Sports Analytics Formulas & Metrics

Comprehensive collection of sports analytics formulas with mathematical explanations

222

Total Formulas

Sports Covered

120 / 53 / 49

Basic / Inter / Adv

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BABIP

intermediate Advanced Batting

Baseball

Batting average on balls put into play. Used to identify luck or unsustainable performance; league average is around .300. Variables: H = Hits, HR = Home Runs, AB = At-Bats, K = Strikeouts, SF = Sacrifice Flies

Formula:

\(\text{BABIP} = \frac{H - HR}{AB - K - HR + SF}\)

Example:

Player with 150 H, 25 HR, 500 AB, 100 K, 4 SF: BABIP = (150-25)/(500-100-25+4) = 125/379 = .330

Isolated Power

ISO

intermediate Advanced Batting

Baseball

Measures raw power by removing singles from slugging percentage. Shows extra bases per at-bat. Variables: SLG = Slugging Percentage, AVG = Batting Average, 2B = Doubles, 3B = Triples, HR = Home Runs

Formula:

\(\text{ISO} = \text{SLG} - \text{AVG} = \frac{2B + 2(3B) + 3(HR)}{AB}\)

Example:

Player with .550 SLG and .300 AVG: ISO = .550 - .300 = .250

OPS Plus

OPS+

intermediate Advanced Batting

Baseball

Park and league-adjusted OPS. 100 is league average, with each point representing a percentage above or below. Variables: OBP = On-Base Percentage, SLG = Slugging Percentage, lgOBP = League OBP, lgSLG = League SLG (adjusted for park)

Formula:

\(\text{OPS+} = 100 \times \left( \frac{\text{OBP}}{\text{lgOBP}} + \frac{\text{SLG}}{\text{lgSLG}} - 1 \right)\)

Example:

OBP .380, lgOBP .320, SLG .500, lgSLG .400: OPS+ = 100 × (1.1875 + 1.25 - 1) = 144

Weighted Runs Above Average

wRAA

advanced Advanced Batting

Baseball

Offensive runs above average based on wOBA. Foundation for the batting component of WAR. Variables: wOBA = Player wOBA, lgwOBA = League wOBA, wOBA Scale = ~1.15 (converts to runs), PA = Plate Appearances

Formula:

\(\text{wRAA} = \frac{(\text{wOBA} - \text{lgwOBA})}{\text{wOBA Scale}} \times PA\)

Example:

Player with .400 wOBA, lgwOBA .320, wOBA Scale 1.15, 600 PA: wRAA = ((.400-.320)/1.15) × 600 = 41.7 runs

wOBA

advanced Advanced Batting

Baseball

Weights each method of reaching base by its actual run value. Considered the best single measure of offensive contribution. Linear weights are updated annually. Variables: BB = Walks, HBP = Hit By Pitch, 1B = Singles, 2B = Doubles, 3B = Triples, HR = Home Runs (weights are approximate, vary by year)

Formula:

\(\text{wOBA} = \frac{0.69(BB) + 0.72(HBP) + 0.88(1B) + 1.24(2B) + 1.56(3B) + 2.00(HR)}{AB + BB + SF + HBP}\)

Example:

Player: 60 BB, 5 HBP, 100 1B, 30 2B, 5 3B, 25 HR, 500 AB, 4 SF: wOBA = (41.4+3.6+88+37.2+7.8+50)/569 = 228/569 = .400

wRC+

advanced Advanced Batting

Baseball

Park and league-adjusted runs created. 100 is league average; each point above/below represents a percentage better/worse than average. Variables: wRAA = Weighted Runs Above Average, PA = Plate Appearances, lgR/PA = League Runs per PA, lgwRC/PA = League wRC per PA

Formula:

\(\text{wRC+} = \left( \frac{\text{wRAA}}{\text{PA}} + \text{lgR/PA} \right) \times \frac{1}{\text{Park Factor}} \times \frac{1}{\text{lgwRC/PA}} \times 100\)

Example:

A wRC+ of 140 means the batter created 40% more runs than league average after park adjustment.

Defensive Runs Saved

DRS

advanced Advanced Fielding

Baseball

Comprehensive defensive metric from Baseball Info Solutions. Measures runs saved across all defensive components. Variables: rPM = Plus/Minus Runs, rGDP = GDP Runs, rARM = Outfield Arm Runs, rHR = Home Run Robbing Runs, rGFP = Good Fielding Play Runs

Formula:

\(\text{DRS} = \text{rPM} + \text{rGDP} + \text{rARM} + \text{rHR} + \text{rGFP}\)

Example:

DRS of +20 means the player saved 20 runs above average through defense.

Ultimate Zone Rating

UZR

advanced Advanced Fielding

Baseball

Advanced defensive metric measuring runs saved above average based on play-by-play data and zone information. Variables: RngR = Range Runs, ErrR = Error Runs, DPR = Double Play Runs

Formula:

\(\text{UZR} = \sum(\text{Zone Runs}) = \text{RngR} + \text{ErrR} + \text{DPR}\)

Example:

UZR of +15 means the fielder saved 15 runs above average over the season.

Strikeout Percentage

intermediate Advanced Pitching

Baseball

Percentage of plate appearances ending in strikeouts. Rate-based version of K/9, unaffected by innings pitched. Variables: K = Strikeouts, TBF = Total Batters Faced

Formula:

\(\text{K\%} = \frac{K}{TBF} \times 100\)

Example:

Pitcher with 180 K in 700 TBF: K% = (180/700) × 100 = 25.7%

Walk Percentage

BB%

intermediate Advanced Pitching

Baseball

Percentage of plate appearances resulting in walks. Better command indicator than BB/9. Variables: BB = Walks (excluding IBB), TBF = Total Batters Faced

Formula:

\(\text{BB\%} = \frac{BB}{TBF} \times 100\)

Example:

Pitcher with 45 BB in 700 TBF: BB% = (45/700) × 100 = 6.4%

Expected Fielding Independent Pitching

xFIP

advanced Advanced Pitching

Baseball

FIP with home runs regressed to league-average HR/FB rate. Better at predicting future performance than FIP. Variables: FB = Fly Balls, lgHR/FB = League HR per Fly Ball rate (~10-11%), others same as FIP

Formula:

\(\text{xFIP} = \frac{13(FB \times \text{lgHR/FB}) + 3(BB + HBP) - 2(K)}{IP} + C\)

Example:

If pitcher has 200 FB and lgHR/FB is 10.5%: Expected HR = 21, then calculate like FIP

FIP

advanced Advanced Pitching

Baseball

Estimates ERA based only on strikeouts, walks, HBP, and home runs—outcomes the pitcher controls. C is a constant to put FIP on ERA scale (usually around 3.10). Variables: HR = Home Runs, BB = Walks, HBP = Hit By Pitch, K = Strikeouts, IP = Innings Pitched, C = FIP Constant (~3.10)

Formula:

\(\text{FIP} = \frac{13(HR) + 3(BB + HBP) - 2(K)}{IP} + C\)

Example:

20 HR, 50 BB, 5 HBP, 180 K, 180 IP: FIP = (260+165-360)/180 + 3.10 = 0.36 + 3.10 = 3.46

Skill-Interactive ERA

SIERA

advanced Advanced Pitching

Baseball

Advanced metric considering strikeouts, walks, and ground ball rates with interaction effects. Best predictor of future ERA. Variables: SO/PA = Strikeouts per PA, BB/PA = Walks per PA, GB/FB = Ground Ball to Fly Ball Ratio (full formula has additional terms)

Formula:

\(\text{SIERA} = 6.145 - 16.986(\text{SO/PA}) + 11.434(\text{BB/PA}) - 1.858(\text{GB/FB}) + 7.653(\text{SO/PA})^2 + ...\)

Example:

SIERA is complex to calculate by hand; best obtained from FanGraphs. Elite pitchers are under 3.00.

