On Sunday, Daniel Bard became a major leaguer. If he can sustain his incredible minor-league success (a 1.13 ERA, 29 strikeouts and 11 baserunners in 16 innings with Triple-A Pawtucket this year), the Red Sox prospect would represent a form of gold for a baseball organization: a young, talented pitcher who is capable of dominance while earning the major-league minimum.

Yet while Bard will earn a percentage of a $400,000 rookie salary while in the majors this year, the timing of his call-up creates at least a chance that he might start earning bigger bucks a year earlier than had he been called up a couple weeks later. If Bard were to remain in the majors all year long, he would accumulate 148 days of big-league service time this season. Presuming that he never got optioned back down to the minor leagues, he would, in all likelihood, become eligible for salary arbitration following the 2011 season.

If never sent back down to the minors, Bard would almost certainly qualify for arbitration as a “Super Two” player after 2011, meaning that his service time rank among the top 17 percent of players with at least two years but less than three years in the majors. (For a full explanation of Super Twos and salary arbitration, check Maury Brown’s fine entry on The Biz of Baseball.) This past offseason, the cutoff was 2+140 (2 years, 140 days — the amount of service time by Rockies reliever Taylor Buchholz). In the past three years, the cutoff for Super Two status has never fallen below 2+130.

If Bard ends up qualifying for arbitration one year earlier than if he’d remained in the minors for another three weeks, the implications would be potentially significant for years to come. Arbitration-eligibility can lead to significant bumps in salary. Closer Jonathan Papelbon went from making $775,000 in 2008, when the Sox had the right to assign him a contract, to a one-year, $6.25 million deal in 2009, in his first year of arbitration eligibility.

Papelbon, however, is a unique case, since his first three years as a closer were historic. More reasonable potential comparisons for Bard — assuming that he becomes an elite setup man — might be Sox reliever Manny Delcarmen and Cubs reliever Carlos Marmol, who received the highest salaries for relievers with 2+ years of service time but were not yet arbitration eligibile this year.

As a player with two years and 133 days of service time, Delcarmen just missed this year’s cutoff for Super Two status (by seven days). He and the Sox agreed to a one-year, $476,000 deal. Marmol was at 2+84, and reached agreement with the Cubs on a one-year, $575,000 deal.

Had either qualified for arbitration as a Super Two, they both almost surely would have earned more than the $1.055 million garnered by Taylor Buchholz (the member of this year’s Super Two class with the least service time). Delcarmen might have earned in the vicinity of $1.2-$1.5 million, while Marmol likely would have been pushing a bit closer to $1.5-2 million.

So, the Red Sox and Cubs each saved in the vicinity of $700,000-$1.4 million for the simple fact that their relief pitchers did not qualify for arbitration. Moreover, because of their lower base wages this year, both Delcarmen and Marmol are likely to earn less in future years than they would have had they been arbitration eligible this year, since raises are always a function of the previous year’s salary.

In all likelihood, the issue will become moot. Bard seems likely to face a bit of back-and-forth between Boston and Pawtucket going forward. That is a time-honored tradition for young players with minor-league options, no matter how talented they are: in recent seasons, Kevin Youkilis, Jonathan Papelbon, Justin Masterson, Manny Delcarmen, Jon Lester, Clay Buchholz, Michael Bowden and Jacoby Ellsbury have all shuttled between Triple-A and the majors after making their big-league debuts with the Sox. (Among current homegrown Sox players, only Dustin Pedroia received a one-way ticket to the majors and never went back down to the minors.)

Moreover, the Sox have rarely had players qualify for Super Two status. Since Theo Epstein became general manager prior to the 2003 season, the Sox have had only one player (Bronson Arroyo, following the 2004 season) who became arbitration-eligible before his third full year in the majors.

So, while Bard could, in theory, become arbitration eligible as a Super Two after the 2011 season based on his call-up date, that outcome is by no means a certainty. With a few more weeks in the minors, his first year of arbitration eligibility would be pushed back until at least 2012.