My one rule is that I don't include anyone who received Rookie of the Year votes:
C Jason Castro
The rebuilding Astros were terrible again in 2013, losing 111 games and finishing dead last in their first season in the American League West. But Castro, the team's lone All-Star representative, was one of their few bright spots. In his third big league season, the tenth overall pick of the 2008 draft built off a solid 2012 by hitting .276/.350/.485, good for a 130 OPS+. He showed good power, too, crushing 35 doubles and 18 home runs in just 120 games. Throw in his not-terrible baserunning (especially for a catcher) and respectable defense, and he was worth 4.5 bWAR. He's worth keeping an eye on in 2014--his age 27 season.
1B Matt Adams
The beefy slugger asserted himself while Allen Craig was out by popping 17 home runs in just 296 official at-bats. He batted a rock solid .284/.335/.503 in his sophomore season, leading Cardinals fans to wonder what kind of fireworks he has in store for 2014.
2B Matt Carpenter
Carpenter was arguably the most valuable player in the National League this season with more runs (126), hits (199), and doubles (55) than anybody in baseball. And yet, MVP voters felt Yadier Molina to be the more valuable Cardinal.
3B Josh Donaldson
Unheard of coming into the season, he was being hailed as a legitimate MVP candidate come September. He finished fourth behind Miguel Cabrera, Mike Trout and Chris Davis after leading Oakland to its second straight division title. All the 27 year-old did was hit .301/.384/.499 (148 OPS+) with 24 home runs and 93 RBI. Donaldson's potent bat combined with top-notch defense at the hot corner made him an eight-win player in 2013. Manny Machado has a case to be made as well, but we all knew he was going to be great.
SS Jean Segura
The 23 year-old Dominican emerged as one of the best shortstops in baseball. Coming off an unspectacular 45-game debut in 2012, Segura settled in as the Brewers' everyday shortstop and proved he belonged in the Show. He made his first All-Star team on the way to batting .294 with 44 steals--second only to Eric Young in the Senior Circuit. He also flashed decent power with 12 home runs, 10 triples and 20 doubles, putting together a Starlin Castro-esque season that was worth close to four wins above replacement.
LF Domonic Brown
Hailed by many during the preseason as a breakout candidate, Brown made good on those predictions in his first full big league campaign. He was named to the All-Star team after a sizzling five-week stretch from May 2nd through June 8th in which he bashed 16 home runs and drove in 36 runs over a 35-game span. May's NL Player of the Month cooled off considerably after that and was slowed by injuries as well, but still finished the season with 27 big flies, 83 RBI and an .818 OPS. The slugging left fielder needs to show more plate discipline but certainly has the potential for a 30 homer, 100 RBI season in 2014.
CF Carlos Gomez
I covered Gomez's sterling first half in June, and while he wasn't able to maintain that pace he still wound up with some pretty amazing numbers. Like his 8.4 bWAR--more than any National League position player--which he owes mainly to tremendous defense in center field as well as his excellent baserunning. With 24 roundtrippers and 40 steals in 47 attempts, Gomez was the best blend of power and speed in the game (better than Trout, Andrew McCutchen, and the next guy on this list).
RF Will Venable
It's strange to see a 30 year-old break out in his sixth major league season, but that's exactly what Venable did. He had been a serviceable outfielder for San Diego but took his game to new heights in 2013. He set career highs in numerous categories, including the three triple crown categories (.268--22--53) in what was easily his best season to date.
U Daniel Nava
Nava's incredible life story is well-known by this point, but few expected him to be much of anything for the Red Sox in 2013, let alone their best hitter outside of David Ortiz. The 30 year-old outfielder batted .303/.385/.445, posting the fifth-best OBP in the American League and forcing his way into 134 games. He was one of the most pleasant surprises on a team that exceeded everyone's expectations by winning the World Series.
SP Hisashi Iwakuma
Iwakuma took a major leap in his second big league season and his first as an everyday starting pitcher. He finished third in the AL Cy Young race behind Max Scherzer and Yu Darvish thanks to his 2.66 ERA (third among AL hurlers) and 1.01 WHIP (second) in almost 220 innings (second), a marriage of excellence and durability that was worth seven wins above replacement. More impressively, he managed to outpich star rotationmate Felix Hernandez.
SP Andrew Cashner
Following three middling seasons as a reliever, Cashner established himself as a capable starting pitcher after moving into the Padres rotation. Along with the best walk and home run rates of his career, Cashner posted a 3.09 ERA and 1.13 WHIP in 175 innings.
SP Patrick Corbin
Wasn't anything special as a rookie in 2012 but made the All-Star team in 2013 on his way to going 14-8 with a 3.41 ERA and 178 punchouts in 208.1 innings. He emerged as the ace of the Diamondbacks staff, outpitching more established hurlers such as Wade Miley, Ian Kennedy, and Brandon McCarthy.
RP Luke Hochevar
Terrible as a starter (5.44 ERA), the seven-year veteran came out of the Royals bullpen exclusively in 2013 and was one of the team's top relievers. In 58 appearances he managed a 1.92 ERA, 0.83 WHIP and 4.82 K/BB ratio. Finally realizing that Hochevar was not cut out to be a starter has to rate as one of the organization's smartest decisions in the past two decades.
RP Jason Grilli
With Joel Hanrahan gone, Grilli emerged as one of the National League's premier closers. A first-time All-Star at age 36, he saved 33 games for Pittsburgh in his first season as a full-time closer. He also posted a 2.70 ERA, 1.06 WHIP, and an outrageous 13.3 K/9 rate.