Just about every great player in modern history has played in at least one All-Star Game, as have most of the really good players and a fair number of just-OK players. All-Star rosters are huge, after all, and the rules are designed to select a wide range of players, including the lone "team representative" of some hapless organization. Over 1,600 different players have appeared in an All-Star Game since 1933, so the net has been cast pretty wide.

Still, some very good players have wriggled through, thanks to bad luck, bad karma or the bad math that rewarded less-than-meaningful statistics like win-loss record and batting average from 1933 until, let's face it, today. The guys below all played their entire career in the All-Star era, yet they somehow avoided the Midsummer Classic despite some impressive accomplishments. If you built an All-Star team around these top 10 non-All-Stars, they would beat many real All-Star teams.

10. Earl Torgeson. Most of the players on this list have several things in common. (1) Their batting averages were relatively low, which made them easy to overlook in the decades when batting average was king. (2) They played for mediocre teams: too bad for fans to notice but just good enough that the player never got a shot as the team's official representative. (3) They were square pegs who did not fit into neat slots on a ballot or warm places in a manager's mind: junkballers, utility infielders who played 150-plus games per year, ornery individualists and so on. (4) Injuries kept them from accumulating the kind of statistics that would get them noticed. (5) They were stuck at a position in the league where they had zero chance of earning the fan vote.

Torgeson was all of those things. His career batting average of .265 was low for a first baseman and easy to ignore in the 1940's and 1950's. He played for mediocre Braves and Phillies teams in his prime, only reaching the competitive White Sox late in his career. He was a bespectacled brawler who would remove his glasses before charging the mound, which would look strange now but must have been a sight to behold in 1950. He was also a big guy whose value came from walks and baserunning, but managers of the era usually stuck him in the middle of the lineup because they could not wrap their brains around a 6-foot-3 leadoff hitter. His aggressive style and personality led to numerous injuries, and he also had the occasional run of terrible luck; he once separated his shoulder after tripping over his dog.

With players like Stan Musial and Gil Hodges stomping around the league, there was little room for a big, feisty guy with glasses whose claims to fame were on-base percentage and stolen base percentage, two stats that no one would care about for another 40 years. Torgeson was a great player in 1950-51 and a very good one in several other seasons. You just had to look hard to spot him.

9. Tom Candiotti. Because there is no fan vote, pitchers have enjoyed more of an All-Star meritocracy than position players; 39-year-olds with one foot in Cooperstown don't take spots away from up-and-comers. It takes some complicated circumstances for a good pitcher to skirt through his career without earning a single selection, but Candiotti's career was full of complicated circumstances. He was a knuckleballer who (like many knuckleballers) got stuck in the minors for years and was ineffective in his first big-league stint. He wound up on the Indians during one of their all-too-typical down eras, putting up the kinds of lines that very good pitchers must settle for on bad teams (16-12, 3.57 in 1986; 13-10, 3.10 in 1989).

Candy's problems only got worse when he went to Los Angeles just in time for the Dodgers to collapse: he went 11-15 despite a 3.00 ERA in 1992, for a team that lost 99 games and had a comically terrible offense. His 151-164 career record would have looked much better on stronger teams, and he would have made a few All-Star Games if he wasn't hovering around .500 at the break in his best seasons. But then, that's been the fate of many knuckleballers.

8. Jose Valentin. Through most of baseball history, a shortstop who hit 24-30 homers per year would be a no-brainer for the All-Star team. But the late '90s and early '00s were different. Home run totals were so inflated that Valentin's figures did not stand out; his 28 home runs in 2001 only tied him for 17th in the American League.

Valentin also suffered from fates that plague many of the other best non-All-Stars. His batting averages were low, his teams weren't great enough to make him a superstar or terrible enough to make him a lone representative, and he was stuck behind legends at his position. Derek Jeter had a stranglehold on the All-Star fan vote for nearly all of Valentin's career, with the old Cal Ripken Jr. and young A-Rod also gobbling votes, and better-rounded shortstops like Nomar Garciaparra and Miguel Tejada were more likely to get the manager's selection. Still, to look at a season like 2000 -- .273-25-92, 107 runs, and 19 steals as a shortstop -- and realize that Valentin did not get a single whiff of an All-Star Game is truly mind-boggling. The American League representatives that year were Jeter, A-Rod, Garciaparra, and Mike Bordick, who was hitting .303-14-54 at the break. It was a heck of a time to be a slugging shortstop.

7. John Tudor. Tudor was 1-7 with a 3.71 ERA in 1985 when he received a tip from a longtime high school coach about a mechanical flaw in his release. Tudor adjusted, won 20 games with a 1.37 ERA down the stretch, and came in second in the Cy Young balloting while vaulting the Cardinals into the World Series. Unfortunately, the slow start denied him an All-Star opportunity, and his Game 7 World Series meltdown -- he sliced his finger open punching a rotary fan after lasting just 2 1/3 innings in an infamous 11-0 loss to the Royals -- damaged his reputation and began a long history of frequent and sometimes fluky injuries. Tudor suffered a broken leg when a Mets catcher crashed into him while chasing a foul into the dugout in 1988, and Tudor's odd delivery led to all manner of elbow and shoulder problems.

When he could pitch, Tudor was often amazing, posting ERAs in the mid-2s while coaxing grounders and fooling batters with an arsenal of off-speed pitches. Frequent trips to the disabled list, low win totals and a reputation as a bit of a handful (Whitey Herzog called him the "Cranky Yankee") made it easy for managers to overlook him when assembling All-Star staffs.