Base Running Runs

BsR

advanced Baserunning

Baseball

Total baserunning value in runs. Combines stolen base value, advancement on hits, and avoiding double plays. Variables: wSB = Weighted Stolen Base Runs, UBR = Ultimate Base Running (advancement), wGDP = Weighted GDP runs

Formula:

\(\text{BsR} = \text{wSB} + \text{UBR} + \text{wGDP}\)

Example:

BsR of +5 means the player added 5 runs of value through baserunning above average.

Batting Average (AVG)

AVG

basic Batting

Baseball

The ratio of hits to at-bats. One of the oldest and most recognized batting statistics, though it does not account for walks, hit-by-pitches, or the type of hit. Variables: H = Hits, AB = At-Bats

Formula:

\(\text{AVG} = \frac{H}{AB}\)

Example:

A player with 180 hits in 540 at-bats: AVG = 180/540 = .333

On-Base Percentage (OBP)

OBP

basic Batting

Baseball

Measures how frequently a batter reaches base. More valuable than batting average as it includes walks and hit-by-pitches. Variables: H = Hits, BB = Walks, HBP = Hit By Pitch, AB = At-Bats, SF = Sacrifice Flies

Formula:

\(\text{OBP} = \frac{H + BB + HBP}{AB + BB + HBP + SF}\)

Example:

Player with 150 H, 60 BB, 5 HBP, 500 AB, 4 SF: OBP = (150+60+5)/(500+60+5+4) = 215/569 = .378

On-Base Plus Slugging

OPS

basic Batting

Baseball

Combines on-base ability with power. Simple addition of OBP and SLG, providing a quick overall offensive measure. Variables: OBP = On-Base Percentage, SLG = Slugging Percentage

Formula:

\(\text{OPS} = \text{OBP} + \text{SLG}\)

Example:

Player with .378 OBP and .550 SLG: OPS = .378 + .550 = .928

Slugging Percentage (SLG)

SLG

basic Batting

Baseball

Measures the power of a hitter by weighting extra-base hits. Total bases divided by at-bats. Variables: 1B = Singles, 2B = Doubles, 3B = Triples, HR = Home Runs, TB = Total Bases, AB = At-Bats

Formula:

\(\text{SLG} = \frac{1B + 2(2B) + 3(3B) + 4(HR)}{AB} = \frac{TB}{AB}\)

Example:

Player with 100 1B, 30 2B, 5 3B, 25 HR in 500 AB: TB = 100+60+15+100 = 275, SLG = 275/500 = .550

Runs Per Win

RPW

advanced Comprehensive

Baseball

Conversion factor from runs to wins. Typically around 10 runs per win in modern baseball. Variables: RS/G = Runs Scored per Game, RA/G = Runs Allowed per Game (there are multiple formulas)

Formula:

\(\text{RPW} \approx 9 \times \sqrt{\frac{\text{RS/G} + \text{RA/G}}{2}} \times 1.5 + 3\)

Example:

In a typical environment: RPW ≈ 10, so 10 runs above average ≈ 1 additional win.

WAR

advanced Comprehensive

Baseball

Comprehensive metric estimating total value in wins above a replacement-level player. The gold standard for player evaluation. Variables: Batting/Baserunning/Fielding = Runs above average in each area, Positional = Position adjustment, League = League adjustment, Replacement = Runs vs replacement level, RPW = Runs Per Win (~10)

Formula:

\(\text{WAR} = \frac{\text{Batting} + \text{Baserunning} + \text{Fielding} + \text{Positional} + \text{League} + \text{Replacement}}{\text{RPW}}\)

Example:

A player with 50 runs above replacement and 10 RPW: WAR = 50/10 = 5.0 (All-Star level)

Fielding Percentage

FPCT

basic Fielding

Baseball

Traditional fielding metric showing percentage of plays made without error. Limited because it doesn't account for range. Variables: PO = Putouts, A = Assists, E = Errors

Formula:

\(\text{FPCT} = \frac{\text{PO} + A}{\text{PO} + A + E}\)

Example:

Fielder with 200 PO, 300 A, 10 E: FPCT = (200+300)/(200+300+10) = 500/510 = .980

Range Factor

intermediate Fielding

Baseball

Putouts and assists per nine innings. Early attempt to measure range; higher is better. Variables: PO = Putouts, A = Assists, Inn = Innings Played

Formula:

\(\text{RF} = \frac{(\text{PO} + A) \times 9}{\text{Inn}}\)

Example:

SS with 250 PO, 400 A in 1400 innings: RF = (650 × 9)/1400 = 4.18

Earned Run Average (ERA)

ERA

basic Pitching

Baseball

The average number of earned runs a pitcher allows per nine innings. The most traditional measure of pitching effectiveness. Variables: ER = Earned Runs, IP = Innings Pitched

Formula:

\(\text{ERA} = \frac{\text{ER} \times 9}{\text{IP}}\)

Example:

Pitcher with 60 ER in 180 IP: ERA = (60 × 9)/180 = 3.00

Strikeouts Per Nine Innings

K/9

basic Pitching

Baseball

Average strikeouts per nine innings pitched. Measures a pitcher's ability to miss bats. Variables: K = Strikeouts, IP = Innings Pitched

Formula:

\(\text{K/9} = \frac{K \times 9}{IP}\)

Example:

Pitcher with 200 K in 180 IP: K/9 = (200 × 9)/180 = 10.0

Walks Per Nine Innings

BB/9

basic Pitching

Baseball

Average walks per nine innings. Measures command; lower is better. Variables: BB = Walks, IP = Innings Pitched

Formula:

\(\text{BB/9} = \frac{BB \times 9}{IP}\)

Example:

Pitcher with 45 BB in 180 IP: BB/9 = (45 × 9)/180 = 2.25

WHIP

basic Pitching

Baseball

Measures how many baserunners a pitcher allows per inning. Lower is better; elite pitchers are under 1.00. Variables: BB = Walks, H = Hits, IP = Innings Pitched

Formula:

\(\text{WHIP} = \frac{BB + H}{IP}\)

Example:

Pitcher with 40 BB, 150 H in 200 IP: WHIP = (40+150)/200 = 0.95

Run Expectancy

advanced Run Expectancy

Baseball

Expected runs to score from current base-out state until end of inning. Foundation for linear weights. Variables: 24 base-out states (8 base states × 3 out states). Updated annually from league data.

Formula:

\(\text{RE} = E[\text{Runs}|\text{Base State}, \text{Outs}]\)

Example:

Bases loaded, 1 out: RE ≈ 1.54 runs. Bases empty, 2 outs: RE ≈ 0.10 runs.

Run Expectancy Change

RE24

advanced Run Expectancy

Baseball

Change in run expectancy from a plate appearance, plus any runs that scored. Measures contextual value. Variables: RE_before = Run expectancy before PA, RE_after = Run expectancy after PA

Formula:

\(\text{RE24} = \text{RE}_{\text{after}} - \text{RE}_{\text{before}} + \text{Runs Scored}\)

Example:

2-run HR with bases empty, 0 out: RE24 = 0.48 - 0.48 + 2 = 2.0 runs of value

Exit Velocity

basic Statcast

Baseball

Speed of the ball immediately after contact. Higher exit velocity correlates with better outcomes. Variables: Measured in miles per hour (mph). League average ~88-89 mph, elite hitters 92+ mph

Formula:

\(\text{EV} = \text{Speed of ball off bat (mph)}\)

Example:

A batted ball leaving the bat at 105 mph has excellent exit velocity.

