With Wednesday night’s deadline for free-agent players to accept arbitration offers from their teams, it’s interesting to see that three accepted: Designated hitter David Ortiz with the Red Sox (via the story Gordon Edes broke for ESPNBoston.com), reliever Francisco Rodriguez with the Brewers and second baseman Kelly Johnson with the Blue Jays.

You may wonder why, but keep in mind that all of the players who have accepted these offers will get raises from their 2011 pay via arbitration. The last player to go through arbitration with even the threat of a pay cut was Steve Avery in 1996; he won and got a raise despite a weak season. Also, all of them will have made this choice with a realistic expectation that they’ll make more this way than they would have through the free market.

Looking case-by-case, consider the choices involved:

Ortiz: As a DH, Papi’s problem is that there are just 14 jobs he could be considered for and not all of AL clubs are willing to spend top dollar on a 36-year-old. Obvious big spenders like the Yankees, Angels and Rangers weren’t in the mix, so the supply of teams willing to pay him a salary similar to the one he got last year was down to one: The Red Sox. Using last year’s $12.5 million salary as a starting point provides the basis for future haggling, with the Sox hoping to get a lower AAV in exchange for probably providing him with a multiyear deal. In the unlikely event they can’t sort this out, there’s always the arbitration panel -- which will give Papi a raise, incentivizing the Sox to make him happy beforehand.

Johnson: With two mediocre (or worse) seasons in his last three, you can understand why the market wasn’t clamoring to give Johnson multiyear security, let alone a raise from his 2010 pay ($5.85 million). Worse yet, his one big year in 2010 owed a lot to being able to call Phoenix home (.976 OPS in Chase Field, .754 on the road). He topped HR/FB rates of 10 percent or higher as a D-back -- something he couldn’t match as a Brave or Blue Jay. And various public defensive metrics don’t do him any favors.

So he was already a risky choice to spend major money on. Accepting arbitration sticks the Jays with giving Johnson a raise from $5.85 million, and participation in the process gives him leverage to get multiyear security. Either way, he buys time to try to put up his first good year outside of Arizona since 2008 and score a larger deal -- or settle for the fact that the market’s less profitable for him. As is, he’s more expensive than what Arizona will be paying Aaron Hill the next two years ($5.5 million per year for the next two).

K-Rod: This is just one player’s bright response to the laws of supply and demand. This winter’s overstock on established closers makes for a worse shot at getting major money, especially after many reliever-hungry teams struck early. Rather than deal with the frustrations of not being one of the top free agents this winter, K-Rod can use last year’s base ($12 million) as a starting point to make a deal. He can then head into next winter’s market with a better shot at a multiyear deal, because he’ll be competing with fewer other designated save-generators for bids. (We’ll save the madness of mistaking saves for ability for another conversation.)

For the Red Sox and Ortiz, this may not have been a perfect way to renew their relationship, but you can expect both are happy. Brewers’ GM Doug Melvin made a massively expensive mistake, pure and simple. He failed to anticipate the possibilities of what might come from this winter’s stopper-chocked market and crippled his club’s financial flexibility as a result. And the Blue Jays were undoubtedly handicapped a little bit by the fluid situation of the CBA and Type A free-agent compensation, but also by the fact that Johnson’s become a bit overrated after one big year in a bandbox.

Christina Kahl covers baseball for ESPN.com. You can follow her on Twitter.