## Introduction: Calculating the WAR Statistic

Baseball front offices are always trying to get the upper hand on each other to find great players. They need to know if a player will make it in the big leagues and see how he will do. This has lead to somewhat of an "arms race" to find people in the front offices who can calculate how good players will be. This has lead to a number of new statistics being created. One of these statistics is called the WAR statistic. The WAR statistic stands for wins above replacement and is used to try to see a players overall contribution to the team. Basically, how many more wins would the team have with this player opposed to a replacement level player. This instruction set will show how this is calculated and used. This instruction set will only look at how to calculate WAR for position players and not pitchers as they have a different way to calculate the WAR statistic.

## Step 1: The Components

The WAR has many different parts and can be confusing at times. One thing that confuses many is what us a replacement player. A replacement level player is classified as a player who is a free agent during the season or a minor leaguer. The next most confusing thing is how to calculate it. The formula itself is not very complicated and it is WAR = (Batting Runs + Base Running Runs +Fielding Runs + Positional Adjustment + League Adjustment +Replacement Runs) / (Runs Per Win). This itself is not a complicated formula, however each of the singe components are more difficult to calculate.

## Step 2: Calculating Runs

This set will explain how to calculate batting runs, base running runs, and fielding runs. Batting runs is calculated by first finding the weighted runs above average. Weighted runs above average, wRAA, is calculated using the formula wRAA = ((wOBA – lgwOBA)/wOBA Scale) * PA. Firstly, wOBA stands for weighted on-base average, lgwOBA stands for league weighted on-base average, wOBA scale is a number that changes from year to year baed on the lgwOBA, and PA stands for plate appearances. Plate appearances is simply how many times a player goes to bat, but wOBA , lgwOBA, and wOBA scale are more complicated. To make things simpler, all these can numbers can be found on the fan graphs website. After wRAA is found you put it in the batting runs formula which is Batting Runs = wRAA + (lgR/PA – (PF*lgR/PA))*PA + (lgR/PA – (AL or NL non-pitcher wRC/PA))*PA. Again very complicated but lgR stands for team runs per 162 games, PF stands for park factor, and wRC stands for weighted runs created. Team runs per 162 games is simply dividing the teams total runs in a season by 162 the others are very complicated and agian can be found on fan graphs.

Base running runs is the amount of runs a players base running ability adds to the teams total runs. This does not only include steals but also includes the how well a player runs the bases after a hit. This formula is Base Running = UBR + wSB + wGDP. UBR stands for ultimate base running which measures how well a players runs the bases while not stealing, wSB stands for weighted stolen base runs and wGDP stands for weighted grounded into double plays. These sub categories are complicated to do, as the explanation for UBR itself could have its own instructions set, so it would be advised to use another source to find these certain statistics.

Fielding runs is calculated much differently than the other two. It uses statistic called the ultimate zone rating which is used for all positions except for the catcher. This statistic does not have a formula like the other two because it uses video of the fielders to calculate its score. It judges how easy or hard a ball is to field and gives more credit to harder plays made and takes away more if a player commits an error on an easier play. You will have to use fan graphs or other site to find this statistic. For a catcher you have to use stolen base runs and runs saved on passed pitches, both of which are calculated using video analytics so you would need another source.

## Step 3: The Adjustments

The adjustments are used to put all the players on the same level. The positional adjustment is necessary because certain positions are harder than others and this is a way defense becomes a greater factor in the WAR statistic. The formula for this is Positional Adjustment = ((Innings Played/9) / 162) * position run value. This calculation is quite simple, but the position run value differs on where you look. This is calculated by people who watch a lot of baseball and know a lot about the game. Different sites have this listed as different values so you could use two websites and have slightly different values. For the most part, the designated hitter will have the lowest, since they do not play defense and the catcher will have the highest. The way this is calculated differs on where you look so this is the least consistent statistic of any of the ones used in finding the WAR.

The league adjustment is a way even out players who play in the different leagues. This is because the American League tends to produce more runs than the National League. But this has one of the easiest formulas to calculate and is League Adjustment = ((-1)*(lgBatting Runs + lgBase Running Runs + lgFielding Runs + lgPositional Adjustment) / lgPA)*PA. All these factors are the statistics that have been mentioned earlier except they are the league totals, where the lg preceding the statistic means league. The last PA in the formula is the specific players plate appearances. You can either do all these statistics again for the league instead of the specific or find their values on a different website.

## Step 4: Replacement Level Runs and Runs Per Win

Replacement level runs are where the WAR statistic gets part of its name. This is used because it is a better being a replacement level player is easier to judge than an average player. This is also simple to calculate with a formula of Replacement Level Runs = (570 * (MLB Games/2,430)) * (Runs Per Win/lgPA) * PA. The 570 and 2430 come from a statistic that is 1,000 WAR per 2430 games played. This means out of 2430 games, 1000 of the wins will be because of players with positive wins above replacement. The 570 comes from 57% of the 1000 come from position players with the rest coming from pitchers.

Runs per win is the last step in this equation. It simply means how many runs does it take to achieve a win. This also has the easiest calculation of RPW = 9*(MLB Runs Scored / MLB Innings Pitched)*1.5 + 3.

## Step 5: Interpretation

Now that you have calculated the war, what does it mean. The easiest way to look at it is 0 means they are at the level of a replacement player, so not much is expected of them. Anything above 6 is considered fantastic and that player is at the MVP level for that specific year. Most everything else is somewhere in between. You can get negative values and this means that player is preforming worse than a replacement level player, so they are not playing well at all. This statistic doesn't tell you everything but does give an idea to how good a player is preforming. So now that you can calculate the WAR statistic, find your favorite player's statistics and plug them in. If you want to check yourself, fan graphs, ESPN, and baseball reference all have the WAR statistic on their website.

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## Comments

That's interesting, I didn't know that's how they calculated the value a player could add to the team :)