Every AL team's best player not in the Hall of Fame -- and should he get in?

While we're stuck amid a spring and summer unfortunately free of both Major League Baseball (so far) and the Hall of Fame's induction weekend because of the coronavirus pandemic, the Hall that so many of us visit in our mind's eye whenever we take stock of greatness or look back on baseball's history is open year-round. Last week, I mused about who the next Hall of Famer for each National League team might be; now it's time to tackle the American League.

For this exercise, I've chosen one player per team, generally the most worthy pending honoree, whether he's on the upcoming writers' ballot, still active or not yet eligible for inclusion, or stuck in Era Committee limbo. For each, the idea is to choose a player who's good enough for the Hall and could plausibly wear that team's hat on his plaque; that doesn't have to be a certainty. For a few teams, finding such a player means looking at an active one who's still a ways away but has a reasonable shot at getting there.

As with most Hall-related topics, I'm consulting my JAWS (Jaffe WAR score) system, which takes the average of a player's career WAR and seven-year peak WAR (Baseball Reference version for both) for comparison to that of the average Hall of Famer at his position. I'm open to considering other factors such as postseason and historical importance, and for PED-related candidates, I'm inclined to penalize only those players whose infractions date back to the testing and suspension era (2004 onward) -- but that's not to say all voters feel the same way.

Finally, I've divided up the players into three groups: overdue (deserving players on the current Baseball Writers' Association of America ballot or likely to be on the next appropriate Era Committee ballot), on track (active or recently retired players awaiting their time on the ballot) and OK, we'll see (mainly active players who have significant work to do before they fit into the other two categories, but also some historical long shots). Within each group, I've alphabetized by the team the player is representing.