For my choice as the Red Sox most underrated player in history, I felt it necessary to select someone from my era of baseball-watching (roughly 1998-on). I certainly know my fair share about Red Sox history, but to deem a player "underrated" from an era that I was not alive would just be a foolish errand. Despite all the access to stats we have, it's hard to truly understand the perception of any given player in history, and that is a very big component in deciding whether or not someone was underrated.
In what will always be the peak of my baseball fandom, the 2003 and 2004 Red Sox seasons, we remember a lot of heroes and moments. We remember David Ortiz as an absolute legend, for his clutch moments and of course that personality. We remember Pedro's dominance, Manny being Manny, Schilling's bloody sock, and of course Dave Roberts stolen base in Game 4 of the '04 ALCS.
In my opinion the most unsung hero of that period is Bill Mueller, who played with the team from 2003-2005. Sure, it's easy to forget him. There were a lot of BIG personalities on those teams, and he was a relatively quiet guy. He almost always was batting at the bottom of the lineup, which is truly a testament to how stacked those lineups were. What makes me think of him as "underrated" is the fact that he did so many memorable things, and never seems to get enough credit for his contribution to those fateful years.
I'm going to limit myself to just a few examples of why Mueller's impact was and is so underrated.
July 29, 2003 - Bill Mueller became the only player in Major League History to hit a grand slam from each side of the plate in the same game. I know this is a very small example, as nearly any MLB player could accomplish something amazing on any given day (see: Dallas Braden), but this was just so awesome, and I'll never forget watching this in awe as a 13 year old.
2003 Batting Champion - A lot of people seem to forget that Bill Mueller (with a little help from Manny) won the 2003 American League Batting Title with a .326 average. This was while hitting out of the eight hole, with no lineup protection. Again, we had a BATTING CHAMPION hitting EIGHTH on a nightly basis, and many people don't remember that! That is the definition of underrated!
2004 ALCS - When asked what was the most pivotal moment of the 2004 ALCS, most people will instantly say Dave Roberts' stolen base. I completely understand why, because it set an entire 4-game win streak in motion. When you think of the most clutch moment, you think of the walk off home run that David Ortiz hit later in that game. What seems to be so forgotten is the fact that it was Bill Mueller who ripped the clutch single off Mariano Rivera to score Roberts and tie the game in the ninth inning. Yes, I understand how hard it is to steal a base when the entire world knew Roberts would be trying to steal during that at-bat. However, let's remember that's a guy who only got caught stealing three times in 41 attempts during the '04 regular season, running on a guy (Posada) who threw out 27% of would-be base stealers. The odds were in his favor. Mueller was facing one of the most dominant postseason closers of all time, who had a .223 BAA during the '04 season. The odds were not in his favor. Yet, he pulled off what I believe is the most underrated moment in the curse-breaking season, his game tying single up the middle to keep hopes alive. If he didn't get that hit, who knows if Mientkiewicz or Damon would have been able to get the job done, if Dave Roberts' stolen base meant nothing and the '04 Red Sox were swept. Also, many people forget that the Red Sox went on to load the bases that inning, and none other than David Ortiz popped out to send the game into extra innings.
Bill Mueller was so crucial to the Red Sox breaking the curse, and was one hell of a player both situationally and over the course of this tenure here. I can tell you that if I went up to Red Sox fans and asked them to name the most important names from those seasons, Mueller would hardly be one of the first names out of anyone's mouths. For that, I believe he is truly the most underrated Red Sox player of all time.