Launch Angle

basic Statcast

Baseball

Angle at which the ball leaves the bat relative to the ground. Optimal for home runs is 25-35 degrees. Variables: Measured in degrees. Ground balls < 10°, Line drives 10-25°, Fly balls 25-50°, Pop-ups > 50°

Formula:

\(\text{LA} = \text{Vertical angle of ball off bat (degrees)}\)

Example:

A ball hit at 28° launch angle with 100+ mph EV is typically a home run.

Barrel Rate

Brl%

intermediate Statcast

Baseball

Percentage of batted balls that are "barrels" - optimal combination of exit velocity and launch angle resulting in minimum .500 BA and 1.500 SLG. Variables: Barrels = Batted balls with ideal EV/LA combo, BBE = Batted Ball Events

Formula:

\(\text{Barrel\%} = \frac{\text{Barrels}}{\text{BBE}} \times 100\)

Example:

Player with 40 barrels in 300 BBE: Barrel% = (40/300) × 100 = 13.3% (excellent)

Hard Hit Rate

HardHit%

intermediate Statcast

Baseball

Percentage of batted balls with exit velocity of 95 mph or higher. Proxy for quality contact. Variables: BBE = Batted Ball Events, threshold is 95 mph exit velocity

Formula:

\(\text{HardHit\%} = \frac{\text{BBE with EV} \geq 95}{\text{Total BBE}} \times 100\)

Example:

Player with 150 hard-hit balls in 350 BBE: HardHit% = (150/350) × 100 = 42.9%

Expected Batting Average

xBA

advanced Statcast

Baseball

Expected batting average based on quality of contact (exit velocity and launch angle). Helps identify luck vs skill. Variables: Based on historical outcomes of similar batted balls (EV/LA combinations)

Formula:

\(\text{xBA} = f(\text{EV}, \text{LA}, \text{Sprint Speed})\)

Example:

Player with .280 AVG but .310 xBA has been unlucky; regression toward xBA is expected.

Expected Weighted On-Base Average

xwOBA

advanced Statcast

Baseball

Expected wOBA based on quality of contact. The Statcast equivalent of wOBA for measuring true offensive skill. Variables: Based on expected outcomes from exit velocity and launch angle combinations

Formula:

\(\text{xwOBA} = f(\text{EV}, \text{LA}) \text{ for BBE} + \text{actual BB, HBP, K values}\)

Example:

xwOBA of .380 when wOBA is .350 suggests the hitter has been unlucky on batted balls.

Outs Above Average

OAA

advanced Statcast

Baseball

Statcast metric measuring outs saved using actual catch probability based on distance, time, and direction. Variables: Based on comparing actual catches to expected catches given probability estimates

Formula:

\(\text{OAA} = \sum(\text{Catch Probability Difference})\)

Example:

OAA of +12 means the fielder made 12 more outs than expected based on catch difficulty.

Leverage Index

advanced Win Probability

Baseball

Measures importance of a situation relative to average. LI of 1.0 is average; 2.0 is twice as important. Variables: Based on range of possible WPA outcomes in the situation vs average PA

Formula:

\(\text{LI} = \frac{\text{WPA Swing}_{\text{situation}}}{\text{Avg WPA Swing}}\)

Example:

Tie game, bottom 9th, runner on 3rd: LI ≈ 4.5 (very high leverage)

Win Probability Added

WPA

advanced Win Probability

Baseball

Change in win probability from a single play. Context-dependent, giving more weight to clutch situations. Variables: Win probability based on score, inning, base-out state, and home/away

Formula:

\(\text{WPA} = P(\text{Win})_{\text{after}} - P(\text{Win})_{\text{before}}\)

Example:

Walk-off HR: WPA = 1.00 - 0.40 = +0.60 (if team had 40% win probability before).

Block Percentage

BLK%

intermediate Defense

Basketball

Percentage of opponent two-point attempts blocked while player is on court. Variables: BLK = Blocks, Opp2PA = Opponent Two-Point Attempts

Formula:

\(\text{BLK\%} = \frac{\text{BLK} \times \text{TmMin}/5}{\text{Min} \times (\text{Opp2PA})} \times 100\)

Example:

BLK% of 5% is excellent (elite rim protectors are 6%+).

Steal Percentage

STL%

intermediate Defense

Basketball

Percentage of opponent possessions ending in a steal by this player. Variables: STL = Steals, OppPoss = Opponent Possessions

Formula:

\(\text{STL\%} = \frac{\text{STL} \times \text{TmMin}/5}{\text{Min} \times \text{OppPoss}} \times 100\)

Example:

STL% of 2.5% is excellent (league average ~1.5%).

Net Rating

NetRtg

basic Efficiency

Basketball

Point differential per 100 possessions. Measures overall impact on both ends. Variables: ORtg = Offensive Rating, DRtg = Defensive Rating

Formula:

\(\text{NetRtg} = \text{ORtg} - \text{DRtg}\)

Example:

ORtg 115, DRtg 105: NetRtg = +10 (elite two-way impact)

Defensive Rating

DRtg

intermediate Efficiency

Basketball

Points allowed per 100 possessions. Lower is better. Individual DRtg is difficult to measure from box score. Variables: Points Allowed = Opponent scoring, Possessions = Team possessions while player on court

Formula:

\(\text{DRtg} = \frac{\text{Points Allowed}}{\text{Possessions}} \times 100\)

Example:

DRtg of 105 means allowing 105 points per 100 possessions (good defense).

Offensive Rating

ORtg

intermediate Efficiency

Basketball

Points produced per 100 possessions. Individual version measures a player's offensive efficiency. Variables: Points Produced includes scoring and assist credit. Possessions = floor estimate of possessions used.

Formula:

\(\text{ORtg} = \frac{\text{Points Produced}}{\text{Total Possessions}} \times 100\)

Example:

ORtg of 115 means producing 115 points per 100 possessions (excellent).

Effective Field Goal Percentage

eFG%

basic Four Factors

Basketball

First of Dean Oliver's Four Factors. Most important factor (~40% weight). Variables: Same as eFG% above

Formula:

\(\text{eFG\%} = \frac{\text{FGM} + 0.5 \times \text{3PM}}{\text{FGA}}\)

Example:

eFG% of 54% is excellent (league average ~52%).

Four Factors - Free Throws

FT Rate

basic Four Factors

Basketball

Fourth of Four Factors. Free throws made per field goal attempt (~15% weight). Variables: FTM = Free Throws Made, FGA = Field Goal Attempts

Formula:

\(\text{FT Rate} = \frac{\text{FTM}}{\text{FGA}}\)

Example:

FT Rate of 0.25 means 25 free throws made per 100 field goal attempts.

Offensive Rebound Percentage

ORB%

basic Four Factors

Basketball

Third of Four Factors. Offensive rebounding rate (~20% weight). Variables: ORB = Team Offensive Rebounds, OppDRB = Opponent Defensive Rebounds

Formula:

\(\text{ORB\%} = \frac{\text{ORB}}{\text{ORB} + \text{OppDRB}}\)

Example:

Team ORB% of 28% means getting 28% of offensive rebounds (good).

Turnover Percentage

TOV%

basic Four Factors

Basketball

Second of Four Factors. Lower is better (~25% weight). Variables: TOV = Turnovers, FGA = Field Goal Attempts, FTA = Free Throw Attempts

Formula:

\(\text{TOV\%} = \frac{\text{TOV}}{\text{FGA} + 0.44 \times \text{FTA} + \text{TOV}}\)

Example:

Team TOV% of 12% is good (lower = fewer turnovers per possession).