6. Garry Maddox. "Two-thirds of the earth is covered by water. The other third is covered by Garry Maddox," according to the late, great Phillies broadcaster Harry Kalas. If only the sea creatures could vote for the All-Star Game. All-Star balloting is tough on defensive wizards in the outfield: a Mark Belanger can outshine the light-hitting competition at shortstop, but all outfielders are pooled together, so the sluggers rule. Maddox batted .330 in 1976, .315 at the break, but teammate Greg Luzinski joined Dave Kingman and George Foster in the fan-selected outfield. They should have invited Maddox just to shag the fly balls those three could not reach, which was pretty much all of them.

Maddox's bat deteriorated well before his glove, so by the time the Phillies reached the World Series, he was no longer an All-Star caliber player. But as a lifetime .285 hitter with eight Gold Gloves and a little bit of pop, Maddox deserved to play in the Midsummer Classic at least once.

5. Dwayne Murphy. If Murphy did not exist, Bill James might have had to invent him for the original Baseball Abstracts. Murphy's batting averages were typically terrible (.246 career), but nearly every other element of his game was excellent, making him exactly the kind of player whose value was misrepresented by old-school stats. He had power, hitting 33 homers in 1984. He drew a ton of walks, so his on-base percentage was usually about 100 points higher than his batting average. He was a Gold Glove center fielder.

Murphy batted second behind Rickey Henderson for much of his prime, and he adjusted his approach so Henderson could do what he did best. Murphy took a lot of pitches and bunted more than a man with his power should have, but it often got Henderson to third base, leading to an easy RBI opportunity for Tony Armas or Kingman. Henderson ensured that Murphy was only the second-best outfielder on the A's for most of his career, so it was only natural that All-Star voters overlooked him. At least a generation of budding statisticians noticed him.

4. Tim Salmon. The Kingfish won AL Rookie of the Year honors with a .283-31-95 line in 1993, but the offensive surge of the late '90s suddenly made Salmon look like just another slugging outfielder, even when we has batting .330 with 34 homers. The American League roster with flooded with players like Ken Griffey Jr., Albert Belle, Juan Gonzalez, Bernie Williams and Manny Ramirez, plus established superstars like Kirby Puckett and Joe Carter who gummed up the fan vote in Salmon's early seasons.

Salmon was also a little bit of a slow starter. That .330-34-105 season in 1995 was only .291-15-47 season at the break -- darn good, but easy to overlook when balls are entering orbit all around the country. The "slow start" argument does not explain 1996, however, when he hit 22 home runs before the break, and a 13-homer June should have caught manager Mike Hargrove's attention. Salmon spent a decade waiting in line behind old-timers, one-year big-stat flukes, Yankees outfielders who could boast more wins and a wider voting base, and guys like Belle and Ramirez who were hard to root for when they weren't at the plate. If we could do the late '90s over again, we would probably find room for Salmon on a few of those All-Star rosters.

3. Tony Phillips. Phillips began his career as an ordinary utility player, then slowly grew into a sabermetrics object lesson come to life. He walked a hundred times per year, ran well and had some power. All he lacked was a natural position in the field and a consistently high batting average, but Sparky Anderson knew a leadoff man when he saw one, so he kept Phillips at the top of his Tigers lineup while shuffling him from left field to second base to third base to DH. Phillips led the league in runs scored in 1992, and he batted .313 with 132 walks in 1993, but it's hard to make the All-Star team when you don't even have a defensive position. Phillips was one of the best true utility players in major league history, but he arrived a decade early for the statistical revolution.

2. Hal Trosky. Skip Bayless would have had a field day with Trosky if First Take were around in the 1930s. (Thank heavens it wasn't; the Depression was hard enough.) Trosky was a slugging first baseman who hit .343-42-162 in his best year and had other seasons that were nearly as good, but he was also an innovator of the kind of intrigue that keeps talk shows in business these days. In 1940, he led an Indians clubhouse revolt against manager Ossie Vitt, who as a skipper appears to have been somewhere between Larry Bowa, David Brent and a rabid ferret. The press sided with Vitt, however, and Trosky became ringleader of the Cleveland Crybabies.

Trosky also often took himself out of the lineup because of migraines, a serious health problem which was not that well understood at the time. Yankees manager Joe McCarthy, who selected the American League All-Star bench most seasons, once saw Trosky lollygag through batting practice. The incident took place in May, 1938, when Trosky was hitting at least .370 and probably knew what he had to do to get ready to bat against the Yankees, but McCarthy snubbed him that year.

Controversy aside, Trosky's biggest obstacles were the facts that offensive levels were up -- his .302 career batting average is not quite as awesome as it looks -- and Lou Gehrig played the same position in the same league. If Trosky played today, his undeserved "malcontent slugger with a mystery illness" reputation might make him an ESPN daytime staple, but he would probably still squeeze his way into an All-Star Game.

1. Kirk Gibson. Gibson was almost the complete package as a player. He hit 20-something home runs per year, usually with a good batting average. He stole 20-30 bases per year and was rarely caught. He was a disciplined hitter with high walk totals. He didn't throw well for a right fielder, but that was a minor quibble. He played for some great Tigers and Dodgers teams. So how come he was never an All-Star?

The answer is simple: the All-Star Game did not snub Gibson; Gibson snubbed the game. He turned Sparky Anderson (his own manager) down in 1985, because he felt the game focused too much on individual accomplishments. He earned another invitation in 1988, his first season with the Dodgers, but Gibson was homesick for Michigan and wanted a few days with his family. Gibson was always a rugged individualist (still is), and his decisions to put team-first and family-first attitudes ahead of the Midsummer Classic resulted in a truly one-of-a-kind accomplishment. Gibson is the only player in modern times to win an MVP award, yet never appear in an All-Star Game as a player.