At the suggestion of a few posters on Nick Kirby’s article yesterday, I decided to toss this post together to try and give a nice, easily accessible place to look up some of the advanced metrics used in some of our articles here on Redleg Nation. This can be found in many other places on the internet, as well, but you can bookmark this one to give us more page hits!
I originally planned to do this for hitting and pitching stats, but doing the hitting stats took my longer than I expected last night, and it ended up being longer than I expected, so I’ll call for another RLN writer to pick up the slack for pitching stats!
Please let me know if you find any errors or discrepancies and I’ll get them fixed up. Or if I’ve left anything out you’d like to see included.
So without further delay, let’s jump right in with the basics.
These should be second nature for every baseball fan, but for the sake of completeness we’ll include them here. Counting stats are needed to determine just about every other “advanced” stat.
Home Run (HR)
Hits (H) = 1B + 2B + 3B + HR
Base on Balls (BB, uBB)
Intentional Base on Balls (IBB)
Strike Outs (K, SO)
Hit By Pitch (HBP)
Sacrifice Fly (SF)
Sacrifice Hit (SH): These count sac bunts and balls-in-play scored as sacrifices.
Total Bases (TB) = 1B + 2*2B + 3*3B + 4*HR
Runs Batted In (RBI)
Stolen Bases (SB)
Time Caught Stealing (CS)
Runs Scored (R)
Grounded Into Double Play (GDP, GIDP)
At-Bats (AB): See *note below
Plate Apperances (PA): See *note below
Batting Average (BA, AVG)
Simply dividing the number of hits by the number of at-bats gives you AVG.
Formula: AVG = (1B+2B+3B+HR)/AB
League Average (2015): .254
On-Base Percentage (OBP)
This metric takes AVG a step further by giving a batter credit for walks and hit-by-pitches.
Formula: OBP = (1B+2B+3B+HR+BB+HBP)/(AB+BB+HBP+Sac Flies)
League Average (2015): .317
*Note: Plate Appearances (PA) versus At-Bats (AB)
PA counts every appearance a batter makes at the plate. An AB only counts hits, reaching on errors, fielder’s choices, and any out not caused by a sacrifice. Notice the denominator in the OBP formula is basically PA, but it doesn’t count sacrifice bunts since they are often used ‘strategically’ by a manager and should not count against a hitter’s personal stats.
Slugging Percentage (SLG)
SLG is a measure of how many total bases a hitter achieves per at-bat. For example, a SLG of .500 means a player averages 1 total base every 2 at-bats.
Formula: SLG = (1B + 2*2B + 3*3B + 4*HR)/AB
League Average (2015): .407
On-Base Plus Slugging (OPS)
OPS is good measure of total offensive output and is simply calculated by adding together OBP and SLG. It is widely used and is often seen as an entry-point for people to start exploring more than the traditional AVG/HR/RBI view of a player.
Formula: OPS = ((1B+2B+3B+HR+BB+HBP)/(AB+BB+HBP+SF))+((1B + 2*2B + 3*3B + 4*HR)/AB)) = OBP + SLG
League Average (2015): .722
Isolated Power (ISO)
ISO is an attempt to describe a hitter’s “power” in a more meaningful way than SLG. It attempts to do this by only giving a hitter credit for the amount of extra bases he achieves, essentially stripping out the effect singles (and the first total base in an extra base hit) have on SLG.
Formula: ISO = ((2B + 2*3B + 3*HR)/AB) = SLG – AVG
League Average (2015): .150
Walks Per Strike Out (BB/K)
This is a seldom used stat, but shows how many times a player walks for each time he strikes outs, in decimal form.
Formula: BB/K = BB/K (nice, eh?)
League Average (2015): 0.38
Walk Percentage / Walk Rate (BB%)
This shows what percentage of player’s PA end in a BB.
Formula: BB% = BB/PA
League Average (2015): 7.7%
Strikeout Percentage / Strikeout Rate (K%)
This shows what percentage of a player’s PA end in a K.
Formula: K% = K/PA
League Average (2015): 20.4%
Note: Technically, all of AVG, OBP, and SLG are “rate stats,” but I chose to include them above in “the basics.”
Weighted stats are called “weighted” because they use linear weights to determine the value of each different outcome and then aim to give credit in the proper weight to the batter. The idea of weighting is crucial to understanding advanced metrics. You can identify a weighted statistic by observing the lowercase w in front.
Let’s look at AVG as an example for why weighting is important. In AVG, which simply counts hits and divides them by at-bats, a 1B is counted the exact same as a HR. A .300 hitter in 100 AB could be a hitter who has 30 singles and 0 HR, or a hitter who has 0 singles and 30 HR. I think we all know which one has been more valuable.