Field Goal Percentage

FG%

basic Offense

Basketball

Percentage of field goal attempts made

Formula:

\(FG% = FGM / FGA\)

Player Efficiency Rating

PER

advanced Player Rating

Basketball

John Hollinger's all-in-one rating. League average is 15.0. Favors volume scorers and doesn't fully capture defense. Variables: Complex formula involving all box score stats, league pace, and team performance factors. g = league factor

Formula:

\(\text{PER} = \frac{1}{\text{Min}} \times [\text{3PM} + \frac{2}{3}\text{AST} + (2 - g \times \frac{\text{tmAST}}{\text{tmFG}}) \times \text{FGM} + ...]\)

Example:

PER of 25+ is MVP-caliber; 20+ is All-Star level; 15 is league average.

Assist Percentage

AST%

intermediate Playmaking

Basketball

Percentage of teammate field goals assisted while player is on court. Measures playmaking. Variables: AST = Assists, TmFGM = Team Field Goals Made, FGM = Player Field Goals Made

Formula:

\(\text{AST\%} = \frac{\text{AST}}{\frac{\text{Min}}{\text{TmMin}/5} \times \text{TmFGM} - \text{FGM}} \times 100\)

Example:

AST% of 35% means player assisted on 35% of teammate baskets while on floor.

Box Plus/Minus

BPM

advanced Plus-Minus

Basketball

Estimates player contribution to team point differential using box score stats. 0.0 is league average. Variables: Regression coefficients applied to box score stats. Includes position, team strength, and interaction terms.

Formula:

\(\text{BPM} = a_1(\text{3PAr}) + a_2(\text{AST\%}) + a_3(\text{TOV\%}) + a_4(\text{USG\%}) + ...\)

Example:

BPM of +8 means the team is 8 points better per 100 possessions with this player.

Real Plus-Minus

RPM

advanced Plus-Minus

Basketball

ESPN's metric combining RAPM with box score information to improve stability. Variables: RAPM = Regularized Adjusted Plus-Minus, Box Score Prior = Predicted RAPM from box score

Formula:

\(\text{RPM} = \text{RAPM} + \text{Box Score Prior}\)

Example:

RPM of +5 (ORPM +3, DRPM +2) indicates elite two-way player.

Regularized Adjusted Plus-Minus

RAPM

advanced Plus-Minus

Basketball

Plus-minus adjusted for teammates and opponents using ridge regression. Foundation for modern plus-minus metrics. Variables: Uses all lineup combinations. Ridge penalty prevents overfitting to small samples.

Formula:

\(\text{RAPM} = \text{Ridge Regression on} \sum_{\text{stints}}(\text{Point Margin})\)

Example:

RAPM of +3 means team outscores opponents by 3 points per 100 possessions with this player.

Value Over Replacement Player

VORP

advanced Plus-Minus

Basketball

Box Plus/Minus converted to cumulative value above replacement level (-2.0 BPM). Variables: BPM = Box Plus/Minus, Min% = Minutes Percentage, -2.0 = Replacement level

Formula:

\(\text{VORP} = [\text{BPM} - (-2.0)] \times \frac{\text{Min\%}}{0.2} \times \frac{\text{Team Games}}{82}\)

Example:

BPM of +6, playing 80% of minutes for 82 games: VORP = 8 × 4 × 1 = 32.0

Defensive Rebound Percentage

DRB%

intermediate Rebounding

Basketball

Percentage of available defensive rebounds grabbed. Variables: DRB = Defensive Rebounds, TmDRB = Team Defensive Rebounds, OppORB = Opponent Offensive Rebounds

Formula:

\(\text{DRB\%} = \frac{\text{DRB} \times \text{TmMin}/5}{\text{Min} \times (\text{TmDRB} + \text{OppORB})} \times 100\)

Example:

DRB% of 25% is very good for a center (elite is 30%+).

Total Rebound Percentage

TRB%

intermediate Rebounding

Basketball

Percentage of available rebounds grabbed while player is on court. Variables: TRB = Total Rebounds, TmTRB = Team Rebounds, OppTRB = Opponent Rebounds

Formula:

\(\text{TRB\%} = \frac{\text{TRB} \times \text{TmMin}/5}{\text{Min} \times (\text{TmTRB} + \text{OppTRB})} \times 100\)

Example:

TRB% of 15% means grabbing 15% of all available rebounds while on court.

Free Throw Rate

FTr

basic Shooting

Basketball

Free throw attempts per field goal attempt. Measures ability to draw fouls. Variables: FTA = Free Throw Attempts, FGA = Field Goal Attempts

Formula:

\(\text{FTr} = \frac{\text{FTA}}{\text{FGA}}\)

Example:

Player with 8 FTA in 16 FGA: FTr = 8/16 = 0.50

Three-Point Attempt Rate

3PAr

basic Shooting

Basketball

Percentage of field goal attempts that are three-pointers. Measures shooting profile. Variables: 3PA = Three-Point Attempts, FGA = Field Goal Attempts

Formula:

\(\text{3PAr} = \frac{\text{3PA}}{\text{FGA}}\)

Example:

Player with 6 3PA in 15 FGA: 3PAr = 6/15 = 0.40 (40%)

True Shooting Percentage

TS%

intermediate Shooting

Basketball

The most accurate measure of shooting efficiency, accounting for free throws and three-pointers. The 0.44 factor estimates possessions used by free throws. Variables: PTS = Points, FGA = Field Goal Attempts, FTA = Free Throw Attempts. 0.44 is FTA modifier (and-ones, technicals, etc.)

Formula:

\(\text{TS\%} = \frac{\text{PTS}}{2 \times (\text{FGA} + 0.44 \times \text{FTA})} \times 100\)

Example:

Player with 25 PTS, 18 FGA, 6 FTA: TS% = 25/(2 × (18 + 2.64)) = 25/41.28 = 60.5%

Pace

basic Team

Basketball

Possessions per 48 minutes. Measures game tempo. Variables: TmPoss = Team Possessions, OppPoss = Opponent Possessions, TmMin = Team Minutes

Formula:

\(\text{Pace} = \frac{48 \times (\text{TmPoss} + \text{OppPoss})}{2 \times (\text{TmMin}/5)}\)

Example:

Pace of 100 means 100 possessions per 48 minutes. NBA average ~100.

Possessions

Poss

basic Team

Basketball

Estimated number of offensive possessions. Foundation for per-possession statistics. Variables: FGA = Field Goal Attempts, ORB = Offensive Rebounds, TOV = Turnovers, FTA = Free Throw Attempts

Formula:

\(\text{Poss} \approx \text{FGA} - \text{ORB} + \text{TOV} + 0.4 \times \text{FTA}\)

Example:

80 FGA, 10 ORB, 15 TOV, 20 FTA: Poss = 80 - 10 + 15 + 8 = 93

Usage Rate

USG%

intermediate Usage

Basketball

Percentage of team possessions used by a player while on court. Measures offensive involvement. Variables: FGA = Field Goal Attempts, FTA = Free Throw Attempts, TOV = Turnovers, TmPoss = Team Possessions

Formula:

\(\text{USG\%} = \frac{\text{FGA} + 0.44(\text{FTA}) + \text{TOV}}{\text{TmPoss}} \times \frac{\text{TmMin}}{5 \times \text{Min}} \times 100\)

Example:

USG% of 30% means the player uses 30% of possessions while on court (very high).

