Sports Info Solutions has made updates to its Defensive Runs Saved stat which can be found on Fangraphs stats pages. The following article is a comprehensive look at the changes they’ve made.

Prior to the 2020 MLB season, Sports Info Solutions (SIS) announced major upgrades to its flagship defensive metric, Defensive Runs Saved (DRS). These upgrades centered around the incorporation of infielder starting positions in the calculations and the improvements that were consequently able to be made.

Knowing where infielders started on the play allows us to separate out their Positioning from their other contributions on a play, namely their Range and their Throwing. Therefore, the new system is called the PART System, which stands for Positioning, Air balls, Range and Throwing. It is currently referenced as rPM on player, team, and leaderboard pages on Fangraphs.

The PART System has replaced the Range and Positioning System (formerly known as the Plus/Minus System) as the primary component of DRS for infielders for all seasons since 2013. (Outfielders will continue to be evaluated using the Range and Positioning System.) This article focuses specifically on this new component, although further explanations and descriptions for the others can be found in the original DRS Glossary entry or at FieldingBible.com.

The PART System

At its core, the PART System’s goal is to split a fielder’s contributions into its individual components. This differs from its predecessor, which calculated and reported a fielder’s positioning, range and throwing contributions as a single number.

One of the primary reasons for the development of this new system was the massive increase in shift usage in recent years, since DRS had not included shift plays in its analysis of players before this update. In 2010, less than 2% of all balls in play featured a shift being employed by the fielding team, per SIS charting. In 2019, that number was over 40%.

In 2012, SIS realized that this increase in shifts was skewing individual player numbers—the example cited was Brett Lawrie, a third baseman who was often stationed in short right field when the team shifted its fielders. Because of this, he was making plays in “zones” that no other third baseman could and receiving tremendous amounts of credit as a result. At the time, the solution was to eliminate these shift plays from consideration when evaluating a fielder’s contributions, and instead calculate Shift Runs Saved at the team level. In an era where shifting was still a rarity, this decision made sense, but now that teams are shifting on nearly half of all balls in play (and showing no signs of slowing down), a different approach has become necessary to continue accurately and completely evaluating players.

This new approach is the PART System. Rather than exclude plays where fielders are lined up dramatically differently from a traditional alignment, the PART System is able to handle these plays by incorporating the fielder’s starting position into the calculation of his Runs Saved on the play. Thus, what was becoming a large gap in individual player defensive evaluation has effectively been filled, all the while opening the door for greater and more in-depth analysis.

Positioning and Shifts

The PART System utilizes the starting positioning data collected by SIS to separate a fielder’s positioning from everything else they do on the play.

The primary benefit of this is that players can be credited for what they can actually control. Positioning has been effectively removed from a player’s DRS total on the premise that teams now control where a player is standing more than the player does. Whatever credit the fielder may receive or lose on a play is based on where they were standing when the ball was hit, rather than simply assuming they were standing in a traditional starting location.

Positioning, while removed from players’ DRS totals, is still aggregated and accounted for on the team level. Each team is now credited with a certain number of Infield Positioning Runs Saved, which is composed of the team’s positioning on both shifted and unshifted plays.

Speaking of shifts—until this update, SIS had not included plays where the defense was shifted in its evaluation of individual fielders. This was because, in shifts, fielders could be positioned in vastly different locations than they would be in a standard alignment and therefore receive large amounts of undue credit for making plays that no other player at the position even had a chance of making.

Fortunately, this is no longer a concern with the introduction of the PART System. No plays are excluded from the calculation, and, because the players’ positioning is used to determine the amount of credit they receive, “The Lawrie Problem” is a non-issue. If the ball is hit at or near the fielder, they will receive a lower amount of credit than if it is hit far away, regardless of where they were standing at the time of the pitch.

Despite the inclusion of plays classified as shifts in player evaluation, SIS continues to estimate the number of runs each team is saving using the shift. In fact, the new calculation more accurately measures how many runs were saved by shifts independent of the quality of fielders who were in the field at the time. The new Shift Runs Saved, which is a subset of Infield Positioning Runs Saved, only takes into account the team’s positioning on shifts, as opposed to the previous version of Shift Runs Saved that could not make a distinction between the team’s positioning and the fielders’ out-converting abilities.

