Understanding Sabermetrics by Gabriel B. Costa, Michael R. Huber, John T. Saccoma

shutouts in a single season. Those shutouts directly contributed to their low earned run averages, which in turn correlates to a high pitching runs value.
    What about recent pitchers? Let’s compare the Cy Young Award seasons of the four winners in the American League from 2005, 1995, 1985, 1975.

     
    Table 7.4 Comparison of Cy Young Award winners
     

    At first glance, Randy Johnson’s 1995 season stands out as one in which his personal ERA was almost half of the league ERA. His winning percentage was phenomenal. However, one-third of his starts resulted in a no-decision for him. Calculating the pitching runs, we find that Johnson leads these four pitchers with a pitching runs total of 56.67. Jim Palmer’s 1975 season netted 51.32 runs, followed by Bret Saberhagen’s 1985 season (33.46 runs), and Bartolo Colon’s 2005 season (only 17.57 runs). It is interesting to see that Palmer lost eleven games but still had an ERA of about two runs per game (his ten shutouts averaged out his losses).

Fielding Runs
     
    Back to Earl Weaver’s theorem for winning ballgames. After good pitching, a team should be able to execute the fundamentals of the game. Part of that involves defense. Weaver’s Baltimore Orioles teams always had players winning Gold Glove Awards for being the best at their respective defensive positions. He and other managers would sacrifice a good bat for a good glove, especially for middle infielders. Consider second basemen Davey Johnson (3 Gold Gloves, .261 BA) and Bobby Grich (4 Gold Gloves, .266 BA), shortstop Mark Belanger (8 Gold Gloves, .228 BA), third baseman Brooks Robinson (a record 16 Gold Gloves, .267 BA), center fielder Paul Blair (8 Gold Gloves, .250 BA), and pitcher Jim Palmer (4 Gold Gloves). They all flashed their leather for the Orioles. Luis Aparicio won three of his eight Gold Gloves playing shortstop for the Orioles before Belanger came along. How does this defense transform into runs? Thorn and Palmer developed a defensive-runs formula, based on linear weights.
    What if each Gold Glove Award recipient was replaced with an average fielder who was a better hitter? How many runs might not be saved? Is the fielding percentage of a player the best measure for defensive skills? The linear-weights fielding-runs formula for second basemen, shortstops and third basemen involves calculating a league average for each position, followed by a rating for the team in question at each position. The Pirates’ Bill Mazeroski set the defensive runs record for infielders with 46.5 in 1963. The average position relative to the league, is given by

where PO = putouts, A = assists, E = errors, DP = double plays, and K = strikeouts. Then the team rating is given by
    Team Runs per position = 0.20 x [PO + (2 x A) - E + DP] team at position - Average position league x (team PO - team K)
     
    Notice that the coefficient for assists is two; assists are doubly weighted because more skill is required to get an assist than to record a putout. Individual players are evaluated by prorating the putouts. In 1971, Mark Belanger recorded 280 putouts in 149 games at shortstop for Baltimore. The Orioles as a team recorded 297 putouts at the shortstop position. Thus, Belanger would get credit for 280/297 = 94.3 percent of the putouts made at short. Using the formulas above, the Orioles shortstop rating in 1971 was 14.25 runs, so Belanger gets credit for 0.943 × 14.25 = 13.43 runs. This left Earl Weaver in a position to decide whether Mark Belanger’s glove was worth more runs than his bat. (Coincidentally, the Blade batted .266 in 1971, 38 points higher than his career average.)
    For catchers, Thorn and Palmer modified the defensive linear weights fielding runs by taking strikeouts away from the catchers’ putouts. For first basemen, double plays and putouts were taken away, as they require much less fielding skill except in an occasional instance. This leaves only 0.20 × (2 A - E) in the formula’s numerator. For