Points Above Replacement Explained

A players value, based on his current performance for the season, should be defined as

 

The total number of points a team is expected to move up in the standings if the player replaces an available free-agents.

 

This is what the the player rankings aim to calculate. Obviously current performance is not equal to future performance and the rankings should only be used as guide to give value to each category. It is also a helpful tool in determining when you should accept a 2 for 1 (or vice-versa) in a trade.

Using the definition of value above, the value of a batter is

where X denotes the average production from free-agency in the category X and ΔX is the average separation in the standings for category X.

Let’s understand this formula a little better. The first term,

,

says that if Ryan Howard puts 110 RBIs for a season, but the typical free-agent valued player only puts up RBI=60 RBIs, while each team is typically seperated by ΔRBI=20 RBIs in the final standings, he will gain 2.5 points relative to someone you can pick up.

Obviously, even with the same rules, a player’s value can change from league to league, since RBI and ΔRBI are league dependent. For example, if RBI’s are very tight in a league, i.e. ΔRBI is small, RBI’s becomes an even more valuable category. Therefore, we will need to make a few assumptions so that the rankings can be applied to all leagues in the Elite Fantasy Players universe.

 

First, since it is hard to quantify the available production from free-agents we will change the definition of a player’s value to be

 

The total number of points a team is expected to move up in the standings if the player replaces the average contribution of the highest ranking starters.

 

That is RBI will now be the average RBI production for the top 156 batters Note that the top 156 batters will be determined recursively by applying these rankings until the players’ values converge. Similarly for pitchers. Later we will adjust the players’ values to more accurately reflect our original definition of replacement against free-agents.

 

Next, since the spread of a category is very league dependent, we will replace ΔX with σ_X, the standard deviation of category X over the highest ranking starters. In the end, this leads to the more technical definition of a players value in a category

 

The significance of the players production over highest ranking starters.

 

but intuitively very similar to the original definition. Under this new definition, the “average player” (for example, approximately the 78th ranked player for batters) will have a value close to zero. Free-agents will have a negative value, and since we are really interested in replacement against free-agents, we will subtract the free-agent value (about the value of 156th batter) from a players value.

We arrive at the final definition of a players value, which is very close to the original definition above,
 

The significance of the players production over the average starting player minus the significance of a free-agent player.

 

Please send me an email, or leave a comment, if you have any questions.