Air-Range-Throwing Breakdown

So far, Positioning is the only component of PART that has been discussed. The other components—Air, Range and Throwing—are what actually comprise each player’s ART Runs Saved total, the component that is replacing the former Range & Positioning Runs Saved in the new version of DRS.

Range is perhaps the most intuitive of the three, although there is still some clarification needed. In this system, range represents a fielder’s ability to reach a batted ball in an efficient and timely manner. If a fielder reaches a ball that no one else would’ve, they will receive positive range credit. However, if they fail to reach a ball, or take longer than expected to reach it, they will receive negative range credit. It’s also worth specifying that, because of the way SIS data is collected, range is only concerned about when or if the fielder touches the ball, not whether they field it cleanly.

Everything that happens after the fielder touches the ball is considered part of the Throwing sub-component, which, obviously, means that the name is vastly oversimplified.

This means that on a given play, a fielder might receive Throwing credit despite not throwing the ball at all, a typical example being a fielder who steps on a base for a putout. It also means that, when a throw actually is made, this sub-component measures the fielder’s ability to field the ball cleanly, plant their feet (or not) and fire a ball quickly and accurately to whomever is receiving the ball. Ideally, each of those would be measured individually sometime in the future.

Last, and probably least, is Air. As of this writing, SIS only collects infielder starting positioning data on all groundballs and short line drives (GSL). Therefore, the PRT sub-component splits only apply on those types of balls in play, which, in fairness, make up approximately 80% of all balls fielded by infielders. On the other ~20% of non-bunt balls in play fielded by infielders—composed essentially of bloops and popups—any credit or debit a fielder earns on a play will apply toward their Air Runs Saved. Because SIS does not record infielder starting positioning on these plays, non-GSL plays in which the defense is shifted will continue to be excluded from a player’s DRS total.

When combined, a player’s Air, Range and Throwing runs saved will comprise their ART Runs Saved. Each sub-component is reported separately over at FieldingBible.com to allow for the comparison of individual skills and attributes of various players.

Directional Ability

Another upgrade comes in the form of evaluating a player’s ability by direction. Because a player’s starting positioning was not known in the previous system, this could only be done in terms of where a fielder was traditionally positioned. For example, a third baseman could be judged on plays down the line, in the hole, or straight on, but on a ball considered “straight on”, there’s no guarantee that it was actually hit at them. If the fielder was positioned close to the line, the ball would have been to their left; if they were positioned in the hole, it would have been to their right. While the breakdown was useful, especially in understanding how fielders were positioned, it did not accurately reflect a player’s ability to field balls in particular directions.

That is no longer the case thanks to the starting positioning data. Knowing where the ball traveled in relation to where the fielder started the play allows for evaluation of a fielder based on what direction they had to move to field the ball.

For each of the three directional groups, a fielder is compared against others at their position in terms of both Plays Above Average and Runs Above Average (or Runs Saved). Again, these numbers are reported at FieldingBible.com for those who wish to view them.

Evaluation of Multiple Fielders on a Play

Knowing where each fielder started on a play allows for an additional benefit: the evaluation of multiple fielders on a play. Under the Range and Positioning System, and by most if not all other public defensive metrics, if a team successfully records an out on a play, the fielder who recorded the assist or putout is given credit and every other player on the field receives nothing. Usually, this is a fair thing to do. Most plays will only feature one relevant fielder who should be credited or debited. But what about the cases where that’s not appropriate?

Consider a ball that is hit in the third base-shortstop hole, directly between the two fielders. The third baseman, who was positioned shallower than the shortstop, goes for the ball, but it gets by him. Behind him, the shortstop fields the ball and throws it to first for the out.

In any other defensive system, the shortstop would get credit for making the play, and that would be that. But why should that be it? We know the third baseman had a chance of making the out himself—in fact, we know exactly how likely he was to make the out. If there was an inferior shortstop behind him, the ball might have made it to the outfield, or the shortstop might not have gotten the throw to first base in time. The third baseman’s credit on the play is determined by something completely out of his control—the quality of his teammate.

The PART System offers a solution to this. By knowing where each player started on the field, it can assess multiple fielders on the same play under the assumption that fielders who are positioned shallower (closer to home plate) are able to act on the ball before fielders who are positioned deeper (further away from home plate). In this example, not only would the shortstop be given credit, but the third baseman would also be debited for having failed to make the play himself.

