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## Teams

### GB (Games Behind)

W1 = First place team's wins
L1 = First place team's losses
W = Team's Wins
L = Team's Losses

GB = ((W1 - L1) - (W - L)) / 2

### Luck

The number of wins more (or less) than a team's pythagorean wins

W = Wins
pW = Pythagorean wins

Luck = W - pW

### Pythagorean Record

The PythagenPat method is used to calculate pythagorean record.

RS = Runs scored
RA = Runs allowed
IP = Innings pitched
G = Games
exponent = ((RS + RA) * 9 / IP)^.285

Pyth (Pythagorean Winning Percentage) = (RS^exponent / (RS^exponent + RA^exponent)
Pythagorean Wins = Pyth * G

### Base Runs Record

While there are a number of different ways to calculate Base Runs, The Baseball Gauge uses TangoTiger's formula.

A factor = H + BB + HBP - .5 * IBB
B factor = 1.1 * (1.4 * (1B + 2B * 2 + 3B * 3 + HR *4) - .6 * H - 3 * HR + .1 * (BB - IBB + HBP) + .9 * (SB - CS - GIDP))
C factor = AB - H + CS + GIDP
D factor = HR
The B factor is adjusted to fit the league wide run scoring environment

Base Runs = ((A * B) / (B + C)) + D

IP = Innings pitched
G = Games
Off = Offensive Base Runs
Def = Defensive Base Runs
exponent = ((Off + Def) * 9 / IP)^.285
Base Runs Winning Percentage = (Off^exponent / (Off^exponent + Def^exponent)
Base Runs Wins = Base Runs Winning Percentage * G

### Run Differential

RS = Runs scored
RA = Runs allowed

Run Diff = RS - RA

### Def +/- (Runs Allowed Below Average)

# of runs per 9 innings a team has allowed fewer than the average team
RA = Runs allowed
IP = Team's innings pitched
LgRA/IP = League's Run allowed per innings pitched

RA +/- = (LgR/IP * Adj) * IP - RA

### Off +/- (Runs Scored Above Average)

# of runs per 9 innings a team has scored more than the average team
RS = Runs scored
Inn = Team's offensive innings (estimated as innings pitched minus home wins plus away losses
LgR/Inn = League's Run scored per inning

RS +/- = RS - (LgR/Inn * Adj) * Inn