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Bat 571 sez,

Bat571: So with apologies, let me bring up another comparison. Which pair would you rather have - Josh Willingham at DH and Jeter at SS, or Edgar at DH and Brad Miller or Chris Taylor at SS. Jeter was a VERY good player for many years and I wholeheartedly agree he set a standard along with Ripken on how to play. But teams found him annoying rather than fearing him at the plate, and he was not a good SS. If Edgar is not a HoFer, Jeter is certainly not an inner-circle HoFer as many are trying to portray him. Pujols, Trout, Joey Bats, Miggy, and others today are more impactful game in, game out. Worth the money, yes, but how much was the style in NY a factor?

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Jeter has what, 10% or 20% more career WAR than Edgar; he was All-Star level for quite a few more seasons than Edgar was.  

Also, from a roster-construction point of view, Dr. D puts a VERY heavy thumb on the scale for position scarcity.  Gimme a cleanup-hitting catcher or 2B over Albert Pujols any day.  I'll then be able to improve the rest of the roster more dynamically and fluidly.  The question goes beyond the 2B's stats vs the DH's stats.  Even if the DH gives you a few more runs overall, the second- and third-order roster options change.

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On the other hand, I'd take Edgar in his very peak years.  In 1995, with Griffey injured, Edgar produced a jaw-dropping 12.4 runs per 27 outs -- nine Edgars would have scored you 2,008 runs that season!  It's kind of hard to argue that Derek Jeter is worth 2,000 runs a year ... ;- )

From 1995 to 2001, Edgar's RC/27 was over 10 runs per game.  For the entire period.  This leaves us with these player-pairs:

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Three remarks:  

First, Jeter's actual RC/27 is 6.2 for his career.  Willingham's is 6.0.  We moved those two hitters up towards their peaks, without doing that for Taylor.

Second, when was the last time the Mariners got 6.5 RC/27 from a DH?!  This player-pair assumes a minor star at DH, not an average DH.  By contrast, Chris Taylor is not a minor star at SS.

Third, the Edgar-Taylor combo improves the ballclub defensively.  

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Without any doubt, I take the peak Edgar and a league-average SS over Derek Jeter and a league-average DH.  Edgar Martinez, for the 12 years between 1992 and 2003, was an OBP/PWR machine that single-handedly bestowed a powerful offense on the city.  The day Edgar stopped being Edgar, the Seattle Mariners stopped scoring runs.

I like position scarcity, but nothing's an absolute.  If you are talking about a 10 runs per game monster, I'll figure my shortstop out later, dunk you very much.  

Frank Thomas, by the way, was the most-comparable player to Edgar in that era.  The Big Hurt had a few more WAR than Jeter did.  WAR's evaluation of defensive 1B's vs DH's blows chunks, and Thomas had a few more good years than Edgar did.  The point is, a worthless defensive 1B / DH could be worth more than Jeter was, despite the position.

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Of course, Jeter had 20 years as a star, not 12.  Also, we should concede the point that Jeter was a ballplayer, as opposed to a hitter.  In my opinion, he's legitimately had a slightly better career than Edgar did.  

But:  "Please send more Edgars.  The first one hit perfect."  Given my own choice of drafting Derek Jeter's son or Edgar Martinez', I will draft the Son of Edgar.  I literally wouldn't trade you one Edgar for two Jeters.

BABVA,

Dr D