Right now, this assessment of multiple fielders is only utilized on plays where the defense is shifted, although that may be changed in the future. This was done to keep players’ unshifted DRS as similar as possible to how it was being reported previously (at least methodologically—obviously, excluding positioning from DRS is still a major change). On plays where the defense is not shifted, fielders are less likely to be standing close to each other anyway, so it’s unlikely that a play would occur where two or more fielders both have a non-insignificant chance of making an out and therefore unlikely to matter as much. That said, this is an area that SIS expects to research heavily in the coming months as more upgrades are made to the PART System, especially as it pertains to fielders deferring to their teammates on balls either of them could field.

How the Numbers are Changing

Understanding how the PART System differs in its evaluation of players from the Range & Positioning System is difficult. To show how two systems relate, let’s use Javier Baez as an example.

Using the Range & Positioning System, Baez saved 15 runs in 2019, good for third among shortstops. Using the PART System, he saved 26 runs, tied for first among shortstops. So where did those 11 runs come from?

To keep things as simple as possible, instead of looking at total DRS—which includes things like Double Play Runs Saved and Good Fielding Play Runs Saved, for example—just Baez’s Range & Positioning Runs Saved and PART Runs Saved will be looked at. In 2019, Baez saved 8 and 19 runs, respectively, by those components of DRS. The 11-run difference is still there. That’s important to note—this singular component of DRS is the only component that’s changing. All the other components are staying the same.

But anyway, the 11-run difference: On plays where the Cubs didn’t use a shift in 2019, the Cubs’ positioning of Baez cost the team one run. That’s part of the difference—PART Runs Saved doesn’t count that against him, unlike the Range & Positioning System. Secondly, Baez saved 10 runs with his range and throwing on plays where the Cubs were shifted. Again, those plays weren’t included in his Range & Positioning Runs Saved total, but they are included in his PART Runs Saved total.

Now to add the numbers back together. Baez is given back the one run his positioning cost the Cubs, since the PART System does not credit or debit fielders for their positioning. Starting from his eight Range & Positioning Runs Saved, that brings him to nine. Then, adding the 10 runs he saved when the Cubs were shifted brings him to 19 runs saved, the exact number that the PART Runs Saved System awarded him.

To summarize:

Range & Positioning Runs Saved – Non-Shift Positioning Runs Saved + Shift ART Runs Saved = PART Runs Saved

Now, I’ll admit I cherry-picked this example and this will not work out as nicely as it did for Baez for every fielder. Because there were other small improvements and bug fixes made as part of this upgrade, this math won’t add up exactly for everyone. But it’s close. Using the above equation for every infielder (excluding pitchers and catchers) who played in 2019, the average of the absolute values of the differences between the left-hand and right-hand sides of the equations was 0.58 runs. So, if you’re confused about how a player’s PART value was determined, using that equation will get you almost entirely the way there.

Here are the players who changed the most between the two systems in 2019:

Context

The scale for evaluating players’ DRS hasn’t changed much with the update. The same tiers that had been used with DRS still applies to the new totals. As a reminder, those tiers are:

Methodology

While it may seem much more complex, in reality, the PART System is not that much more complex than the Range & Positioning System. Both rely on the Plus/Minus technique, where credit is given or taken away based on how difficult of a play it was for the fielder. For example, imagine a batted ball with a given velocity and spray angle. Past balls in play with similar characteristics were turned into an out 60% of the time. If the fielder ends up making the play, they would receive 0.4 plays worth of credit (1.0-0.6); if they don’t make the play, they would be debited 0.6 plays (0.0-0.6). In this way, fielders get credited more for making more difficult plays and credited less for making easy plays. An average fielder would then save a net of zero plays for the season.

The difference with the PART System is that it uses the Plus/Minus technique for three different components: Positioning, Range and Throwing (as noted above, Air Runs Saved is an independent calculation). To do this, three different Out Rates must be calculated:

A – The chance that the play will be made given only information about the batted ball (trajectory, location, and velocity) and the batter (speed)

B – The chance that the play will be made given information about the batted ball (trajectory, location, and velocity), the batter (speed), and the initial positioning of the fielders relative to the ball in play

C – The chance that the play will be made at the point that the fielder obtains the ball given the distance he has to throw and how long he has to complete the play before the batter/runner reaches safely

Combined with this is a variable (here referred to as D) that is set to either 1 if the fielder made the play, or 0 if they did not. With those Out Rates in hand, determining how much credit to assign to each component is simple subtraction:

Positioning          = A – B

Range                    = C – B

Throwing             = D – C

An example may help to make things clearer. Take a groundball hit up the middle over the pitcher’s mound, just barely on the third base side of the field. The majority of shortstops wouldn’t make this play given where they would usually be standing, so Out Rate A is low, say 0.2.