Win Shares Per 48 Minutes

WS/48

intermediate Wins

Basketball

Rate version of Win Shares. League average is .100. Variables: WS = Win Shares, Min = Minutes Played

Formula:

\(\text{WS/48} = \frac{\text{WS}}{\text{Min}} \times 48\)

Example:

WS/48 of .200+ is MVP-caliber efficiency.

Defensive Win Shares

DWS

advanced Wins

Basketball

Wins contributed through defense. More evenly distributed than OWS. Variables: Min% = Minutes Percentage, Tm DRtg = Team Defensive Rating, DRtg = Player Defensive Rating

Formula:

\(\text{DWS} = \frac{\text{Min\%} \times \text{Tm DRtg} \times (1.08 \times \text{lgPPP} - \text{DRtg})}{0.32 \times \text{lgPPP}}\)

Example:

DWS of 4+ indicates strong defensive player.

Offensive Win Shares

OWS

advanced Wins

Basketball

Wins contributed through offense. Based on marginal points produced above baseline. Variables: Points Produced = scoring + assist credit, lgPPP = League Points Per Possession, Poss = Possessions

Formula:

\(\text{OWS} = \frac{\text{Points Produced} - 0.92 \times \text{lgPPP} \times \text{Poss}}{0.32 \times \text{lgPPP} \times \text{Tm Pace}}\)

Example:

OWS of 8+ indicates elite offensive player.

Win Shares

advanced Wins

Basketball

Estimate of wins contributed by a player. Based on marginal offense and defense. Variables: OWS = Offensive Win Shares, DWS = Defensive Win Shares

Formula:

\(\text{WS} = \text{OWS} + \text{DWS}\)

Example:

WS of 12+ for a season is All-NBA caliber.

Defense-adjusted Yards Above Replacement

DYAR

advanced DVOA

Football

Cumulative version of DVOA. Measures total value above replacement level. Variables: DVOA = Rate efficiency, Replacement Level = baseline (-15%), Plays = Volume

Formula:

\(\text{DYAR} = (\text{DVOA} + \text{Replacement Level}) \times \text{Plays}\)

Example:

DYAR of 500 means 500 equivalent yards of value above replacement.

DVOA

advanced DVOA

Football

Football Outsiders' efficiency metric. Compares team to league average, adjusted for opponent and situation. Variables: Success Value = yards and first downs compared to baseline, Opponent Adj = strength of opponent faced

Formula:

\(\text{DVOA} = \frac{\sum(\text{Success Value} - \text{Average}) \times \text{Opponent Adj}}{\text{Plays}}\)

Example:

DVOA of +15% means 15% better than average after adjustments.

Success Rate

basic Efficiency

Football

Percentage of plays that are "successful" - gaining enough yards to stay on schedule. Variables: Success: 1st down = 40% of yards needed, 2nd = 60%, 3rd/4th = 100%

Formula:

\(\text{SR} = \frac{\text{Successful Plays}}{\text{Total Plays}}\)

Example:

60% success rate on 1st down means gaining 4+ yards 60% of the time.

Yards Per Play

YPP

basic Efficiency

Football

Simple but effective measure of offensive efficiency. Variables: Total Yards = Passing + Rushing yards, Total Plays = All offensive plays

Formula:

\(\text{YPP} = \frac{\text{Total Yards}}{\text{Total Plays}}\)

Example:

400 total yards on 65 plays: YPP = 6.15

EPA Per Play

EPA/Play

intermediate Expected Points

Football

Average EPA per play. Best single measure of offensive or defensive efficiency. Variables: EPA = Total Expected Points Added, Total Plays = Number of offensive snaps

Formula:

\(\text{EPA/Play} = \frac{\sum \text{EPA}}{\text{Total Plays}}\)

Example:

EPA/Play of +0.10 is above average offense; +0.15 is elite.

Expected Points

advanced Expected Points

Football

Expected points to be scored from current game state. Foundation for EPA. Variables: Based on historical outcomes from similar situations. Accounts for down, distance, yard line, score differential, time.

Formula:

\(\text{EP} = E[\text{Points}|\text{Down}, \text{Distance}, \text{Field Position}, \text{Time}]\)

Example:

1st & 10 at own 25: EP ≈ 1.0. 1st & goal at 1: EP ≈ 6.0.

Expected Points Added

EPA

advanced Expected Points

Football

Change in expected points from a single play. The gold standard for measuring play value in football. Variables: EP_before = Expected Points before play, EP_after = Expected Points after play

Formula:

\(\text{EPA} = \text{EP}_{\text{after}} - \text{EP}_{\text{before}}\)

Example:

15-yard gain on 2nd & 10: EP before = 1.5, EP after = 3.0. EPA = +1.5

Air Yards

basic Passing

Football

Yards the ball travels through the air before being caught. Measures aggressiveness and depth of target. Variables: LOS = Line of Scrimmage. Negative for behind LOS throws. Count all attempts including incompletions.

Formula:

\(\text{AY} = \sum(\text{Yards from LOS to catch point})\)

Example:

10 passes averaging 8 air yards each = 80 total air yards.

Average Depth of Target

aDOT

basic Passing

Football

Average distance of targets downfield. Higher indicates more aggressive passing attack. Variables: Air Yards = Total intended air yards, Targets = Total pass attempts

Formula:

\(\text{aDOT} = \frac{\sum \text{Air Yards}}{\text{Targets}}\)

Example:

400 air yards on 40 attempts: aDOT = 10.0 yards

Adjusted Net Yards Per Attempt

ANY/A

intermediate Passing

Football

Yards per attempt adjusted for touchdowns, interceptions, and sacks. Excellent predictor of team success. Variables: Yds = Passing Yards, TD = Touchdowns, INT = Interceptions, Sack Yds = Yards Lost to Sacks, Att = Pass Attempts

Formula:

\(\text{ANY/A} = \frac{\text{Yds} + 20(\text{TD}) - 45(\text{INT}) - \text{Sack Yds}}{\text{Att} + \text{Sacks}}\)

Example:

300 yds, 3 TD, 0 INT, 2 sacks (-15 yds), 35 att: ANY/A = (300+60-0-15)/37 = 9.32

CPOE

advanced Passing

Football

Difference between actual and expected completion rate based on throw difficulty. Measures accuracy independent of receiver skill. Variables: Expected Comp% based on distance, coverage, pressure, and other factors from Next Gen Stats

Formula:

\(\text{CPOE} = \text{Actual Comp\%} - \text{Expected Comp\%}\)

Example:

CPOE of +5% means completing 5% more passes than expected given difficulty.

ESPN QBR

QBR

advanced Passing

Football

ESPN's Total Quarterback Rating. Scaled 0-100 with 50 as average. Accounts for EPA, clutch situations, and divides credit between QB and receivers. Variables: EPA = Expected Points Added, includes rush, sack, scramble adjustments. Proprietary formula.

Formula:

\(\text{QBR} = f(\text{EPA}, \text{Clutch}, \text{Division of Credit})\)

Example:

QBR of 70+ is elite. Patrick Mahomes often grades 75-80+.

