Replacement LevelFor my work, I define Replacement Level as equal to a winning percentage one weighted standard deviation below Positional Average. Separate standard deviations are calculated for players at fielding positions, players at offense-only positions (DH, PH, PR), starting pitchers, and relief pitchers. Unique standard deviations are calculated in this way for each year. These standard deviations are then applied to the unique Positional Averages of each individual player. Overall, this works out to an average Replacement Level of about 0.454 (0.463 for non-pitchers, and 0.439 for pitchers). A team of 0.454 players would have an expected winning percentage of 0.362 (59 - 103 over a 162-game season). The derivation of my choice of Replacement Level is described next.
Derivation of Replacement Level
Hitting versus Fielding
Some analysts distinguish between replacement-level hitting – the level of hitting that could be found from freely-available talent – and replacement-level fielding – the level of fielding that could be found amongst freely-available talent. The problem with this is that, except for designated hitters, a team can’t actually replace a player’s hitting and a player’s fielding independent of one another. In fact, in many cases, it’s quite reasonable to think of situations where a player’s replacement is actually better than the player he is replacing at either hitting or fielding, but is nevertheless a worse overall player. Instead, a team must make a tradeoff and settle for the replacement player who provides the best combination of hitting and fielding. Hence, in my opinion, it only makes sense to talk about replacement level at an overall level, taking into account all aspects of a player’s game: batting, baserunning, fielding, and, if appropriate, pitching.
Replacement Level by Position
Some analysts also argue that replacement level differs by position – that is, one should calculate the replacement level for first basemen differently from the replacement level for second basemen. This seems to me to be a more reasonable position and is certainly worth investigating. On the other hand, the pool of replacement third basemen is likely to overlap considerably with the pool of replacement shortstops, for example, and any possible replacement starting pitcher is likely to also be a replacement relief pitcher. Certainly, however, at a minimum, the pool of replacement non-pitchers will be distinct from the pool of replacement pitchers.
I will begin by investigating all players to get a sense of where a general Replacement Level might be. From there, I will investigate Replacement Level by position.
Replacement Player Winning Percentages
The first step, it seems to me, would be to define precisely what is meant by Replacement Level. The most obvious definition of Replacement Level to me, or, perhaps more precisely, the definition of Replacement Level which leads most obviously to a means of measuring it, would be the average winning percentage of marginal major-league baseball players.So, how does one go about determining Replacement Level?
Conceptually, I think that it is. The question, however, is where to draw the line between “roster-level” and “replacement-level”. Drawing the line at 25 players per team makes some obvious sense, of course, as (before September 1st) there are 25 roster spots per team. Of course, no team uses only 25 players in a single season. On average, for the seasons for which I have calculated Player won-lost records, the average major-league team played 39.7 players per season (which is quite a bit higher than I would have guessed). Given that, how much difference is there between, say, the 23rd player on a typical team and the 28th player on a typical team?Is this really the best way to measure Replacement Level?
|Winning Percentage||Cumulative % of|
|Roster Spot||at Roster Spot||below Roster Spot||Total Games|
Winning Percentages by PositionI noted above that some people like to calculate unique Replacement Levels by position. This is an idea worth at least examining.
|Position||Raw Wins||Adjusted Wins|
Final ResultsPutting all of this together, these results lead to my final decision to set Replacement Level at one standard deviation below Positional Average with standard deviations calculated separately for non-pitchers and pitchers. A single standard deviation is used for non-pitcher position players across all fielding positions. In the case of DH's, PH's, and PR's, however, all of their value is offensive. Hence, the overall standard deviation for non-pitcher offense is used to calculate replacement level at these positions.