So, how does one determine what each play is worth? Lots and lots of data. Statisticians have determined the overall run value of each play for a given era by examining every single plate appearance in that era and then averaging the effect of every type of play.
Weighted On-Base Average (wOBA)
wOBA is one of the best measure of overall offensive output. It gives a batter credit, using the proper weights, for everything he does. The measure is then scaled (using something called “wOBA scale”) to be similar to OBP to make it more easily understood. For example, a .400 OBP is phenomenal, as is a .400 wOBA.
League Average (2015): .313
Weights can be found here.
Weighted Runs Created (wRC)
wRC is the measure of how many runs were “created” by a player, using proper weights, during his plate appearances. It is based on the same linear weighting as wOBA and is expressed as “runs.” For example, a player with 48 wRC has “created 48 runs.”
Formula: wRC = (((wOBA – league wOBA)/wOBA scale) + (League R/PA))*PA
Each of ‘league wOBA,’ ‘wOBA scale,’ and ‘League R/PA’ change with the season. For 2016, the formula is as follows: wRC = (((wOBA-.317)/1.245)+(.113))*PA
Weighted Runs Above Average (wRAA)
Basically, this metric takes wRC and scales it so it only shows how many runs you’ve created above a league average player. So, a wRAA of 0 means you’ve been a league average hitter in terms of creating runs.
ADJUSTED AND INDEXED STATS
Some statistics are adjusted based on factors such as the ballpark being played in and the run environment of the era. This is an important step to take in order to be able to evaluate players who played in different eras, as well as being able to evaluate a player who hits a Coors Field against a player who hits a Petco Park.
Adjusted stats are denoted by the “+” at the end.
On-Base Plus Slugging Plus (OPS+)
This stat takes OPS and adjusts it, based on park and league effects, and then indexes it where league average is 100. So, an OPS+ of 155 means the hitter has been 55% better than league average at OBP and SLG combined. This stat is a mainstay at Baseball Reference.
Formula: OPS+ = 100 * ((OBP / lgOBP)+(SLG / lgSLG) – 1) / Batting Park Factor
Weighted Runs Created Plus (wRC+)
This stat is a favorite for most sabermetric-minded baseball fans. Not only does that stat use proper weighting for each individual player action, it then adjusts that number based on league and park effects, and then scales it to an easy to understand metric where 100 is league average and every point above or below 100 is 1% better or worse than league average. Since it is measuring “creating runs,” which is the goal of an offensive player, many people swear that this is the single best metric for measuring the offensive output of a player. Just a fun note… Joey Votto is tied for 15th in MLB history (minimum of 4000 PA) with a wRC+ of 155. What this literally means is that, to date, Joey Votto has been one of the 15 best hitters in the history of baseball. Of course, if he plays past 40 years of age, we’ll expect that number to come down, but it’ll still be very likely that Votto will retire as being one of the 30 or so best hitters to ever play the game.
Formula: wRC+ = (((wRAA / PA) + (lgR / PA)) + ((lgR / PA) – (Park Factor * lgR/PA))) / (lgwRC / PA [excluding pitchers])
Weights and park factors can be found here.
MEASURES OF VALUE
Value stats attempt to determine the value of a player, generally in terms of wins since wins are easily understood.
Wins Above Replacement (WAR)
WAR is a metric showing the overall value of a player across the three main facets of baseball; hitting, fielding, and base running. It is calculated by first determining the amount of runs a player provides in each facet listed above. Those runs are then compared against the run output of a theoretical “replacement-level player,” which can be thought of as those ubiquitous AAAA players who can come up and play for awhile without being too terrible, but also aren’t good options for long-term play. They also make league-minimum, usually. The idea is that these players are all over the place and easy to find. Thus, a player should not get credit for all his accomplishments, just his accomplishments above and beyond what a regular replacement-level player could do. Once the runs above replacement are determined, a “runs per win” scale is used to convert runs to wins, and you have WAR!
Important to note is that, in terms of WAR, a run created at the plate is equivalent to a run prevented on defense, or a run created on the base paths. Robbing a solo home run is literally just as valuable as hitting a solo home run. This is why WAR is such a great metric. It lets us evaluate players like Billy Hamilton, who aren’t good hitters, but provide solid overall value because they excel so greatly at the other 2 facets of the game.
I can’t provide a formula for WAR, since both FanGraphs (fWAR) and Baseball Reference (bWAR) keep their formulas in the safe.
(Formulas for all of the complicated stats are courtesy of FanGraphs. Formula for OPS+ courtesy of Baseball Reference. Most other stuff courtesy of my noggin’.)