However, the shortstop in this instance was positioned well, and so they only have to move a few feet to field the ball. Given that it’s a relatively easy play when the fielder’s position was known, Out Rate B is reasonably high—let’s say 0.7. In other words, 70 percent of shortstops make this play when they’re standing where this one was in relation to where the ball was heading.

This shortstop has particularly good instincts (we’ll call them Ambrelton Timmons) and they get to the ball quicker than an average shortstop would. Because of the extra time afforded to the shortstop to get the ball to first base, their expected out rate makes another jump—Out Rate C is then 0.9. And, predictably, the shortstop makes the out, so D is 1.0.

On this play, here’s how the shortstop’s credit would break down:

Positioning          = 0.7 – 0.2 = 0.5

Range                    = 0.9 – 0.7 = 0.2

Throwing             = 1.0 – 0.9 = 0.1

Of course, those components are all still in the units of plays saved, and they still have to be converted to runs. But that right there is the essence of how the PART System works. Instead of receiving 0.8 plays’ worth of credit (1.0 – 0.2), the shortstop here would only receive 0.3 plays’ worth of credit (1.0 – 0.7), split between range and throwing. Of course, it’s actually slightly more complicated than that.

One adjustment that needs to be made is for poorly positioned fielders on plays where the team was well positioned. The most common example of this is a play in which the team in the field is employing a shift—the second baseman moves over to short right field, and the shortstop moves over to the right-hand side of second base. On a ball hit to the shortstop, the second baseman would initially be determined to have been positioned poorly. While a traditionally positioned second baseman may have been able to make the play, the one in this example had no chance because of their positioning in shallow right field. However, the ball was hit straight to the shortstop, so the team was still positioned well.

To account for this, adjustments are made such that no fielder can receive negative positioning credit when their team is positioned well, and no fielder can receive positive positioning credit when their team is positioned poorly.

The other primary adjustment, at least on shift plays, arises from the fact that multiple fielders are assessed on each play. When a ball is fielded by a shallower fielder, the deeper fielder’s range obviously should not be penalized, as it was impossible to know if he would have made the play or not. So, on shift plays, any fielder who was positioned deeper than the one who first touched the ball will not receive any range credit or debit.

Furthermore, the fielder that first touched the ball on these plays will “steal” the out rates from those behind them. This is done to prevent players from being over-credited when they make a play that would have otherwise been easy for the fielder behind them. For example, on a routine grounder to the shortstop, the third baseman decides to instead cut the ball off and make the play himself.

The third baseman may have had a low chance of converting the out, but they would not receive credit as if it were a difficult play because it was not, at least for the team. Whatever the shortstop’s expectation of making the play was would be added to the third baseman’s, and the third baseman’s range credit would then be determined based off that new expected out rate. If the third baseman’s initial out rate was 0.05 and the shortstop’s was 0.90, the third baseman would be debited 0.95 plays’ worth of credit.

Conclusion

The PART System has replaced the Range & Positioning System in DRS going back to 2013, the first year for which SIS collected the infield starting position data. Going forward, SIS will continue to make improvements to the PART System and DRS as a whole as it continues to strive toward its goal of being at the forefront of defensive analytics.

Most Important Takeaways

• Positioning is no longer factored into a player’s Defensive Runs Saved total

• This system allows for the evaluation of all infield plays, not just ones involving an unshifted defense

• Transition from evaluating: “How often did a player make that play?” to “How often did a player make that play given where they were positioned?” with the PART System

• The result is a more accurate overall depiction of defensive performance

This article is adapted from The Fielding Bible – Volume V. For more information on this stat, check out FieldingBible.com

One of the hallmark statistics available at FanGraphs is Wins Above Replacement (WAR) and we’ve just rolled out an updated Library entry that spells out the precise calculations for pitchers in more detail than ever before. There’s always been a clear sense of the the kinds of things that go into our WAR calculation, but until this point finding the specific formula for pitcher WAR has been a little complicated.

