The Detroit Tigers signed Miguel Cabrera to a massive contract extension last week. The slugger will make $292 million over the next 12 years, which is more money per at-bat than the median household income of Michigan, according to ESPN's Darren Rovell. On the surface, the deal looks overwhelmingly expensive, something many pundits have harped on over the past few days. The numbers tell a different story.

He's hardly overpaid ... for now
When his extension begins in 2016, Cabrera will have the largest average annual salary among all non-pitchers in the MLB. But that doesn't mean he's overpaid. Compared to other highly paid hitters, his contract, at least in terms of immediate value this season, is reasonable.

Data via Spotrac, FanGraphs. Chart compiled by author. *Annual average begins in 2016, when extension starts. **Annual average begins in 2015, when extension starts. ***Calculated by multiplying projected 2014 WAR (using ZiPS methodology) and the average value of an MLB win above replacement ($5.2M). For a basic explanation of WAR, read this article.

More often than not, the highest paid players appear to be overvalued. Over half of the top 20 -- those in red in the chart above -- likely won't deliver the output their salaries demand this season. And among this group, only a few look to be significantly underpaid. If Mike Trout, for example, plays as well in 2014 as he has the past two seasons, his production will be worth over $40 million!

The longer-term picture
Of course, a multiyear contract cannot be judged in the short run alone. Overpaid players like Matt Kemp, Carl Crawford, and Mark Teixeira once had lofty projections before the injury bug bit. At the age of 30, Cabrera's numbers look nice now, but what if he, too, gets hurt or experiences a drop off in performance? 

Deadspin recently attempted to find an answer.

Graph via Regressing-Deadspin, by Reuben Fischer-Baum.

As the outlet explains, it's possible that, due to age, "Cabrera will get worse ... but the price of a win will also inflate, at something like 5% per year." Thus, he's worth $213 million through 2025 under the assumption that the average cost of an MLB win is $5.2 million, something many analysts agree on. Because Cabrera will make significantly more than that -- $292 million -- from his contract, this point of view sees him as overpaid. 

On the other hand, there's reason to believe an MLB win could be worth more. Lewie Pollis of SB Nation pegs it at $7 million, and as Nate Silver recently wrote, $6.5 million is also reasonable. Deadspin's "optimistic model" incorporates Pollis' value, and if that's the case, Cabrera's production should far exceed his contract -- by about 30%.

These figures also assume a clean bill of health. While Cabrera has averaged 157 games per year since 2004 -- his first full season -- the slugger is nearly 31. And whether it's Albert Pujols or Alex Rodriguez, plenty of previously bulletproof players have experienced major, career-altering injuries in their thirties. If Cabrera misses just one full year of his deal, the numbers begin to work against the Tigers.

Going beyond the statistics
In the search to determine the true value of Cabrera's deal, two factors don't show up in the statistics: position scarcity and Detroit's desire to win.

The former is a term that appears in fantasy baseball, and it's equally as useful in the real world. Put simply, it's the idea that depending on a player's position, he may be worth more, or less, to his club.

In 2013, there were only seven truly "elite" third basemen who generated a WAR above 5.0. That same season, nearly twice as many outfielders broke the 5.0-WAR barrier. Although Cabrera moved to first base this year, he's still skilled enough to play the hot corner, a position the Tigers say he'll probably return to in interleague games. Because of position scarcity at third base then, it's justifiable to think Cabrera's production is worth more per win than the average MLB player.

Detroit's desire to win may also skew things. The team has won the AL Central in three consecutive years, but has come up short where it counts: the postseason. The Tigers haven't won a World Series since 1984, and with its roster largely unchanged -- save for a swap of Prince Fielder for Ian Kinsler -- it certainly has the chance to do it this season.

That, and one of the most supportive fan bases in the league, made it more prudent for Detroit to extend Cabrera than if he played for, say, the Houston Astros. With revenue of $262 million, the team was eighth in baseball last year according to Forbes, and home attendance ranked sixth. Cabrera sells a ton of jerseys too -- he regularly ranks among the top 15. The Tigers clearly had both the financial ability and justification to lock him up through 2025.

Image via Roger DeWitt, Flickr.

The bottom line
Baseball is back, and at least for this season, Miguel Cabrera's mammoth contract appears fair. It's always a risk to give $30 million a year to a player past the age of 30, but Detroit would've been ridiculed if they didn't lock him up beyond 2015. Because of its commitment to the slugger, the team should remain a World Series contender for years to come.

Injuries obviously happen, though, which is why playing in the American League can help the Tigers. As he ages, I wouldn't be surprised if Cabrera eventually becomes a full-time designated hitter. The model has worked well for the Boston Red Sox and David Ortiz, and it's not like fans come to the ballpark to see Cabrera play defense.

Is it a lot of money to shell out for Cabrera? Sure. Is it among the worst deals in the league? Not by a long shot.