Recent advances in baseball statistical analysis have made it possible to assess the totality of contribution each player makes to team success or failure. Using the metric Wins Above Average (WAA)--the number of wins that the 2016 Red Sox, for example, added because they had Mookie Betts in right field, instead of an average player--the author undertakes a fascinating review of major league baseball from 1901 through 2017. The great teams are analyzed, underscoring why they were successful. The great players of each generation are identified using simple, reliable metrics--from Ty Cobb through Mike Trout, and pitchers from Christy Mathewson to Clayton Kershaw. Surprises abound. The importance of pitching is found to be vastly exaggerated. Many Hall of Fame pitchers (and some hitters) achieved immortality almost entirely on the backs of their teammates, while a few over-qualified players still await induction. Focusing on today's rosters, the WAA assessment shows that the game is threatened by an unprecedented shortage of great players.