As of today, we’ve resolved that and I encourage you to go check out our basic primer on WAR and our detailed breakdown of how we calculate it for pitchers. If you’re a hands-on learner, grab a pen and paper or spreadsheet and follow along. I’m going to walk you through a complete example of how to calculate WAR for pitchers. Let’s use the 2016 version of Marcus Stroman as our exemplar. Please note that I will being rounding off certain numbers in the example to keep the page as neat as possible, so if you wind up being off by 0.1 WAR or so, don’t sweat it.

See also: Position Player Formula | Position Player Example

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Baseball statistics are designed to answer questions. Some questions are simple, such as “who reached base most often in 2016?” while others are more complicated, like “who was the best base runner in the American League?” Statistics allow us to gather up data points from individual events and summarize them in ways that are easy to understand.

Different statistics answer different questions and therefore have different uses. You can’t figure out who the best hitter is solely by looking at his batting average. Batting average tells you something, but batting average itself answers a very specific and limited question. Over the years, we’ve attempted to expand the statistics we use to better capture the game we love. Instead of batting average, we moved to OBP, then OPS, then wOBA, and so on. The key is to decide on your question and then find which available statistic(s) best answers that question.

One issue that comes up regularly is whether a statistic is predictive of the future or merely descriptive. You’ve likely heard that FIP is a better predictor of future ERA than current ERA. For this reason, many people believe that FIP was designed as a predictive statistic. As I discuss here, that is not accurate, but the perception persists because FIP is useful for prediction.

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One fundamental aspect of baseball is how well you can describe every situation. With modern technology, this is becoming true of every sport, but the ability to categorize baseball stretches far back into history. We don’t have batted-ball type from 1951, but we know who was batting and pitching, the number of outs and base runners, the inning, the score, the park, and loads of other information for every plate appearance. The data gets better as we approach the present day, but organizing the game based on a collection of variables has a long history.

Want to know how well a batter hit against left-handed pitchers at home in 2004? That’s a question we can answer using something commonly known as “splits.” Some splits, such as handedness splits, are particularly meaningful. Others, such as day of the week splits, are entirely trivial. The compartmentalized nature of baseball, in which individual events occur in an orderly fashion, allows us to record tons of data and then sort it later however we choose.

This post covers basic information you will want to know as you dive into this realm of baseball data. If you’re an advanced consumer of baseball statistics, you probably won’t find a ton of information that’s new to you.

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Earlier this year, FanGraphs began carrying shift data compiled by our friends at Baseball Info Solutions. With shifting on the rise every year, this kind of information has become more and more vital to fans and analysts. This posts walks you through how to access and use the data available on FanGraphs.

First, let’s start by describing what data is available. We have pitcher and hitter shift data going back to 2010 that is viewable on the leaderboards (for players, teams, and league) and player splits pages. The data exists for balls in play only (non-home run batted balls), so if a team shifts mid-plate appearance we only have the alignment for the final pitch. This also means we don’t have data for walks, hit batters, strikeouts, and home runs. If you want to know about how well a team deploys the shift while on defense, you want to look at pitchers. If you want to know about which hitters get shifted against, you want to look at hitters.

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If you have at least a passing familiarity with sabermetrics, you’ve probably heard something like this: Fielding Independent Pitching (FIP) is what a pitcher’s ERA should have been based on his walks, hit batters, strikeouts, and home runs. In other words, FIP is described as a predictive tool to tell you what should have happened rather than as a retrospective assessment of actual pitcher performance.

But this is wrong. This is a shorthand way of describing FIP that well-meaning analysts (myself included) have used, but I’ve come to realize that by aiming to put FIP in terms of ERA, we’ve actually made it more difficult for people to grasp and embrace what FIP is really telling us. It’s time to change the way we talk about FIP, because while the concept of defense independent stats has gained popularity, there is often push back (by some) against FIP as a measure of value, in part, because of less than ideal presentation.

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We feature many statistics on FanGraphs, but one of the most fundamental is Weighted On-Base Average (wOBA). If you’re not familiar with the merits of wOBA in general, I invite you to head over to our full library page on it or to learn about why it’s a gateway sabermetric statistic. For our purposes, I’ll simply include the summary:

wOBA is designed to weigh the different offensive results by their actual average contribution to run scoring. Batting average treats all hits equally and ignores walks. OBP treats all times on base equally. Slugging percentage weighs hits based on the number of bases achieved but ignores walks. Adding OBP and SLG is better than any one of AVG/OBP/SLG, but it still isn’t quite right.

