Baseball fans will gather soon in stadiums and sports bars across the country to watch Opening Day and argue the merits of player deals made during the off season. Among the questions they will debate: Are superstars worth the big salaries? And do long-term contracts help or hurt player performance?

Anthony Krautmann, an economics professor at DePaul University, and two colleagues have been pondering these questions as well, and they provide answers in two recent studies published in the Journal of Sports Economics.

Krautmann and co-author James Ciecka, also a DePaul economics professor, measured the worth of large-salaried Major League Baseball players to their teams from 2004 to 2007 in a study titled "The Post-Season Value of an Elite Player to a Contending Team," which appears in the April edition of the journal.

Their conclusion: those superstar salaries may seem bloated, but for teams with playoff potential, they are worth it.

The two researchers developed an economic model that examined the salaries of elite players (defined as hitters in the top 20 percent in terms of productivity, who get paid an average of $2.8 million more than other players) and the economic impact these players have had on the contenders they joined (defined as teams that finished within 10 games back of making the playoffs during the prior season).

"Adding a superstar on a sixth-place team may increase the team’s wins by, say, 10 games and raise the team to fourth place – but not enough to get the team into the playoffs," according to the study. But "the same superstar on a second-place team may increase wins by only, say, four games, but these four games may be enough to propel the team into the post-season. Given that the expected extra revenues associated with making the playoffs may be in the $10 to $12 million range, paying such a player an extra $2.8 million should be considered a bargain."

In another study, "The Dynamics of Performance Over the Duration of Major League Baseball Long-term Contracts," Krautmann and co-author John Solow, associate professor of economics at the University of Iowa, explore whether long-term baseball contracts without performance incentives result in player "shirking." Published in the February issue of the Journal of Sports Economics, the study expands on previous research that only examined how players performed during the season after they signed multi-year deals.

Krautmann and Solow’s research found that whether players slack off after signing depends on whether they anticipate signing future contracts.

Performance data from 527 free-agent hitters who signed contracts during 1997 to 2007 were used in the analysis. With this data, Krautmann and Solow created a model to measure expected and actual performance of players over each year of multi-year contracts, taking into account variables such as experience, injuries and positions played, as well as the prospect for future contracts.

"Our results indicate that long-term fixed-salary contracts do provide a significant incentive to shirk," the authors concluded. "When we consider players who are not expected to sign a subsequent contract, these incentives lead to a large and statistically significant reduction in performance compared to expectations. The incentive to perform well in anticipation of signing the next contract is equally large and offsetting, however, so that players who expect to sign another contract largely play up to expectations. To the extent that those players engage in opportunistic behavior, shirking effects are likely to be small and most noticeable at the beginning of the longest contracts."

Click here to access the study, "The Post-Season Value of an Elite Player to a Contending Team."

Click here to access the study, "The Dynamics of Performance Over the Duration of Major League Baseball Long-Term Contracts."