Passer Rating

advanced Passing

Football

Traditional NFL quarterback rating. Components: a = completion %, b = yards/attempt, c = TD %, d = INT %. Each capped between 0 and 2.375. Variables: a = ((Comp/Att - 0.3) × 5), b = ((Yds/Att - 3) × 0.25), c = (TD/Att × 20), d = (2.375 - (INT/Att × 25)). Each bounded [0, 2.375]

Formula:

\(\text{PR} = \frac{(a + b + c + d)}{6} \times 100\)

Example:

25/35, 300 yds, 3 TD, 0 INT: a=1.61, b=1.39, c=1.71, d=2.375. PR = (7.085/6) × 100 = 118.1

Catch Rate

Catch%

basic Receiving

Football

Percentage of targets caught. Context matters (deep targets lower catch rate). Variables: Receptions = Catches, Targets = Pass attempts to this receiver

Formula:

\(\text{Catch\%} = \frac{\text{Receptions}}{\text{Targets}} \times 100\)

Example:

80 catches on 100 targets: Catch% = 80%

Yards After Catch

YAC

basic Receiving

Football

Yards gained after the catch. Measures receiver skill in creating yards. Variables: Total yards from catch point to where play ends

Formula:

\(\text{YAC} = \text{Total Receiving Yards} - \text{Air Yards on Completions}\)

Example:

800 receiving yards with 500 air yards: YAC = 300 yards

Receiver Air Conversion Ratio

RACR

intermediate Receiving

Football

Receiving yards divided by air yards targeted. Shows efficiency on opportunities. Variables: Receiving Yards = Total yards gained, Air Yards = Intended air yards on all targets

Formula:

\(\text{RACR} = \frac{\text{Receiving Yards}}{\text{Air Yards}}\)

Example:

1000 rec yards on 950 air yards: RACR = 1.05 (above 1.0 means creating YAC)

Yards After Catch Over Expected

YAC+

advanced Receiving

Football

YAC compared to expectation based on catch location and defenders nearby. Variables: Expected YAC based on field position, distance to nearest defender, and play type

Formula:

\(\text{YAC+} = \text{Actual YAC} - \text{Expected YAC}\)

Example:

YAC+ of +1.5/reception means 1.5 extra yards per catch vs expectation.

Yards Per Carry

YPC

basic Rushing

Football

Average yards gained per rush attempt. Simple but affected by situation. Variables: Rushing Yards = Total yards on runs, Carries = Rush attempts

Formula:

\(\text{YPC} = \frac{\text{Rushing Yards}}{\text{Carries}}\)

Example:

1200 yards on 280 carries: YPC = 4.29

Broken Tackles Per Touch

BTT

intermediate Rushing

Football

Rate of broken tackles on rushing and receiving plays. Measures elusiveness. Variables: Broken Tackles = Missed tackles, Touches = Carries + Receptions

Formula:

\(\text{BTT} = \frac{\text{Broken Tackles}}{\text{Touches}}\)

Example:

30 broken tackles on 250 touches: BTT = 0.12 (12%)

Rushing Yards Over Expected

RYOE

advanced Rushing

Football

Yards gained compared to expectation based on blocking, box count, and situation. Variables: Expected Yards based on Next Gen Stats tracking: defenders in box, gap, time to contact

Formula:

\(\text{RYOE} = \text{Actual Yards} - \text{Expected Yards}\)

Example:

RYOE of +1.5/carry means gaining 1.5 extra yards per rush vs expectation.

Win Probability

advanced Win Probability

Football

Probability of winning from current game state. Updates after every play. Variables: Calculated using logistic regression on historical data. Factors include score differential, time remaining, field position, timeouts.

Formula:

\(\text{WP} = P(\text{Win}|\text{Score}, \text{Time}, \text{Field Pos}, \text{Possession})\)

Example:

Up 7 with 2 minutes, opponent ball at own 20: WP ≈ 95%

Win Probability Added

WPA

advanced Win Probability

Football

Change in win probability from a single play. Context-dependent value measure. Variables: WP_before = Win Probability before play, WP_after = Win Probability after play

Formula:

\(\text{WPA} = \text{WP}_{\text{after}} - \text{WP}_{\text{before}}\)

Example:

Game-winning TD: WPA = 1.00 - 0.35 = +0.65 (if WP was 35% before)

Expected Threat

advanced Ball Progression

Soccer

Change in probability of scoring from moving the ball. Values all ball progression, not just shots. Variables: Based on grid of pitch divided into zones, each with historical scoring probability

Formula:

\(\text{xT} = P(\text{Scoring from position})_{\text{end}} - P(\text{Scoring from position})_{\text{start}}\)

Example:

Pass from midfield to edge of box: xT = 0.08 - 0.01 = +0.07

Expected Assists

intermediate Chance Creation

Soccer

Sum of xG values from chances created. Measures quality of chances created for teammates. Variables: Based on xG of shots resulting from player's passes/actions

Formula:

\(\text{xA} = \sum(\text{xG of resulting shots})\)

Example:

Creating 5 chances worth 0.3, 0.1, 0.5, 0.2, 0.4 xG = 1.5 xA

Expected Goals Assisted

xGBuildup

advanced Chance Creation

Soccer

Total xG from possessions where player was involved (excluding assists and shots). Variables: Measures contribution to build-up play separate from direct goal involvement

Formula:

\(\text{xGBuildup} = \sum(\text{xG of possessions involved in})\)

Example:

xGBuildup of 8.0 means involved in possessions creating 8 xG of chances.

Aerial Duel Win Rate

Aerial%

basic Defense

Soccer

Percentage of aerial duels won. Important for defenders and target strikers. Variables: Aerial Duels Won = Headers won, Total Aerial Duels = All contested headers

Formula:

\(\text{Aerial\%} = \frac{\text{Aerial Duels Won}}{\text{Total Aerial Duels}} \times 100\)

Example:

35 won of 50 duels: Aerial% = 70%

Interceptions

Int

basic Defense

Soccer

Number of opponent passes intercepted. Measures reading of the game. Variables: Counted when player intercepts an opponent pass attempt

Formula:

\(\text{Int} = \text{Passes intercepted}\)

Example:

2.5 interceptions per 90 is excellent for a midfielder.

Tackles Won

Tkl Won

basic Defense

Soccer

Percentage of tackle attempts that win possession. Variables: Successful Tackles = Tackles winning the ball, Tackle Attempts = All tackle attempts

Formula:

\(\text{Tkl Won} = \frac{\text{Successful Tackles}}{\text{Tackle Attempts}} \times 100\)

Example:

20 successful tackles of 28 attempts: Tkl Won = 71.4%

Expected Goals Against

xGA

intermediate Defense

Soccer

Sum of xG values from shots faced. Measures quality of chances conceded. Variables: xG values of all shots conceded by team/defender

Formula:

\(\text{xGA} = \sum(\text{xG of shots conceded})\)

Example:

Conceding 1.2 xGA per game is solid defensive performance.

Progressive Carries

ProgC

basic Dribbling

Soccer

Ball carries that move at least 10 meters closer to the opponent goal. Variables: Excludes carries in own defensive third

Formula:

\(\text{ProgC} = \text{Carries moving ball } \geq 10\text{m toward goal}\)

Example:

5 progressive carries per 90 is good for a winger.

