Is there a way to compare the defensive value across fielding positions without resorting to comparisons of offensive performance?
One possible way to do so is to compare the performance of a single player at multiple positions.
For example, across all seasons for which I have estimated Player won-lost records, players who played both left field and center field within the same season had an average winning percentage of 0.488 in center field and 0.510 in left field. From this, one could reasonably conclude that center field is a more difficult position to play and one could also use this difference as a basis for adjusting these winning percentages to reflect a common base.

Comparisons of this type were done for all of the infield and outfield positions. Pitchers and catchers are not considered here. In the case of pitchers, this is because pitchers virtually never play a different position. This is also true, although to a lesser extent, of catchers. More problematic, however, in the case of catchers, is the fact that the skill set needed to be a good major-league catcher isn’t really the same skill set needed to be a good fielder at any other position (the same is true to a lesser extent, of course, when comparing infielders to outfielders, and, really, is true to at least some extent in every case here).

This table is read as follows. For a player who played both first base and second base, the average winning percentage at first base is shown in the top row, 0.529 – this is the average winning percentage of second basemen when they are playing first base. The average winning percentage of first basemen when they are playing second base is shown in the first column, 0.491. In all cases here, average winning percentages are calculated as weighted averages where the weights used are the harmonic mean between the player decisions at the two fielding positions being compared.

The average “normalized” winning percentage for a player at position Y when playing other positions can then be calculated as the weighted average of the numbers down the relevant column. The weights used to calculate these averages were the number of games upon which the comparison was based, which, as noted above, was the harmonic mean of the number of Player decisions accumulated at the two positions being compared.

Doing so produces the following average winning percentages by fielding position:

This says that, on average, a first baseman amasses an average winning percentage of 0.484 at other positions. These numbers are only comparable, however, if we assume that the players being considered here are 0.500 fielders. Averaging across the rows, we can calculate the average winning percentage at first base of players who also played other positions: in this case, 0.512. Doing this for every position produces the following baseline winning percentages by position to which the above percentages should be compared:

The first set of winning percentages was adjusted via the Matchup Formula based on this latter set to ensure a combined winning percentage of 0.500 across all positions. These results are as follows:

In words, if a set of first basemen with an average winning percentage of 0.512 amass an average winning percentage of 0.484 at other positions, then we would expect a set of first basemen with an average winning percentage of 0.500 to amass an average winning percentage of 0.472 at other positions.

Based on these winning percentages, the defensive spectrum looks something like this:

The final table here compares these results with relative Fielding winning percentages implied by average offensive performances by position, which I derived in this article.

The most striking difference between relative Fielding winning percentages implied by offensive performances and those based on comparing players who played more than one position is the former results in a much wider spread of implied fielding talent across positions. There are also several differences in the relative difficulty implied by position. Perhaps most strikingly, offensive performances by position imply that middle infielders are much better fielders than center fielders.

**So, which methodology produces better results?**

For my work, I have chosen to calculate my positional averages based on relative offensive performances by position. I do this for several reasons which, I believe, make this a better choice for my purposes.

First, the mathematics here, attempting to normalize winning percentages across fielding positions, is fairly murky. In contrast, simply setting the positional average equal to the average winning percentage compiled at that position seems to me to be much cleaner and more elegant mathematically.

Second, I believe that limiting the analysis only to players who have played more than one position in the same season, as is done here, may lead to issues of selection bias. That is, we are not looking at the full population of all major-league players here – since most major-league players never played a game at shortstop, for example – or a random sample of major-league players. Instead, we are looking at a selected sample of major-league players, who were selected, in part, on the basis of exactly what we’re attempting to study: with very few exceptions, the only major-league players who are selected to play shortstop are those whose manager thought they were capable of playing a major-league caliber shortstop (and the few exceptions likely only played an inning or two in an emergency situation, so they will be weighted very lightly in the above calculations).

I think that this is probably the primary reason why the winning percentages found here are generally closer to 0.500 than those implied by differences across offensive performances. The players considered here are self-selected for their ability to play multiple positions similarly well. Truly bad players at “offense-first” positions – think Frank Thomas at 1B, Manny Ramirez in LF – are so bad that nobody would ever consider trying to play Frank Thomas at 3B or Manny Ramirez in CF. But, at the other end, great defensive players at “defense-first” positions are so great defensively that, for example, Ozzie Smith never played a single inning of major-league baseball at any defensive position besides SS; Willie Mays never played a corner outfield position until he was 34 years old.

