# Simulation Reboot Part 3

In order to test the integrity of the database used in simulation we need to run tests.  Without accurate data or bugs in scripts the estimated probability it produces is inaccurate.  In this part we’ll look at Tier Combo data from three baseball eras; 2000-2019, 1980-1999 and 1950-1969 to test the integrity of this data model.

Real team WAA, using real team wins and losses, the only stat in baseball that determines who makes the playoffs, was tiered in Part 2 of this series.  There is no dispute over real team WAA but there may be dispute over how this data model calculates it for players.  This exercise will deomnstrate if the player WAA and theories espoused by this data model has any merit.

A baseball season is much like any long race like a running marathon, Tour de France, or Indy 500.   Everyone is equal at start and as the race proceeds contestants become more and more separated where winners and losers and those mediocre become more and more defined.

Real team WAA is simply wins – losses.  This data model calculates and assigns WAA to players where the sum of WAA for all players on a team equals that team’s win/loss record.  In April and much of May not only are teams more bunched together with real team WAA, so are players making tiering much more error prone.  This model doesn’t start handicapping now until day 60 which is around third week in May nowadays.  This allows for standard deviations for lineups, starters, and relief squads used to calculate tiers to increase — meaning teams are separated enough to somewhat determine who is truly good this season and who is not good.

Much like marathons or Indy 500s, teams and players often crash and burn by the end of season.  This model quickly adjusts to reflect that.  Stats like batting averages do not.

There are two types of tier combos used in simulation; lineup -> starter and lineup -> relief.  Each game contains two pairs; one pair for away team and a pair for home team.

Tier combos are calculated by subtracting the pitching component tier number (starter or relief) from the lineup tier number.  Tier numbers are calculated by this simple formula:

Tier Number = 2 * ( WAA – league WAA average ) / league standard deviation

WAA for a lineup is the sum of player WAA for that lineup.  WAA league average and standard deviation is a running average of 30 teams’ last 3 lineups ( 90 lineups ).  A snapshot is taken at the beginning of each day, then averages and tier numbers for each team are calculated.

WAA for starters rely on a single player.  WAA for relief is the sum of a relief squad.   Relief squads are estimated from event data and are pretty accurate.

Tier numbers are floating point numbers.  When subtracted to make a tier combo they get rounded up or down to make an integer.  Right now tier numbers have a range of -4 to +4 and tier combos have a range of -6 and +6.  The simulator only cares about tier combos.

The run used to make the below tables looks at all games between 6/1 and 8/31.  Tiers fluctuate too much in April and May and in September player expansion can distort roster value.  Although we may handicap games in September and late May, we’re sticking to a much narrower window for the dataset simulation draws from.

The below tables show all the tier combo sets from -6 to +6 with columns runs/inning, number of innings pitched per game for both the lineup -> relief and lineup-starter.

First let’s look at the modern era from 2000-2019 which encompasses around 25,000 baseball games from 6/1 to 8/31.

### 2000 – 2019 Tier Combos

TC Lineup -> Relief Lineup -> Starter
R/Inn Outs R/Inn Outs
-6 0.359 8.76 0.353 19.86
-5 0.391 8.93 0.372 19.40
-4 0.390 8.86 0.409 18.93
-3 0.415 9.07 0.432 18.47
-2 0.424 9.14 0.449 18.19
-1 0.429 9.09 0.473 17.88
0 0.442 9.21 0.488 17.71
1 0.462 9.38 0.512 17.42
2 0.470 9.30 0.514 17.47
3 0.488 9.47 0.534 17.26
4 0.490 9.37 0.546 17.05
5 0.526 9.62 0.585 16.90
6 0.561 9.60 0.600 16.87

Tier Combo of -6 is a terrible lineup facing a very good relief squad or starter.  The opposite is true for a Tier Combo of +6.  The above shows runs per inning for starters goes from 0.353 at TC = -6 to  0.600 per inning at +6, the best lineups vs. worst starter.  Runs per innings increase almost the same with the lineup -> relief combos.

The number of outs for starters goes from 19.86 outs per game with the best starter facing the worst lineups down to 16.87 outs for the worst starter facing the best lineups.  Divide by 3 to get innings.  Outs per game for relief does not vary much between -6 and +6 probably due to the number of outs a relief staff must pitch has more to do with the starter than the value of the relief squad.