Successful Dribbles

Drib%

basic Dribbling

Soccer

Percentage of dribbles that successfully beat a defender. Variables: Successful Dribbles = Dribbles beating defender, Dribble Attempts = All take-on attempts

Formula:

\(\text{Drib\%} = \frac{\text{Successful Dribbles}}{\text{Dribble Attempts}} \times 100\)

Example:

40 successful of 60 attempts: Drib% = 66.7%

Expected Goals per 90

xG/90

basic Expected Goals

Soccer

Expected goals normalized to per-90-minute rate. Standard for comparing players with different minutes. Variables: xG = Total Expected Goals, Minutes = Minutes played

Formula:

\(\text{xG/90} = \frac{\text{xG}}{\text{Minutes}} \times 90\)

Example:

12 xG in 2500 minutes: xG/90 = (12/2500) × 90 = 0.43

Goals Minus Expected Goals

G-xG

basic Expected Goals

Soccer

Difference between actual goals and expected. Positive indicates overperformance (finishing skill or luck). Variables: Goals = Actual goals scored, xG = Expected Goals

Formula:

\(\text{G-xG} = \text{Goals} - \text{xG}\)

Example:

18 goals from 14 xG: G-xG = +4 (excellent finishing or unsustainable luck)

Non-Penalty Expected Goals

npxG

intermediate Expected Goals

Soccer

Expected goals excluding penalty kicks. Better measure of open-play shot quality. Variables: xG = Total Expected Goals, Penalties = Number of penalties taken, 0.76 = typical penalty xG

Formula:

\(\text{npxG} = \text{xG} - (\text{Penalties} \times 0.76)\)

Example:

Player with 15 xG including 3 penalties: npxG = 15 - (3 × 0.76) = 12.72

Expected Goals

advanced Expected Goals

Soccer

Probability that a shot will result in a goal based on historical data. Most important advanced metric in soccer analytics. Variables: Shot location (distance, angle), shot type (foot, head), assist type, game state, and more

Formula:

\(\text{xG} = P(\text{Goal}|\text{Shot Location}, \text{Type}, \text{Body Part}, ...)\)

Example:

Penalty: xG ≈ 0.76. Header from 6 yards: xG ≈ 0.45. 25-yard shot: xG ≈ 0.03

Clean Sheet Percentage

CS%

basic Goalkeeping

Soccer

Percentage of games without conceding. Team-dependent but useful context. Variables: Clean Sheets = Games with 0 goals against, Games = Matches played

Formula:

\(\text{CS\%} = \frac{\text{Clean Sheets}}{\text{Games Played}} \times 100\)

Example:

15 clean sheets in 38 games: CS% = 39.5%

Save Percentage

Save%

basic Goalkeeping

Soccer

Percentage of shots on target saved. Basic goalkeeping measure. Variables: Saves = Shots on target stopped, Shots on Target = All shots requiring a save

Formula:

\(\text{Save\%} = \frac{\text{Saves}}{\text{Shots on Target}} \times 100\)

Example:

85 saves from 100 shots on target: Save% = 85%

Goals Against Minus PSxG

GA-PSxG

intermediate Goalkeeping

Soccer

Difference between goals conceded and post-shot expected goals. Negative = good shot-stopping. Variables: GA = Goals Against, PSxG = Post-Shot Expected Goals

Formula:

\(\text{GA-PSxG} = \text{Goals Against} - \text{PSxG}\)

Example:

25 GA with 30 PSxG: GA-PSxG = -5 (saved 5 goals above expectation)

Post-Shot Expected Goals

PSxG

advanced Goalkeeping

Soccer

Expected goals based on where the shot is going. Measures shot-stopping separate from defense. Variables: Only includes shots on target. Based on shot location, speed, and placement.

Formula:

\(\text{PSxG} = P(\text{Goal}|\text{Shot placement}, \text{Speed}, ...)\)

Example:

Shot to corner at high speed: PSxG ≈ 0.85. Shot at keeper: PSxG ≈ 0.15

Pass Completion Percentage

Pass%

basic Passing

Soccer

Percentage of passes completed. Context matters - higher risk passes have lower completion. Variables: Completed Passes = Successful passes, Total Passes = All pass attempts

Formula:

\(\text{Pass\%} = \frac{\text{Completed Passes}}{\text{Total Passes}} \times 100\)

Example:

500 completed of 600 attempted: Pass% = 83.3%

Pass Into Final Third

Final 1/3

basic Passing

Soccer

Number of passes entering the attacking third. Measures ability to advance play. Variables: Completed passes that end in opponent's final third

Formula:

\(\text{Final 1/3} = \text{Passes into opponent final third}\)

Example:

10 passes into final third per 90 is very good.

Progressive Passes

ProgP

basic Passing

Soccer

Passes that move the ball at least 10 meters closer to the opponent goal. Measures progressive play. Variables: Typically excludes passes in own defensive third and crosses

Formula:

\(\text{ProgP} = \text{Passes moving ball } \geq 10\text{m toward goal}\)

Example:

8 progressive passes per 90 is above average for a midfielder.

High Press Rate

High Press %

basic Pressing

Soccer

Percentage of pressing actions occurring in the attacking third. Variables: Presses = Defensive actions applying pressure to ball carrier

Formula:

\(\text{High Press \%} = \frac{\text{Presses in Final Third}}{\text{Total Presses}} \times 100\)

Example:

40% High Press means team presses in final third 40% of the time.

Passes Allowed Per Defensive Action

PPDA Against

intermediate Pressing

Soccer

Measures how well team plays through opponent press. Higher = better at building out. Variables: Inverse of PPDA - measures resistance to pressing

Formula:

\(\text{PPDA Against} = \frac{\text{Own Passes in Defensive Third}}{\text{Opponent Defensive Actions}}\)

Example:

PPDA Against of 12 means completing 12 passes per opponent defensive action.

PPDA

intermediate Pressing

Soccer

Measures pressing intensity. Lower PPDA = more aggressive pressing. Variables: Defensive Actions = tackles, interceptions, fouls. Measured in opponent's defensive third.

Formula:

\(\text{PPDA} = \frac{\text{Opponent Passes in Own Defensive Third}}{\text{Defensive Actions in Opponent Defensive Third}}\)

Example:

PPDA of 8 means allowing 8 passes before making a defensive action (high press).

Field Tilt

Tilt

intermediate Team

Soccer

Share of touches in the two final thirds. Measures territorial dominance. Variables: Touches in attacking zones only (excludes middle third)

Formula:

\(\text{Tilt} = \frac{\text{Own Final Third Touches}}{\text{Own + Opponent Final Third Touches}} \times 100\)

Example:

Field Tilt of 65% means having 65% of touches in the two attacking thirds.

Points Per Game Expected

xPts

advanced Team

Soccer

Expected points based on xG and xGA in each match. Shows underlying performance. Variables: P(Win) and P(Draw) calculated from xG difference using Poisson distribution

Formula:

\(\text{xPts} = 3 \times P(\text{Win}) + 1 \times P(\text{Draw})\)

Example:

Creating 2.0 xG, conceding 0.8: xPts ≈ 2.3

Expected Goals For Percentage

xGF%

intermediate Expected Goals

Hockey

Share of expected goals when player is on ice. Better than CF% at predicting outcomes. Variables: xGF = Expected Goals For, xGA = Expected Goals Against

Formula:

\(\text{xGF\%} = \frac{\text{xGF}}{\text{xGF} + \text{xGA}} \times 100\)

Example:

2.5 xGF, 1.5 xGA in a game: xGF% = 2.5/4 × 100 = 62.5%

Expected Goals

advanced Expected Goals

Hockey

Probability of a shot becoming a goal based on location, type, and context. Hockey's key advanced metric. Variables: Shot location (distance, angle), shot type (wrist, slap, etc.), game state, rebound, rush

Formula:

\(\text{xG} = P(\text{Goal}|\text{Shot Type}, \text{Distance}, \text{Angle}, ...)\)

Example:

Slot wrist shot: xG ≈ 0.15. Point slap shot: xG ≈ 0.03.

