# Lineup Pitcher Combo Tables Part 1

This will be a short intro to our lineup pitcher combo tables which will be a many part series.  We are still working on the scripts that creates these tables and requirements necessary to define how they’re made and what they mean.

We have historical record of lineups and starting pitchers for  every game since 1969 and almost every game since 1911 from retrosheet.org.    From this data we can compute WAAs for each of these entities.  Since a lineup consists of 9 players and a starter is only 1 player those values cannot be directly compared.  A starter will be involved in far less games than 9 hitters.

We could compute WinPct, a rate, and make the comparison but as  mentioned throughout this season, rates should provide context to a value.  A player with a higher rate is not necessarily better or worse than a player with a lower rate.   A hitter who has a 0.400 BA into May cannot be compared to Ted Williams who finished the season over 0.400.  We need a way to evaluate the strength of lineups versus strength of starting pitching and strength of lineups versus strength of relief pitching.

Since WAA has proven additive properties we can compute deltaWAA from the beginning of a game to the end of a game.   Both lineups and starters will have either gone up or down depending on what happened that day.  We can easily compute this for lineups, starters, and relievers each game.   A single game deltaWAA for starting pitcher can be added to a single game deltaWAA for lineups.

### Tiers

Lineups, starters, and relief each will be segmented into 5 tiers, tier 1 being the best, tier 5 being the worst.  Tier 3 is average. Standard deviation is a statistical measure used to describe a distribution of a set of values.  The distribution can more or less be divided evenly into 5 sets using the following tier definition.

1. average + 1 standard deviation
2. average + 1/2 standard deviation
3. average
4. average – 1/2 standard deviation
5. average – 1 standard deviation.

There are several methods to compute average.  One is to use an average from the beginning to the snapshot point in time.  Another way is a rolling average where we only look at the last x amount of games.  Overall WAA increases with games played like real wins.  The farther back in the season will depress averages which will move tier boundaries.  Averages are still a work in progress.

Each game consists of two lineup -> starter combos and two lineup -> relief combos.  Our 1970-2016 dataset consists of 86,000 games which means 2*86,1000 = 172,000 combo instances for both starters and relievers.  For now we’ll concentrate on lineup -> starters.

### The First Tables

The following two tables were the result of a mistake in a run that I found rather interesting.  We only use a half dataset (1970-1999) for testing code.

Every player will start a game with a WAA and end a game with either a higher or lower WAA depending upon how they produced for that day.  We call that a deltaWAA and measure it for every player.  Since WAA has additive properties we can add them together to compute deltaWAA for entire lineups.

Below are complete averages for all lineup deltaWAAs for all games in the dataset.  These average records were for integrity and debugging purposes.  The more data in a dataset the more numbers will converge upon a true value.

Tier deltaWAA #Games
1 0.68 21327
2 0.49 16219
3 0.32 44482
4 0.18 20386
5 0.01 19851

As expected average per game deltaWAA declines as tier value decreases.  A Tier 1 lineup will add almost 0.7 wins on average per game.  Not sure what exactly that means however.  Let’s look at average starter deltaWAA per game.

TIER deltaWAA #Games
1 -0.28 17271
2 -0.04 13504
3 0.16 42965
4 0.22 16340
5 0.31 16513

This table is counter intuitive suggesting Tier 1 starters on average lose 0.28 WAA value per game while the worst pitchers, Tier 5 gain 0.31 per game.

More data will follow in this many part series that will shed more light onto this phenomenon.   By the time a starter has reached Tier 5 he’s had plenty of bad games.  It is a current theory that Tier 5 pitchers are on a short leash and get pulled much more quickly than a Tier 1 pitcher.  This means a Tier 1 pitcher would incur higher negatives.

Unfortunately deltaWAA is not a valid comparison because it represents a lineup playing a full game where a starter rarely plays a full game.  We need a direct comparison.  There are other things to count like wins and runs which we do next.

This post was to introduce the concept of tiers.  A lineup -> starter combo is an order pair which will divide the dataset into 5*5 = 25 parts.   These ordered pair tables will somehow alter the probability we derive from the real deltaWAA table described here using real team wins and losses.