The number of runs given up by relief is much less than by starters which should be expected.  Tier Combo 0 is even steven between lineups and relief or starter.  The starter runs per inning is almost exactly league average for this 20 year span.

All runs counted for pitchers above are earned runs.  When determining who wins a baseball game, the commissioner counts unearned runs equally with earned runs.  This model counts and tiers  unearned runs separately for use in simulation because all runs must be accounted for to make the books balance here.  A pitcher should not be blamed for runs not his fault and an official scorekeeper keeps track of that for every play in every game since the beginning of baseball.

The next table will show the 1980 to 1999 era.

### 1980 – 1999 Tier Combos

TC Lineup -> Relief Lineup -> Starter
R/Inn Outs R/Inn Outs
-6 0.361 8.04 0.355 20.84
-5 0.378 8.40 0.374 20.44
-4 0.392 8.11 0.390 19.99
-3 0.375 8.19 0.409 19.51
-2 0.404 8.10 0.435 19.18
-1 0.416 8.12 0.456 18.87
0 0.418 8.41 0.466 18.77
1 0.449 8.27 0.477 18.46
2 0.465 8.49 0.500 18.37
3 0.460 8.24 0.503 18.25
4 0.458 8.67 0.536 17.92
5 0.504 8.63 0.532 17.92
6 0.495 8.92 0.553 18.03

The league had 26 teams for most this era and went to 30 teams in 1998 which means less pitchers.  A 30 team league will have around 150 starters, a 26 team league 130.  The above shows much narrower differences between -6 and +6 tier combos for both relief and starter which should be expected because talent is more concentrated.

This can be a problem in simulation that is still a work in progress.  As we go back to 1950-1969 we get to 16 team leagues with around 1/2 the number of players.  It may not be possible without some kind of adjustment to pull values from a tier combo in a 24 or 16 team league when we’re handicapping a 30 team league with much higher disparity of talent.

As we go back in time starters pitch more outs and relief less.  This means we can’t simply pull a pitchers innings pitch/earned runs from an early era and use that directly in simulation either.

Below is a look at the Tier Combo spread from 1950 to 1969.

### 1950 – 1969 Tier Combos

TC Lineup -> Relief Lineup -> Starter
R/Inn Outs R/Inn Outs
-6 0.320 7.57 0.325 22.06
-5 0.361 6.99 0.344 21.50
-4 0.358 7.14 0.356 21.13
-3 0.365 6.87 0.380 20.48
-2 0.385 7.28 0.389 20.19
-1 0.414 7.22 0.399 19.97
0 0.416 7.23 0.416 19.78
1 0.433 7.69 0.439 19.35
2 0.425 7.72 0.443 19.21
3 0.478 7.84 0.458 19.04
4 0.493 7.92 0.479 19.03
5 0.485 8.41 0.504 18.35
6 0.560 8.63 0.502 18.65

The above are averages.  When looking at % of 9 innings pitched by starters it skyrockets almost an order of magnitude (10x)  higher than modern era baseball.  Runs/inning are even more constricted with mostly 16 team leagues.

In past years this data model pulled data from 1970 – present without any alteration.  This probably introduced error even though it beat Vegas albeit not by enough to advertise.

Adjustments will have to be made on an era by era basis.  There is too much variation to come up with factoring coefficients on a yearly basis.  The eras shown above were thrown together arbitrarily to fit with the logistics of rebuilding this database.  Right now I’m thinking 1920-1960, 1961-1976, 1977-1997, 1998 -2019.

The biggest factor in narrowing Tier Combo results is number of players in a league which is directly related to number of teams.  1961 – 1977 went from 20 teams to 24.  The next era went from 26 to 28, and our modern era since 1998 has been at 30 teams.

The number of innings starters pitched has also declined a lot in recent years but that’s fodder for another post.

Looks like baseball season might be cancelled  <insert sad emoji>.  This model was going to get detailed box scores from mlb.com this season which would have made regular season handicapping much more interesting as roster value — especially relief, will be far more accurate than past seasons.  Unfortunately we may have to wait until next year.

Still working this simulation and the baseball-handbook.com website which will allow easy click through for any team, any player since 1900 and any game since 1920.  Until then ….