Finally, I believe that setting positional averages based on actual empirical winning percentages is more consistent with what I am attempting to measure with my Player won-lost records. Player won-lost records are a measure of player value. At the bottom-line theoretical level, every team must field a player at all nine positions. If one team has a second baseman that is one win above average and another team has a left fielder who is one win above average, then these two teams will win the same number of games (all other things being equal). Hence, in some sense, not only is it a reasonable assumption to view an average second baseman as equal in value to an average left fielder, it is, in fact, a necessary assumption.

I explore the implications of the relative fielding numbers calculated here a bit more in a separate article.

*All articles are written so that they pull data directly from the most recent version of the Player won-lost database. Hence, any numbers cited within these articles should automatically incorporate the most recent update to Player won-lost records. In some cases, however, the accompanying text may have been written based on previous versions of Player won-lost records. I apologize if this results in non-sensical text in any cases.*

Comparisons of this type were done for all of the infield and outfield positions. Pitchers and catchers are not considered here. In the case of pitchers, this is because pitchers virtually never play a different position. This is also true, although to a lesser extent, of catchers. More problematic, however, in the case of catchers, is the fact that the skill set needed to be a good major-league catcher isn’t really the same skill set needed to be a good fielder at any other position (the same is true to a lesser extent, of course, when comparing infielders to outfielders, and, really, is true to at least some extent in every case here).

**Average Winning Percentage at Position X**

1B | 2B | 3B | SS | LF | CF | RF | |

1B | 0.529 | 0.522 | 0.542 | 0.505 | 0.504 | 0.504 | |

2B | 0.491 | 0.492 | 0.497 | 0.485 | 0.486 | 0.484 | |

3B | 0.481 | 0.496 | 0.499 | 0.480 | 0.477 | 0.477 | |

SS | 0.483 | 0.489 | 0.487 | 0.484 | 0.481 | 0.484 | |

LF | 0.487 | 0.503 | 0.496 | 0.510 | 0.510 | 0.501 | |

CF | 0.484 | 0.493 | 0.491 | 0.499 | 0.488 | 0.490 | |

RF | 0.479 | 0.490 | 0.489 | 0.494 | 0.493 | 0.506 |

This table is read as follows. For a player who played both first base and second base, the average winning percentage at first base is shown in the top row, 0.529 – this is the average winning percentage of second basemen when they are playing first base. The average winning percentage of first basemen when they are playing second base is shown in the first column, 0.491. In all cases here, average winning percentages are calculated as weighted averages where the weights used are the harmonic mean between the player decisions at the two fielding positions being compared.

The average “normalized” winning percentage for a player at position Y when playing other positions can then be calculated as the weighted average of the numbers down the relevant column. The weights used to calculate these averages were the number of games upon which the comparison was based, which, as noted above, was the harmonic mean of the number of Player decisions accumulated at the two positions being compared.

Doing so produces the following average winning percentages by fielding position:

1B | 0.484 |

2B | 0.495 |

3B | 0.495 |

SS | 0.500 |

LF | 0.491 |

CF | 0.506 |

RF | 0.495 |

This says that, on average, a first baseman amasses an average winning percentage of 0.484 at other positions. These numbers are only comparable, however, if we assume that the players being considered here are 0.500 fielders. Averaging across the rows, we can calculate the average winning percentage at first base of players who also played other positions: in this case, 0.512. Doing this for every position produces the following baseline winning percentages by position to which the above percentages should be compared:

1B | 0.512 |

2B | 0.493 |

3B | 0.491 |

SS | 0.488 |

LF | 0.503 |

CF | 0.489 |

RF | 0.496 |

The first set of winning percentages was adjusted via the Matchup Formula based on this latter set to ensure a combined winning percentage of 0.500 across all positions. These results are as follows:

1B | 0.472 |

2B | 0.502 |

3B | 0.504 |

SS | 0.512 |

LF | 0.488 |

CF | 0.517 |

RF | 0.499 |

In words, if a set of first basemen with an average winning percentage of 0.512 amass an average winning percentage of 0.484 at other positions, then we would expect a set of first basemen with an average winning percentage of 0.500 to amass an average winning percentage of 0.472 at other positions.

