Our final stop in the mini series of Getting to Know Stats features the calculation of WAR for positional, batting players.

For positional players, WAR uses six components within its formula: Batting Runs, Base Running Runs, Fielding Runs, Positional Adjustment runs and Replacement Level runs based on playing time. This is finally divided by Runs per Win, the amount of runs needed in order to win a game based on the run environment of the entire major leagues. The formula looks something along these lines:

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

The factors Positional Adjustment and League Adjustment act as a neutral context for judging a player’s value. Positional players cannot achieve a greater leverage when hitting with runners in scoring position, for example, or in high-clutch scenarios. It is worth noting that WAR is both park and league adjusted. By that nature, American League positional players get a slight advance over their counterparts in the National League, for the inclusion of the Designated Hitter puts continuous pressure on a Pitcher going through the line-up rather than facing off against a much easier batter in the opposing Pitcher. Lets break down each component that creates Positional Player WAR:

**.Batting Runs****: **This component is influenced more about the league in which a players plays rather than the performance of the player himself. The first step is to find out a player’s **Weighted Runs Above Average (wRAA) **from his **Weighted On Base Average (****wOBA), **as follows:

**wRAA= ((wOBA – ***lg***wOBA)/wOBA scale) * PA**

Essentially, you are generating a value for a player’s non-adjusted batting runs through **wRAA. **This is where league and park elements begin to take effect inside the final equation to determine a player’s batting runs:

**Batting Runs= wRAA + (***lg***R/PA – (PF****lg***R/RA)) * PA + (***lg***R/PA – (AL/NL non-pitcher wRC/PA)) * PA**

This equation is simpler than it appears. The longevity lies in taking into account that this is for positional players, therefore a **Weighted Runs Created (wRC) **value that excludes Pitchers is appropriate. **wRC **is simply taking in a player’s statline into a metric and providing an outcome as to how valuable that player is by how many runs he created for his team.

It is also important to note, that to fit the player’s **Park Factor **in line with the equation, a decimal point should be placed past the first two digits of the value (i.e. 95 into 0.95). Thus, you receive a player’s **wBAA **but adding or subtracting runs based on the park and the league in which he plays in that becomes his **Batting Runs** value.

**.Base Running Runs****: **This is a combination of **Ultimate Base Running (UBR), Weighted Stolen Base Runs (wSB****) **and **Weighted Grounded into Double Play Runs (wGDP). **Using this trio of statistics brings in non-stolen based base running, the value of stolen bases and caught steals towards run scoring and inserting influence of a hitter’s habit of grounding or avoiding double plays. It’s worth noting that **UBR** is non-measurable without video analysis, and **wGDP **compares the amount of double plays a hitter grounds into and their expected amount measured in a runs value.

**BsR = UBR + ***w***SB + ***w***GDP**

It’s very important to monitor how effective a baserunner is in the form of how many runs he contributes or gives up, for the offense of an MLB hitter continues far beyond what occurs at the plate. *w***SB **in particular promotes the notion that the play of advancing one base through stealing is far less valuable than the cost of getting out when caught stealing. If a baserunner steals ten bags but is caught stealing ten times, his *w*SB value will suffer because of the former. Ten outs will take away far more runs than taking ten bases would. This is essentially why Cincinnati Reds OF Billy Hamilton is *not *one of the most dangerous base runners in the game, for he steals far too many times despite his large amount of stolen bases. **UBR **doesn’t account for stolen bases or caught stealing, instead implies linear weights on a variety of baserunning scenarios that involves the potential attempt to advance at least one base.

**.Fielding Runs****: **Centred on **Ultimate Zone Rating (UZR), **Fielding Runs represents the value of a player based on how many runs he can potentially save/ give up for a team in theory. Like with Ultimate Base Running, it cannot be measured without video analysis, for it accounts for the difficulty of an out towards the outcome of every player towards a player’s defensive value. This cannot be done without video analysis.

Credit is given to each fielding position based on the past six years of data surrounding how often certain positions field particular plays that are made by batted balls. For example, batted balls into the outfield would be fielded by the CF around 15% and both LF and RF 7%, with the remaining 71% being classed as hits. This is park variable, so the amount of credit given to a fielder will vary based on where he plays.

