You’ll notice his WAR comes out to 6.2 instead of the listed 6.1, which is a simple rounding issue because I didn’t type out the long chain of digits that go with each of the various constants. WAR = (Batting Runs + Base Running Runs + Fielding Runs + Positional Adjustment + League Adjustment +Replacement Runs) / (Runs Per Win)Ħ.2 = (46.3 – 0.6 + 2.2 – 12.3 + 0.8 +20.7) / (9.264) The WAR equation listed at the top is as follows: For 2013, as we saw a moment ago, it is 9.264. It varies yearly with the run environment and can be found here. We need the MLB Runs Per Win, which is essentially the number of extra runs a team needs to score to add one win to their total. We’ve calculated all of the Votto specific numbers so far and need just one more piece of data. This leaves Joey Votto with 20.7 replacement level runs. We then multiply that by Runs Per Win divided by League PA to convert WAR into runs per PA and then we multiple that by the player’s PA to determine their share of runs. To do this, we start with 570 WAR (or 57% of the total 1,000 WAR) and multiply it by the number of games in the season divided by 2,430 because position players make up 570 WAR per 2,430 games. So far we’ve been talking in runs above or below average, but now we need to shift and refer to Votto’s performance relative to replacement level. This leaves us with a league adjustment for Votto of 0.8 runs above average. Positional Adjustment = ((Innings Played/9) / 162) * position specific run value ![]() To calculate the positional adjustment for each player, you do the following: The positional adjustment allows us to compare players who played different positions, as fielding runs only compares players to the average player at their specific position. That means he had 2.2 Fielding Runs Above Average in 2013. ![]() Fielding RunsįanGraphs uses Ultimate Zone Rating (UZR) for our fielding runs above average for each non-catcher position and Votto had a 2.2 UZR in 2013 at first base. The site lists -0.5, again because of simple rounding differences. If we locate his UBR on the site (0.2) and add it to his wSB (-0.8) we arrive at -0.6 Base Running Runs Above Average. 0035 to use as constants in the wSB equation. This leaves us with a runSB of 0.2, a runCS of -0.384, and a lgwSB of about. Runs Per Out is simply runs scored in the season divided by outs in the season. To do this, we need the MLB R/PA (.110), the NL non-pitcher wRC (9783), and the NL non-pitcher PA (86,959). So if we have 48.9 wRAA, let’s now go through the process of adjusting it for his home park (Park Factor = 101) and for the National League. Some of the constants and park factors you see are rounded off so that the site isn’t a giant string of numbers. This will come up again, so keep it in mind. On the site, it’s listed as 49.1, which is just a matter of rounding on the league constants. To find his wRAA, you need his wOBA (.400), his PA (726), and some data about the league, specifically the league average wOBA (.314) and the wOBA Scale (1.277). So let’s start by calculating his wRAA, although you can also find this pre-calculated on the site. To calculate Batting Runs, you want Weighted Runs Above Average (wRAA) and then you want to park and league adjust it.
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