# Converting WAA to Winning Percentage

The WAA value defined in this data model is in units of (W-L).  Players that contribute more wins to his team than losses will have positive numbers; those that contribute more losses than wins have negative numbers.  But what does this mean?  You can  convert WAA to a winning percentage by the following formula:

Win% =  0.5*WAA/(number of games played) + 0.5

The above is a standard formula.  Let’s say a team goes 61 – 101 for a season.  The WAA measure for that is simply W – L or 61-101=-40.  There are 162 games in a season so plugging in -40 into the above formula we get:

Win% = 0.5(-40)/162 + 0.5 = 0.376

Thus, the above formula allows us to use WAA to calculate a winning percentage for each player.  The next problem is determining number of games.  In a total season calculation it is easy, a simple 162.  An individual player does not play in 162 games — especially pitchers and relievers and platoon players.

For pitchers I have so far decided to use a simple:

Games = (Innings Pitched)/9

Although a game is never exactly 9 innings on average, using 9 is a good estimation and it’s simple — which is why it’s used for ERA.  Let’s take a look at the top 3 pitchers in MLB as of today.

Rank WAA IP ERA G W L Name_Tm Pos
1 6.8 158.3 1.99 22 11 2 Felix_Hernandez_SEA PITCH
2 6.3 142.7 2.02 20 12 5 Adam_Wainwright_SLN PITCH
4 6.0 148.7 2.18 21 10 6 Johnny_Cueto_CIN PITCH

Using the above numbers for WAA and IP (innings Pitched) we can estimate a winning % for each pitcher.  The numbers for Felix Hernandez look like this:

Games = 158.3/9 = 17.6 games

Win% = (6.8)/17.6 + 0.5 = 0.886

Hernandez W/L record of 11-2 gives him a Win%= 11/13 = 0.846

Pitcher wins and losses as defined by MLB use an arbitrary algorithm that cannot be included in any math used in this data model.  This historical algorithm has been around since the beginning of baseball when all math was done by hand using paper and pencil and, for the most part, it does a good job describing a pitcher’s contribution for regular players.  It has its faults.  The algorithm favors  pitchers who are fortunate enough to have most of his team’s runs get scored in the first 5 innings.  This wasn’t an issue when starting pitchers used to routinely pitch complete games.   Pitchers now routinely pitch 6 or 7 and get pulled.   Those who pitch for teams that routinely score near the end of the game have their W/L records skewed downward arbitrarily.  This model includes win/loss records for pitchers in all tables for context.  The true measure of a pitcher’s performance is their WAA value.

Felix Hernandez’ regular W/L record is extremely close to the one derived from WAA.  Adam Wainwright has a 0.897 winning percentage according to WAA and 0.705 % according to the historical W/L methodology.  The Cardinals currently have the second worst hitting in MLB which has skewed his standard W/L percentage downward.  Cardinal pitching has carried that team making them have a 6 “above 0.500″ or W-L= +6 and very much in contention for another playoff run.  Wainwright’s 0.897 winning percentage is a more accurate representation of his  contributions to the Cardinal team so far this season.

And finally, Johnny Cueto weighs in ar 0.863 (WAA) and 0.625 (historical methodology).  Cincinnati has the third worst hitting in MLB right above the St. Louis Cardinals.

Since WAAs are additive this number can be used to determine the winning percentages of say a relief staff or of a particular lineup of batters.   In normal comparison you would simply compare sums of WAA.  In certain cases when dealing with two groups with wildly different number of games played, like a relief staff and a particular lineup, converting to percentages might be  needed to normalize two disparate groups.