# Cubs by the Numbers: Runs Above Replacement (RAR)

Determining the value of a given baseball player has become easier and easier as metrics have improved over time. Runs Above Replacement (RAR) is a very quick way to see how much better an everyday player is than a guy coming off the bench or up from the minors.

Coming up with that number is a little trickier, but what is life about if not the journey? So lets get cracking.  First, what exactly is a replacement level player? FanGraphs defines it as: “one who costs no marginal resources to acquire.” Essentially a league-minimum player

FanGraphs takes the definition a step further though, stating that a team full of replacement level players would win 47.7 games over a full season. Basically, you could take a team of players on the league-minimum salary and reasonably expect them to win 48 games.

With that knowledge in place we can look at how RAR is calculated.

FanGraphs takes two main things into account for offense: batting and baserunning:

• Batting – amount of runs above or below average (0) that a player provides in a given season.
• Baserunning – amount of runs above or below average (0) that a player provides in a given season.

Fielding and positional average are taken into account to give a total number for defense.

• Fielding – amount of runs above or below average (0) a player is worth defensively.
• Positional Average – a value based on position; that number is then added to or subtracted from their fielding number.
• Example: first base is easier to play than shortstop, so first is worth -12.5 runs, whereas short adds 7.5 runs

These combin to give you two numbers, one for offense and one for defense.

After that, there are two more numbers that factor into the total for RAR.

• League Adjustment – a little correction so that each league’s total runs above average equal out to zero; this number is based on a players plate appearances.
• Replacement level – simply put, this is what a replacement player would do given the same number of ABs as the average player.

Example time! Anthony Rizzo’s batting runs above replacement was calculated at 36.8, but is about as average a baserunner as you’ll find, so his value there was -0.3. Do a little math, take into account some rounding and you get 36.4 RAR on offense for Rizzo.

Now let’s look at Rizzo’s fielding, where he was 7 runs above average in 2014. Given the relative ease of first base, the positional adjustment for Rizzo was -10.8.  So, in terms of overall defense, Rizzo was worth -3.8 RAR.

Next we factor in a league adjustment, which is 0.8 in this case. The final step is to add what a replacement level player would do with same amount of ABs; for Rizzo, that number was 17.4. Now we throw everything together and add it all up.

Offense (36.4) + Defense (-3.8) + League Adjustment (0.8) + Replacement level performance (17.4) = 50.9 RAR. Got it? Ok, let’s do another…Starlin Castro is next!

Castro’s batting runs above replacement was 9.6 but his misadventures on the basepaths give him a -2.7 rating, for a total offensive number of 6.9 runs above average. Defensively, Castro was -3.8 runs below average, but since shortstop is harder than most positions, we adjust with a +6.1 giving a defensive total of 2.4.

Yay, more addition! Offense (6.9) + Defense (2.4) + League Adjustment (0.8) + Replacement level performance (16.1) = 26.1 RAR for Castro, which is 2nd on the team behind Rizzo’s 50.9.

Other top performers in RAR were:

• Luis Valbuena (24.8)
• Chris Coghlan (20.5)
• Welington Castillo (20.4)