Because of the ridiculously limited fielding area of a Catcher compared to every other position, as well as his limited percentage of fielding batted balls compared to others, UZR does not exist for the man behind the plate. Instead, Stolen Base Runs is judged on the aspect of **Defensive Runs Saved and Runs Saved on Passed Pitches ****(RPP) **known as **Stolen Base Runs (rSB)****. **Essentially the flip-side of UBR, rSB measures how many runs a Catcher saves/gives up for his team based on how many outs he can generate through caught steals on baserunners. RPP calculates the same outcomes but through the method of blocking passed balls.

**.Positional Adjustment****: **As hinted with the Catcher position in regards to Fielding Runs, circumstances surrounding the measurement of a player’s defensive ability can vary between each position (i.e. frequency of batted balls in area, park factor, etc). This is why adjusting each position to accommodate an equal value of defensive ability from position to position is so essential towards judging their overall value in WAR. For example, it is proven statistically that playing Shortstop is far difficult compared to playing First Base.

**Positional Adjustment= ((Innings Played/9) / 162) * position specific run value**

Position specific run value varies between each position. For example, Catcher is +12.5 runs, whereas Right Field is -7.5 runs. Designated Hitter is -17.5 runs, for this position does not contribute defensively. The higher the specific value, the more difficult that position is. As the equation above states, the formula for calculating Positional Adjustment is simply nine innings played at that position.

**.League Adjustment****: **Due to the different environments of both the AL (Designated Hitter) and NL (Pitchers batting), a formula is generated in order to accommodate how much of an offensive/defensive shift that particular league has towards the impact of a player’s overall value.

**League Adjustment= ((-1)*(***lg***Batting Runs + ***lg***Base Running Runs + ***lg***Fielding Runs + ***lg***Positional Adjustment) / ***lg***PA) * PA**

This is essentially taking in all of the departments already explained, finding the league average of how many runs that are required to be added, then multiplying it by a player’s PA in order to keep it consistent with the values already generated. This will typically result in an influence of 0 to 5 on a player’s WAR depending on the league he plays and how many PA’s he has.

**.Replacement Level Runs****: **To this stage in Batting WAR, league averages dominate the calculations and statistics. Replacement Level Runs ends this trend, for we must generate a figurative replacement level persona** **in which to compare players with. Look at this replacement level as a minor leaguer/free agent/ poor bench player in the majors. Because at this point, a player who plays 600 PA cannot separate himself truthfully from someone who only plays 200 PA.

The replacement level is 1000 WAR per 2,430 games played. Positional players are allocated 57% of such, with 43% going to Pitchers. Calculating replacement level runs is as follows:

**Replacement Level Runs = (570* (MLB games/ 2,430)) * (Runs per Win/***lg***PA) * PA**

It’s worth noting that the mysterious 570 figure indeed represents the 57% of WAR given to positional players, in which you multiply by how many games a player has played to that point in the season. By using the 2,430 games played as a base, you can calculate the Replacement Level Runs value all season long. You then multiply this figure by the value of Runs per Win divided by league average PA, so it translates into a scale of Runs per PA, finally concluding by multiplying *this *by a player’s PA.

This is the calculation of the difference between a replacement level player and an average player given the amount of PA’s attended by the latter. This section of WAR promotes the incentive of having *more *PA’s, for it will automatically provided a greater value towards a given player.

**.Runs per Win****: **The unexplained factor in Replacement Level Runs, Runs per Wins converts runs into wins. This is the figure in which you divide the current total to give you the final WAR value for a positional player. It is simply the calculation of how many runs on average a team must score in order to generate one win to their current total to that point in the season. For example, the 2014 regular season generated a R/W average of 9.36. Therefore, a team would need to score an extra 9.36 runs in order to figuratively add an extra win to their total. It is an excellent reflection of the evolution of baseball from season to season. Between 1994 and 2008, 13 of the 15 seasons featured a R/W of over 10, while the 1968 season generated an astoundingly low figure of 8.1.

This concludes the long and winding journey of Batting WAR and thus this mini series of Getting to Know Stats!

*You can find Darren on twitter @DarrenHelley or join in the conversation @CTBPod*