Based on these winning percentages, the defensive spectrum looks something like this:

1B < LF < RF < 2B < 3B < SS < CF

Several aspects of these results are noteworthy. First, the range of winning percentages is fairly narrow, outside of first basemen. The other interesting comparison, I think, is that third base appears to be a tougher position to play than second base. Bill James discusses this in his Win Shares book, where he discusses the historical shift of the defensive spectrum with second base becoming more important than third base over time. As Bill James puts it:"Third basemen need quicker reactions, since they are nearer the batter, and they need a stronger arm, since they are further from first base. Without the double play, third base is obviously the more demanding position." (The results here confirm this. Second base is, in one sense, the more valuable position, with approximately 20 percent more player decisions accumulated at second base than at third base, a difference which comes entirely from Component 7 (double plays). Yet, comparing how well fielders do when they play both second base and third base in the same season, third base is the more difficult position.Win Shares, p. 183)

The final table here compares these results with relative Fielding winning percentages implied by average offensive performances by position, which I derived in this article.

*Adjusting Fielding Winning Percentage by Fielding Position*

Position | Implied by Relative Fielding |
Implied by Offensive Performance |
---|---|---|

1B | 0.472 | 0.393 |

2B | 0.502 | 0.534 |

3B | 0.504 | 0.502 |

SS | 0.512 | 0.548 |

LF | 0.488 | 0.470 |

CF | 0.517 | 0.487 |

RF | 0.499 | 0.467 |

The most striking difference between relative Fielding winning percentages implied by offensive performances and those based on comparing players who played more than one position is the former results in a much wider spread of implied fielding talent across positions. There are also several differences in the relative difficulty implied by position. Perhaps most strikingly, offensive performances by position imply that middle infielders are much better fielders than center fielders.

For my work, I have chosen to calculate my positional averages based on relative offensive performances by position. I do this for several reasons which, I believe, make this a better choice for my purposes.

First, the mathematics here, attempting to normalize winning percentages across fielding positions, is fairly murky. In contrast, simply setting the positional average equal to the average winning percentage compiled at that position seems to me to be much cleaner and more elegant mathematically.

Second, I believe that limiting the analysis only to players who have played more than one position in the same season, as is done here, may lead to issues of selection bias. That is, we are not looking at the full population of all major-league players here – since most major-league players never played a game at shortstop, for example – or a random sample of major-league players. Instead, we are looking at a selected sample of major-league players, who were selected, in part, on the basis of exactly what we’re attempting to study: with very few exceptions, the only major-league players who are selected to play shortstop are those whose manager thought they were capable of playing a major-league caliber shortstop (and the few exceptions likely only played an inning or two in an emergency situation, so they will be weighted very lightly in the above calculations).

I think that this is probably the primary reason why the winning percentages found here are generally closer to 0.500 than those implied by differences across offensive performances. The players considered here are self-selected for their ability to play multiple positions similarly well. Truly bad players at “offense-first” positions – think Frank Thomas at 1B, Manny Ramirez in LF – are so bad that nobody would ever consider trying to play Frank Thomas at 3B or Manny Ramirez in CF. But, at the other end, great defensive players at “defense-first” positions are so great defensively that, for example, Ozzie Smith never played a single inning of major-league baseball at any defensive position besides SS; Willie Mays never played a corner outfield position until he was 34 years old.

Finally, I believe that setting positional averages based on actual empirical winning percentages is more consistent with what I am attempting to measure with my Player won-lost records. Player won-lost records are a measure of player value. At the bottom-line theoretical level, every team must field a player at all nine positions. If one team has a second baseman that is one win above average and another team has a left fielder who is one win above average, then these two teams will win the same number of games (all other things being equal). Hence, in some sense, not only is it a reasonable assumption to view an average second baseman as equal in value to an average left fielder, it is, in fact, a necessary assumption.

I explore the implications of the relative fielding numbers calculated here a bit more in a separate article.