# Thread: Stat Question

1. ## Stat Question

I'm studying into fielding statistics lately and I'm trying unsuccessfully at finding the fielding runs formula. Does anybody know?

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3. ## Re: Stat Question

Baseball Prospectus has three similar statistics, Fielding Runs Above Average (FRAA), Fielding Runs Above Replacement (FRAR) and another version of FRAR that has a league difficulty adjustment factored in (FRAR2).

I think that the original definition of pure "Fielding Runs", which came from Total Baseball, differs from any of the versions that Baseball Prospectus uses. The Total Baseball version of fielding runs is a bit archaic in terms of sabermetric stats, and many people believe it is largely inaccurate. I got the actual definition of Total Baseball's fielding runs online from a poster on another forum ... no idea where his source site was or if he just copied it straight out of the encyclopedia ... but it seems to match what is in my copy of Total Baseball.

Hope this helps, and good luck, because it's a bit complex ...

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FIELDING RUNS The Linear Weights measure of runs saved beyond what a league-average player at that position might have saved, defined as zero; this stat is calculated to take account of the particular demands of the different positions.

For second basemen, shortstops, and third basemen, the formula begins by calculating the league average for the position:

pos .20 (PO + 2A - E + DP) league at position
AVG = ---------------------------------------
lg (PO league total - K league total)

where A = assists, PO =putouts, E = errors, DP = double plays, and K =strikeouts. Then Total Baseball estimate the number of innings for each player at each position based upon each player's entire fielding record and his number of plate appearances.

Assists are doubly weighted because more fielding skill is generally required to get one than to record a putout.

For catchers, the above formula is modified by removing strikeouts from their formulas and subtracting not only errors but also passed balls divided by two. Also incorporated in the catcher's Fielding Runs is one tenth of the adjusted Pitching Runs for the team, times the percentage of games behind the plate by that catcher.

For pitchers, the above formula is modified to subtract individual pitcher strikeouts from the total number of potential outs (otherwise, exceptional strikeout pitchers like Nolan Ryan or Bob Feller would see their Fielding Runs artificially depressed). Also, pitchers' chances are weighted less than infielders' assists because a pitcher's style may produce fewer ground balls. Thus the formula for pitchers is .10(PO + 2A - E + DP), whereas for second basemen, shortstops, and third basemen it is .20(PO + 2A - E + DP).

For first basemen, because putouts and double plays require so little skill in all but the odd case, these plays are eliminated, leaving only .20(2A E) in the numerator.

For outfielders, the formula becomes .20(PO + 4A - E + 2DP). The weighting for assists is boosted here because a good outfielder can prevent runs through the threat of assists that are never made; for them, unlike infielders, the assist is essentially an elective play, like the stolen base. Outfielders' Fielding Runs were subject to some degree of error because outfielders sometimes switch fields within a game or season (Babe Ruth, for example, was positioned in the field that required the lesser range--right field in Yankee Stadium, left field in most road parks). Also, short distances to left-or right-field walls in some parks tend to depress putout totals.

Since the third edition of Total Baseball, however, researchers there have obtained breakouts of all outfielders' games in left, center, and right fields. Center fielders now have higher ratings than they did in the first and second editions. Abbreviated as FR.

Example: Ozzie Smith in 1978.

Begin by looking at the league average - NL shortstops in 1978, had 3,191 PO, 6,199 A, 332 E, and 1,105 DP. The league as a whole had 52,000 PO and 9905 K. The AVG(POS,LG) is therefore

.20*(3191+2*6199-332+1105)/(52000-9905) = 0.0777

The Wiz in '78 played 1,327 of the 1,433 2/3 innings played by the Padres (0.926 of the total). Ozzie had 264 PO, 548 A, 25 E, and 98 DP. The Padres had 4,301 putouts as a team and fanned 744 hitters. Ozzie's FR are:

.20*(264+2*548-25+98)-((4301-744)*.0777*.926) = 31

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