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.

**COUNTING STATS**

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.

Single (1B)

Double (2B)

Triple (3B)

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

**THE BASICS**

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

**DERIVATIVE STATISTICS**

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

**RATE STATISTICS**

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**

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.

Formula: (0.69*uBB+0.722*HBP+.883*1B+1.257*2B+1.593*3B+2.06*HR)/(AB+BB-IBB+HBP+SF)

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’.)*

Patrick, How about SB% and PO? Also defining the relationship or non-relationship between a CS and a PO as it relates to SB%?

Sure thing. I’ll add some more depth to the stolen base stuff.

Look, I appreciate what you guys tried to do in this article. But at the end of the day, the complicated formulas you gave are still complicated. I felt like I was back in algebra class or some other advanced mathematics class. The formulas you gave still did nothing to help me understand it. I think my brain literally just gave up when trying to read those formulas. It’s been a long time since I was in school, ok, so bear with me here: What do these symbols mean…”/” & “*” in these formulas? But the point that I’m trying to make here is that most people HATE/HATED any kind of advanced math class in school. Most normal people suck at advanced math. That’s why the simpler the better. Call it the “dumbing down” of baseball or America if you want to, I don’t really give a crap. As I said before, hits are what matters. I don’t care what kind of hits they are, just as long as they get hits (and lots of them) to drive in runs. You mentioned Billy Hamilton’s value being more important than his hitting because he excels in a couple other areas. Tell me something, how’s his “defensive runs saved” helping us when our pitchers are giving up towering moon shot after towering moon shot? How’s his ability to steal bases helping us if he can’t get on base with a hit or a walk? Ultimately, I think his lack of offense is hurting the club. Any defensive run he can save doesn’t really matter when you’re losing more than you’re winning. Tell me something else: As any Reds fan knows, last year (2015) Jay Bruce had a terrible BA. But, according to some fans, he was good in other batting statistics. So what I would like from you is an examination of Bruce’s 2015 season with the advanced stats y’all are so fond of and tell me where that ranked him in all of MLB last year and what his overall value is bcuz of those advanced stats. Also, tell me how that helped a team that lost 98 gms and why NO TEAM wanted him in the past off-season! I think that speaks volumes about Bruce’s 2015 campaign and you can’t tell me that it didn’t have something to do with his very low BA last year. I’m sorry, but I just don’t trust these “advanced stats” over the traditional (easier) stats when it comes to putting together a winning or even a championship ballclub. But please still examine Bruce’s season for me, I’m very interested in where he ranked in those advanced stats and what his overall value was to the team last year & how that helped the team last year.

/ = divide

* = multiply

Bruce had a wRC+ of 91 and a WAR of 0.1

So, it was not a great season and did not help the Reds win last year

He did have 87 RBI though, that must be a good result to some

You don’t need to know how to calculate any of the stats. The thing is to know which stats are important and which stats aren’t. All you need to know about a stat like wRC+ is that 100 is average. Better than 100 is good, lower than 100 is bad. It doesn’t take advanced math to understand that. wRC+ is much better than just using batting average because it takes into account everything that a hitter can do to help create runs. All that matters offensively is how many runs you score. This stat best examines how many runs a player helps you add.

Part of what I like to do sometimes is calculate stats on my own. But these are way to complicated for me to calculate. It’s just frustrating is all.

I’m not even sure where to start with all this…

Most of the examples you give contradict themselves… such as discussing Billy’s value by saying the Reds pitchers are bad…

This post was meant to be a reference. If you don’t need it or don’t value the information herein, fine, because you weren’t the target audience anyways.

Look, I like stats. I said that I appreciate what you tried to do in this article. But sometimes it seems as if the game of baseball is being made more complicated than it needs to be. But I do thank you for the information you provided.

Your reasoning is completely flawed. You’re saying that a player should not get any credit for what he does to help his team win, if the team is really bad anyway.

Let’s say someone like Bautista or Stanton or whoever is on a team comprised of mostly fringe major leaguers. Said player has a historic season (let’s even couch it in terms of traditional counting stats), say .360/45 HR/150 RBI. He also plays Gold Glove defense. But because everyone else was so bad, the team loses 98 games.

According to your logic, none of his accomplishments mean anything because it “doesn’t really matter when you’re losing more than you’re winning”. Or that it didn’t really “help a team that lost 98 games”.

That’s just ridiculous. Baseball is a team game, and even the best players can’t win all by themselves. But even on a bad team, a player can still increase his team’s chance of winning by his strong play. Billy Hamilton increases the Reds’ chance of winning every time he takes away a would-be extra-base hit in the gap. He increases the Reds’ chances of winning when he steals two bases and puts himself in position to score with a groundout. These plays help offset the many times he hurts the Reds’ chances of winning by striking out or popping up.