Hitting a single and drawing a walk are both positive outcomes, but they have a different impact on the inning. A walk always moves each runner up one base while a single could have a variety of outcomes depending on who is on base and where the ball is hit. We want a statistic that captures that nuance.

Granted, wOBA doesn’t adjust for park, league, quality of competition, or a number of other factors, but it’s a good starting point on which to build. So how do we take the beautiful chaos of baseball and create the formula listed above?

The exact numbers are going to change each year based on the run environment (how many runs are being scored league wide), but they are consistent enough that we won’t have any problems understanding each other. I’m going to use the 2015 data, but you can view every year here. Allow me to bring a chunk of that table into this post for convenience:

You can ignore the last four columns for the purposes of wOBA, but this is a truncated version of our Guts! page and shows us each year’s league wOBA, the wOBA scale, and the weights for each of our six offensive events of interest. Hopefully those numbers will look similar to the wOBA equation you saw earlier.

Our ultimate goal is to create a statistic that measures each offensive action’s context neutral contribution to run scoring because scoring runs is the currency of baseball. We have decided that we want to measure walks, HBP, singles, doubles, triples, and home runs. If you wanted to, you could build wOBA with more nuanced stats like fly ball outs, ground outs, strikeouts, etc; it would just get more complicated without much added value.

We have a specific goal and the set of offensive actions we want to measure, but now we need a method of putting them together.

Run Expectancy

The first thing we need is a run expectancy matrix. If you need a complete introduction to the concept, head over to this page. In general, run expectancy measures the average number of runs scored (through the end of the current inning) given the current base-out state.

Base-out states are a record of the number of outs (0, 1, or 2) and how many runners are on base and where (no one on, man on 1B, men on 1B and 3B, etc). There are three out-states and eight base-states, meaning that there are 24 base-out states. Each plate appearance has a base-out state.

Let’s use one out, man on first as our example. In order to calculate the run expectancy for that base-out state, we need to find all instances of that base-out state from the entire season (or set of seasons) and find the total number of runs scored from the time that base-out state occurred until the end of the innings in which they occurred. Then we divide by the total number of instances to get the average. If you do the math using 2010-2015, you get 0.509 runs. In other words, if all you knew about the situation was that there was one out and a man on first, you would expect there to be .509 runs scored between that moment and the end of the inning on average.

You repeat the process for the other 23 base-out states and wind up with a table like this:

The table listed here was calculated by Tom Tango using 2010-2015 data for the entire league and serves as a good baseline. At FanGraphs, we park adjust the matrix for each game, so the exact numbers might be a touch different if you’re trying to play along at home in excruciating detail.

Linear Weights

Now that you have a run expectancy matrix, you need to learn how to use it. Each plate appearance moves you from one base-out state to another. So if you walk with a man on first base and one out, you move to the “men on first and second and one out” box. That box has an RE value of 0.884. Because your plate appearance moved you from .509 to 0.884, that PA was worth +0.375 in terms of run expectancy.

Every plate appearance has one of these values, either positive or negative. You can learn more about this by following the earlier link.

What we want to determine is the average run value of a walk, HBP, single, double, triple, and home run. To do this, we take the total RE value of all walks (unintentional in this case), for example, and divide that number by the number of walks in that season. You’re going to wind up getting something around 0.3. You repeat this for the other five actions. This gives you the runs above average produced by each of these kinds of events.

In theory, we could essentially be done right now because we have everything we need to build a statistic that will weigh the offensive actions properly. However, the inventors of wOBA decided that it would probably be best to scale it to something familiar to make it easier to understand. And they picked OBP.

Scaling

We have the runs above average for walks (0.29), HBP (0.31), singles (0.44), doubles (0.74), triples (1.01), and home runs (1.39), but what we want to do now is put wOBA on a scale that will look like OBP. In OBP, an out is worth zero, so the first thing we want to do is adjust the run value scale so that an out is equal to zero.

