# The DH argument Part 1

This will be a multi part series that explores various aspects of this DH issue.  The first question that needs to be answered is which league has better hitting pitchers.  Now that AL and NL play each other AL pitchers must bat when they play in NL parks.  My initial conjecture was NL pitchers would be better because they get more practice at the plate.  Let’s examine this.

Since this data model produces a value metric that is what we will use for this determination.  The raw WAA value system used to rank individual players cannot be used because AL pitchers have more than an order of magnitude less plate appearances per year than NL pitchers.  Since all but a few pitchers are below average hitters that would skew the numbers in favor of AL.

This is where the rate, WinPct is needed.  This model uses WinPct to place minor league player stats into context because those players typically move from league to league.  WinPct provides context to the WAA weighting value.  WinPct is not shown for MLB players because it is deceptive at that level.

Why can WinPct be deceptive?  For example,  a typical 26 mile marathon can be finished by the best marathon runner in a little over 2 hours making their average rate of speed to be around 13 mph.  A good runner 3 hours or a 9 mph rate; average runner 4 hours, 6+ mph rate and so on and so on.

A top runner of a mile can do it in 4 minutes or 15 mph.  If you just look at rates, the mile runner runs faster than the top marathon runner.  Since 15 mph is higher than 13 mph does that make the mile runner a better runner?  Is a golfer who shoots 3 under par for 9 holes ( -0.333 shots/hole ) better than the golfer who shoots 3 under par for 18 holes ( -0.166  shots/hole )?

The answer is no.  They could be better but you can’t tell by the rate.  MLB ranks players and give awards based upon batting average because it is/was a sideshow for baseball to garner interest for the sport. If your favorite team wasn’t doing well then you could root for your favorite player instead.  Now with fantasy leagues and actual gambling sites like Draft Kings that reward certain stats over others this concept has become even more extreme.

That’s all fine and well but batting average or WHIP does not represent value anymore than average running speed represents a runner’s ability or value as a runner.  A high batting average and low ERA often does translate into value that can be ranked but the raw number itself cannot.

This model does not show rate for MLB nor does it ever rank on rates, unlike most  of Sabermetrics.  That said we must use the rate for dissimilar groups of players like  AL and NL pitchers and sometimes it’s useful to provide context for lineups, relief squads, and starting pitchers.  Tiering which has been discussed throughout however uses raw WAA weighting.

### What does all of this have to do with DH?

Nothing other to explain why in these next few exercises we will be using rates instead of raw value.  First let’s explain how WinPct is calculated again.  By definition:

WAA = wins – losses

Not too complicated.  It’s easy to calculate for teams and this model calculates it for players.  Players with positive WAA provide more wins to their teams than losses, vice versa for negative valued players.   The following must also be true:

Sum Team(WAA) = 0

Add all wins – losses for all teams in any league  and it adds to 0.  IOW, for every team that  wins, a team must lose.  Not too complicated!  The following is also true according this this data model.

Sum Player(WAA) = 0

If you add WAA of every player who played in a season it adds to exactly 0.

Sum Player_Team(WAA) = Team(WAA)

The above states that the sum of all players who played for a team while they played on that team is equal to their real win/loss record.  The Cubs had a record of 95-68 last season which is a WAA=+27.  WAA for all players tagged CHN in 2018 will add to that number.

Therefore, Player(WAA) has the same properties as Team(WAA) where a winPct can be calculated as follows.

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

For the Cubs last season that was

Win% = 0.5 * 27 / 163 + 0.5 = 0.583

To calculate a player Win% the number of games played is not the actual games they play in.  Time in baseball is measured by plate appearance for hitters, innings pitched for pitchers.  Baseball has always used 9 innings to represent a game when calculating ERA.  An average game in baseball is not exactly 9 innings but it’s a close enough approximation, easy to remember and easy to calculate before there were calculators.

This model uses the constant 38.4 plate appearances to represent a game for hitters.  Javier Baez had 645 PA last season which translates into 645/38.4 = 16.8 games.  His WAA for his almost MVP season was 7.29 thus,

Javier Baez Win% = 0.5 * 7.29 / 16.8 games  + 0.5 = 0.717

and for context:

Christian Yelich Win% = 0.5 * 8.,44 / 17 games + 0.5 = 0.749

The above is merely an illustration to how this is calculated.  The WAA value ( 8.44 for Yelich, 7.29 for Baez )  is all that matters for ranking purposes.  This model also gives Yelich MVP even though Baez led until the final week  of the  2018 season.

### Would you get to the point of all this?

OK.  We meandered a bit with some background as to how all this is calculated showing it’s not very complicated.   The next set of tables will walk through the variables used to make Win%.  First let’s look at plate appearance numbers for AL and NL pitchers throughout the years.

#### AL and NL Pitching Plate Appearances

YEAR AL PA NL PA
2008 637 4998
2009 642 4994
2010 638 5152
2011 621 5023
2012 605 4908
2013 345 4836
2014 332 4893
2015 333 4643
2016 361 4674
2017 329 4648
2018 311 4526

Plate appearances translates into baseball time.  The above table clearly shows what we already know — that NL pitchers bat far more often than AL pitchers — because NL does not have DH.  The number of plate appearances for both AL and NL  pitchers declined from a peak in 2010 until last season.  Not sure why but it is what it is.  Let’s look at total pitcher hitting WAA for each league.

#### AL and NL Pitching BAT WAA

YEAR AL WAA NL WAA
2008 -10.12 -73.75
2009 -9.03 -72.58
2010 -11.38 -68.54
2011 -8.95 -65.79
2012 -8.95 -66.49
2013 -5.23 -62.45
2014 -5.21 -66.13
2015 -5.08 -66.91
2016 -6.32 -61.76
2017 -4.72 -66.86
2018 -4.54 -67.20

This table does not tell you much other than pitchers bring losses to their teams from their poor hitting.  We saw in the previous table that plate appearances have gone down since 2010 yet WAA remains kind of constant.

With 15 teams in NL, pitchers contribute and average around -4 in the win/loss column per team due to hitting.   For AL it’s much less and the above shows AL pitchers have become much better hitters over the years.  Can’t really tell what’s going on without doing the Win% calculation.

#### AL and NL Pitching BAT Win%

YEAR AL Win% NL Win%
2008 0.195 0.217
2009 0.230 0.221
2010 0.157 0.245
2011 0.223 0.249
2012 0.216 0.240
2013 0.209 0.252
2014 0.199 0.241
2015 0.207 0.223
2016 0.164 0.246
2017 0.224 0.224
2018 0.220 0.215

It must be stressed that these only include hitting stats that have nothing to do with their pitching.  The last couple of years AL and NL pitchers are more or less equal in hitting ability but very very poor.  As shown above, MVP quality hitting is above 0.700.  A textbook completely average hitter would have a WAA = 0 translating to a Win% of exactly 0.500.

The above clearly shows just how bad pitchers in general are at hitting which is one of the reasons for DH.  In order to put the above in context we must compare the above numbers to the worst hitters in each lineup.

Since AL teams have DH they normally do not make pitchers hit.  In order to put the above in context we’ll look at the 9th hitter in each lineup last year and if I get motivated, the last ten years.  The bottom of a lineup is where managers put hitters they want to have the least amount of plate appearances.   What kind of Win% do these players put up?  We’ll see.  Until then ….