I also can’t believe you said you don’t care what kind of hits a player gets. Really? Singles and homers are all the same to you? Even though the homers will end up helping your team win many more games? If you truly believe that, then I don’t you will ever understand what actually leads to winning baseball.

Hamilton will increase his value if he can start getting more and more hits & walks and driving in runs. But you can’t tell me that every time he fails to drive in a runner in scoring position that it don’t hurt the team. Maybe those instances that he fails at the plate negates any runs he saved. That’s possibly the flip side of this whole discussion. What if it were looked at like that?

Of course Billy would be more valuable if he hit and walked more, but his overall contribution–taking into account the balance of negative and positive–is calculated. WAR? I’m new to this, too, but my understanding is that his defense and base running more than makes up for his hitting which is, maybe, showing some glimmers of improvement.

This is right. Billy’s defense and base running (mostly the former because base running rarely plays into it) have been more of a positive than his lack of hitting is a negative. These are judgments baseball teams have been making since there were baseball teams. All WAR does is try to make the calculation less subjective by attempting to quantify the run contribution of offense and run prevention contribution of defense. The accuracy of calculations is still being perfected but improving rapidly. Every major league team has a proprietary form of WAR calculation that they use for their internal decision making.

Billy saves runs with his defense. You over-simplify when you say that it doesn’t matter because the pitchers give up home runs. Of course they do, but not on every–or even a majority–of at-bats.

This is awesome! Can’t tell you the number of times I’ve tried to explain many of these stats, but simply don’t have such a solid grasp of the information.

Anyway this post can be permanently accessible through a link on the home page?

Hope you guys continue to update this page with further stats definitions as necessary.

Great job. Very informative.

One you can maybe add to the basic column is one the Reds lead the Major Leagues in this year, BISA.

Bullpen Innings Set Ablaze.

Today is Friday the 13th. What kind of bad luck will the bullpen bring into the game tonight? Give up a walk-off balk?

BISA will certainly be included in the near future. 😉

BISA is Jackie Gleason caliber funny.

I’m in Vegas today. Took over 8.5, as a hedge against BISA.

Thanks for the post. I think my biggest I struggle is keeping track of the relativity. It is hard to remember what is bad/average/good for each stat. ISO is a good example because first instinct of seeing .150 is to cringe when its really average. It gets better the more I read about them, but certainly takes some time.

+1

Patrick, thanks for doing this. Very useful! I got tired of always Googling terms when reading postings.

Great stuff Patrick!

Great article. Should be stickied if possible.

BTW, the formula for fWAR is located on the Fangraphs web site. Not sure if it is proprietary. If it is please delete this.

“WAR = (Batting Runs + Base Running Runs + Fielding Runs + Positional Adjustment + League Adjustment +Replacement Runs) / (Runs Per Win) “

If the formula is available to the public via their website, can it be proprietary?

Good point. I’m not sure all the components are available, though. Maybe they are!

Aren’t offensive and defensive WAR adjusted for the position of the player? In other words, a player at a weaker hitting position position; such as, 2B, who produces an .850 OPS would have a different oWAR than a RF with an .850 OPS.

A big part of the context of this discussion is how many stats are you looking at? If you want one stat to evaluate what kind of a year someone is having batting average tells you a lot less than wRC+. There’s nothing wrong with citing batting average to discuss a hit skill. But that doesn’t begin to cover all the offensive contributions.

In terms of being able to understand the math, I don’t really care myself. I don’t know how blood pressure readings work either but that doesn’t mean I don’t respect the bottom line.

I’ve always been WAR-skeptic, because the calculations ought to be be very, very close no matter who calculates it. They aren’t, though, which to me suggests some subjective judgment goes into how it is calculated, or how certain metrics are weighted in the calculation. I am also skeptical of reducing a player to one number, just as relying on solely on speed figures to evaluate a thoroughbred deserves skepticism.

I especially don’t like $/WAR, or any attempt to assess what a team will pay for a unit of WAR. It is way too derivative of too many other factors. The calculation of what a unit of WAR is worth is generally derived from what teams pay for free agents (plus perhaps contract extensions). But free agency is an auction, and there is an economic theory that the “winner” of an auction is actually the loser, or the fish, because he paid more for Johnny Cueto (or a painting by Monet at a Sotheby’s auction) than anybody else would pay. In baseball free agency, 29 teams didn’t want to pay what the Giants did, and the $ for WAR argument assumes that the Giants were correct and the other 29 teams were wrong in their assessment of Cueto’s worth. With almost every big contract, the team that signed the player sooner rather than later wishes they hadn’t signed him, proving that the other 29 teams were right. Pujols, for example, is an albatross.

This was a very useful post, and one that should be linked permanently for reference.

Thanks!