There is an easy way to do this. First, we need to find the linear weight for all outs using the same method we used to find the value for the other events. We’ll call it -0.26 for 2015. This means that an out is worth -0.26 runs less than the average PA when it comes to run expectancy. What we want to do now is add 0.26 to each of our run values so that outs are equal to zero. So for walks, which we said are worth 0.29 runs above average, we bump those up to 0.55 runs relative to an out. Using linear weights, walks are worth 0.55 runs more than outs. We repeat this for each of the five other positive offensive outcomes.

As you’ll notice, these are not the weights you saw in the wOBA equation. We’re not done scaling them yet. We know that we want BB, HBP, 1B, 2B, 3B, and HR in the numerator of the wOBA formula and plate appearances (minus weird stuff like sac bunts) in the denominator, so what we’re going to do is calculate “wOBA” for the entire league using the linear weights in this table and the total number of events of each type.

In other words, we’re gong to multiply 0.55 times the number of walks in MLB in 2015 and add that to 0.57 times the number of HBP and so on, and then divide the entire sum by the number of plate appearances (really AB + BB – IBB + SF +HBP). If we do that, we wind up with 0.250.

But remember that we want wOBA to look like OBP. So we need to scale the entire thing so that the league’s wOBA is .313 (to match OBP with IBB removed). To do that, we divide .313/.250 and get 1.251, which we call the wOBA Scale.

We take the wOBA Scale and multiply it against the linear weights from the table above and viola, we have ourselves the weights listed in the wOBA equation. And we’re done!

Concluding Thoughts

It’s important to remember that wOBA is one implementation of a linear weights based offensive metric. Baseball Prospectus has their own version, True Average, which is based on the same pillars and implemented differently. Choosing to scale it to OBP is an aesthetic choice. We could scale it to batting average or to nothing. The important part is just that we understand the scale we’re using.

The main idea is that we’re giving each type of outcome a value based on the average change in run expectancy that particular outcome yields. The idea is to give the right amount of credit to each kind of event. Doing so does not make wOBA a perfect statistic, it simply makes it a better one than the traditional AVG/OBP/SLG.

There are lots of little nuances you can add to something like wOBA to get it closer and closer to the truth. All we’re doing here is creating the foundation for all of that work.

Once upon a time, all we had were box scores. We might know a player went 1-3 with a double and a walk, but we wouldn’t know how exactly all of the game’s events unfolded. We’ve come a long way since then, getting play-by-play data, pitch-by-pitch data, video tracking, PITCHf/x, and Statcast. We have results data stretching back more than a century, but the way those results came about gets easier to understand with new information.

What direction was the double hit? How far did it go? Who fielded it? Hearing a player hit a double seems like specific information, but there’s plenty more you might want to know about that event. One of the ways we communicate that information is through Spray Charts.

There are certainly other ways to communicate information of this nature, but one implementation is to display it visually on a diamond graphic and you can find our implementation of spray charts on the player pages here at FanGraphs.

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Pitchers and catchers are reporting for Spring Training this week and, before you know it, there will be real, live baseball happening in Arizona and Florida. As the season approaches, I’d like to take a little time to welcome any statistical newcomers to the FanGraphs Library.

If you’ve made it this far, you’ve almost certainly read articles on the main site, visited some of our player pages or leaderboards, or played our fantasy baseball game, Ottoneu. But what you might not know is that we have an entire section of the site devoted to helping you get the most out of the information housed at FanGraphs.

The most well-known components of the Library are detailed descriptions of the statistics available at the site. These pages are written presuming no previous knowledge of sabermetrics, statistical theory, or mathematics. If you understand the rules of the game, you’ll have no trouble following along. For example, if you come across “wOBA” in an article or on one of the stat pages and have no idea that it stands for, our Library entry is here to help. Not only can you find a basic description of that stat, but there is also a detailed breakdown of how to calculate it, how to use it, why it is important, and all sorts of other information that will help you get more out of the site.

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While it’s January and many free agents have decided where they will be playing in 2016 and beyond, there are still some notable players without new teams. One thing I’m struck by each offseason is how frequently some people comment on new contracts without a good grasp of how teams and players settle on a term of years and dollars. In particular, it’s common to hear these comments from pundits and fans who aren’t quite as plugged into the game as regular readers of sites like FanGraphs.

So for the new reader, or the old one looking to explain the finer points to their friends, here are some basic principles about free agent contracts to remember when thinking about their prudence.

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