# Converting WAA to Winning Percentage Ctd.

In this post we’ll take a look at how to convert WAAs into a winning percentage for batters.  There might not be a lot of value doing this since the WAA value is much easier and a more accurate measure to compare and contrast different players.  Below are the current top three batters in MLB.

Rank WAA BA OBP PA RBI R Name_Tm Pos
4 5.9 0.302 0.390 454 76 72 Mike_Trout_ANA CF
5 5.6 0.294 0.344 393 79 54 Jose_Abreu_CHA 1B-DH
6 5.6 0.244 0.326 451 73 70 Josh_Donaldson_OAK 3B

The formula is the same as before:

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

We know WAA but what is the number of games played for Mike Trout?  Batters use the following formula:

G = PA/38.3

The number 38.3 is considered by this model a baseball constant.  It represents the average number of plate appearances per game per team since 1980.  Like we use 9 innings per game to estimate the number of games for pitchers, the 38.3 PA/game is good enough to estimate the number of games for batters.  Since Mike Trout usually has 5 plate appearances per game it will take him 7 or 8 actual games to accumulate enough PAs to represent a single game.  A batting squad consists of 9 players and not all those players get an equal amount of plate appearances.    Now  we can calculate Mike Trout’s winning percentage by the following:

Winning Percentage = 0.5*(5.9)/(454/38.3) + 0.5 = 0.749

What does this mean?  Not much for a single player.  If a team had 9 Mike Trouts batting or simply let Mike Trout bat all the time with a pitcher like the three spotlighted in the previous post while playing an average squad, that team should win around 75% of the time.

Let’s take a look at the lineup yesterday for ANA.

 WAA Name_Tm PA 2.7 Kole_Calhoun_ANA 279 5.9 Mike_Trout_ANA 446 3.4 Albert_Pujols_ANA 446 0.9 Josh_Hamilton_ANA 235 1.5 Erick_Aybar_ANA 409 0.9 Howie_Kendrick_ANA 436 -0.1 Efren_Navarro_ANA 71 0.4 David_Freese_ANA 309 0.4 Hank_Conger_ANA 187 16.0 TOTAL 2818

Winning Percentage = 0.609 = 0.5*16/(2818/38.3) + 0.5

At 63-41 Anaheim has a 0.605 winning percentage overall almost matching the winning percentage of the lineup they put out last night.  This suggests Anaheim’s pitching is around average which it is according to this.

Converting WAA to winning percentages can be useful for groups like lineups, relief staffs, and starting pitching.   The quality of starting pitching changes daily.  Lineups can also change on a daily basis introducing swings in winning percentages for that particular group that may differ from a team’s total accumulated WAA for batting.  Significant changes can occur when trades get made or good players get injured or return.  Having the ability to compute winning percentages of entire hitting and pitching staffs can be useful when determining probabilities in  head to head matchups.