved (17). But Cain's .423 slugging percentage would be the lowest for an MVP Award winner since the 1970s. How much should defensive value, which is so difficult to quantify correctly, matter in the MVP Award vote? Hard to say.

10. Eugenio Suarez, Reds
    .930 OPS (5th), 147 OPS+ (5th), 145 wRC+ (tied for 5th), 3.8 bWAR (8th), 3.6 fWAR (tied for 9th)
    This guy has been the best of the non-contending position players in the Senior Circuit (though that's actually a small pool, given how many NL teams are very much mathematically alive). While voters have finally softened the once-prominent stance that the MVP Award must come from a playoff club, Suarez has not attained the Trout-like transcendence required to overcome his club's well-south-of-.500 standing. Still, he's positioned himself in the conversation for a top-10 finish with a well-rounded campaign, as reflected in his rank in several key categories.