Goals Against Average

GAA

basic Goaltending

Hockey

Goals allowed per 60 minutes. Team-dependent but commonly used. Variables: GA = Goals Against, TOI = Time on Ice in minutes

Formula:

\(\text{GAA} = \frac{\text{GA} \times 60}{\text{TOI}}\)

Example:

80 GA in 3000 minutes: GAA = (80 × 60)/3000 = 1.60

Save Percentage

SV%

basic Goaltending

Hockey

Percentage of shots saved. Basic goaltending metric. League average ~.910. Variables: Saves = Shots stopped, Shots Against = Total shots faced, GA = Goals Against

Formula:

\(\text{SV\%} = \frac{\text{Saves}}{\text{Shots Against}} = 1 - \frac{\text{GA}}{\text{SA}}\)

Example:

850 saves on 920 shots: SV% = 850/920 = .924

Goals Saved Above Expected

GSAx

intermediate Goaltending

Hockey

Goals a goalie saved above what was expected. Positive = better than expected goaltending. Variables: xGA = Expected Goals Against, GA = Goals Against

Formula:

\(\text{GSAx} = \text{xGA} - \text{GA}\)

Example:

Faced 30 xGA, allowed 25: GSAx = +5 (saved 5 goals above expected)

Quality Start Percentage

QS%

intermediate Goaltending

Hockey

Percentage of starts with SV% above .913 (league average). Measures consistency. Variables: Quality Start = Game with SV% ≥ .913 (historically-based threshold)

Formula:

\(\text{QS\%} = \frac{\text{Quality Starts}}{\text{Games Started}} \times 100\)

Example:

40 QS in 55 starts: QS% = 72.7%

PDO

basic Luck

Hockey

Sum of shooting and save percentage while player on ice. Regresses strongly to 100 (or 1.000). Variables: SH% = Team shooting percentage, SV% = Team save percentage (while player on ice)

Formula:

\(\text{PDO} = \text{SH\%} + \text{SV\%}\)

Example:

10% SH + 92% SV = 102 PDO (slightly lucky, will regress)

Points Per 60

P/60

basic Offense

Hockey

Points (goals + assists) per 60 minutes of ice time. Rate-based scoring metric. Variables: Points = Goals + Assists, TOI = Time on Ice in minutes

Formula:

\(\text{P/60} = \frac{\text{Points} \times 60}{\text{TOI}}\)

Example:

70 points in 1400 minutes: P/60 = (70 × 60)/1400 = 3.0

Shooting Percentage

SH%

basic Offense

Hockey

Percentage of shots that are goals. League average ~9%. Can indicate luck or skill. Variables: Goals = Player goals, Shots on Goal = Player shots reaching the net

Formula:

\(\text{SH\%} = \frac{\text{Goals}}{\text{Shots on Goal}} \times 100\)

Example:

25 goals on 200 shots: SH% = 12.5%

Individual Expected Goals

ixG

intermediate Offense

Hockey

Sum of expected goals from a player's shots. Measures shot volume and quality. Variables: xG values of all shots taken by the player

Formula:

\(\text{ixG} = \sum(\text{xG of player's shots})\)

Example:

ixG of 25 from 200 shots means average shot worth 0.125 xG

Individual Points Percentage

IPP

intermediate Offense

Hockey

Percentage of team goals player had a point on while on ice. Measures offensive involvement. Variables: Points = Goals + Assists, GF = Goals For while player on ice

Formula:

\(\text{IPP} = \frac{\text{Points}}{\text{GF}_{\text{on ice}}} \times 100\)

Example:

60 points on 80 team goals while on ice: IPP = 75%

Standings Points Above Replacement

SPAR

intermediate Player Value

Hockey

WAR converted to standings points. Each win = 2 points in NHL standings. Variables: WAR = Wins Above Replacement

Formula:

\(\text{SPAR} = \text{WAR} \times 2\)

Example:

WAR of 3.0: SPAR = 6.0 standings points

Goals Above Replacement

GAR

advanced Player Value

Hockey

Total goals above replacement-level player. Comprehensive value metric. Variables: EV = Even strength, PP = Power play, PK = Penalty kill. Each component measured in goals above replacement.

Formula:

\(\text{GAR} = \text{EV Offense} + \text{EV Defense} + \text{PP} + \text{PK} + \text{Shooting} + \text{Penalties}\)

Example:

GAR of 15 means player contributed 15 goals of value above replacement.

Wins Above Replacement

WAR

advanced Player Value

Hockey

GAR converted to wins. Goals per win varies by era (typically 5-6). Variables: GAR = Goals Above Replacement, Goals per Win ≈ 5.5

Formula:

\(\text{WAR} = \frac{\text{GAR}}{\text{Goals per Win}}\)

Example:

GAR of 16.5 with 5.5 goals/win: WAR = 3.0

Corsi

basic Shot Metrics

Hockey

All shot attempts (for or against). Foundation of possession metrics in hockey. Named after Jim Corsi. Variables: SOG = Shots on Goal, Missed = Shots missing net, Blocked = Shots blocked by opponent

Formula:

\(\text{CF} = \text{Shots on Goal} + \text{Missed Shots} + \text{Blocked Shots}\)

Example:

30 SOG + 15 missed + 10 blocked = 55 CF

Corsi For Percentage

CF%

basic Shot Metrics

Hockey

Share of shot attempts when player is on ice. Above 50% is good; measures puck possession. Variables: CF = Corsi For (team shot attempts), CA = Corsi Against (opponent shot attempts)

Formula:

\(\text{CF\%} = \frac{\text{CF}}{\text{CF} + \text{CA}} \times 100\)

Example:

55 CF, 45 CA: CF% = 55/(55+45) × 100 = 55%

Fenwick

basic Shot Metrics

Hockey

Shot attempts excluding blocked shots. Some prefer this as blocked shots are partially luck. Variables: SOG = Shots on Goal, Missed = Shots missing net

Formula:

\(\text{FF} = \text{Shots on Goal} + \text{Missed Shots}\)

Example:

30 SOG + 15 missed = 45 FF

Fenwick For Percentage

FF%

basic Shot Metrics

Hockey

Fenwick possession share. Similar to CF% but excluding blocked shots. Variables: FF = Fenwick For, FA = Fenwick Against

Formula:

\(\text{FF\%} = \frac{\text{FF}}{\text{FF} + \text{FA}} \times 100\)

Example:

45 FF, 40 FA: FF% = 45/85 × 100 = 52.9%

Relative Corsi

Rel CF%

intermediate Shot Metrics

Hockey

Player's CF% compared to team without them. Shows individual impact on possession. Variables: CF% when player on ice minus CF% when player off ice

Formula:

\(\text{Rel CF\%} = \text{CF\%}_{\text{player on}} - \text{CF\%}_{\text{player off}}\)

Example:

Team has 53% CF with player, 48% without: Rel CF% = +5%

Penalty Kill Percentage

PK%

basic Special Teams

Hockey

Success rate killing penalties. League average ~80%. Variables: PK Opportunities = Times shorthanded, PP Goals Against = Opponent PP goals

Formula:

\(\text{PK\%} = \frac{\text{PK Opportunities} - \text{PP Goals Against}}{\text{PK Opportunities}} \times 100\)

Example:

190 kills of 230 PKs: PK% = 82.6%

Power Play Percentage

PP%

basic Special Teams

Hockey

Power play conversion rate. League average ~20%. Variables: PP Goals = Goals scored on power play, PP Opportunities = Power plays

Formula:

\(\text{PP\%} = \frac{\text{PP Goals}}{\text{PP Opportunities}} \times 100\)

Example:

50 PP goals on 230 opportunities: PP% = 21.7%

Special Teams Index

STI

basic Special Teams

Hockey

Combined special teams efficiency. Useful for quick team evaluation. Variables: PP% = Power Play Percentage, PK% = Penalty Kill Percentage

Formula:

\(\text{STI} = \text{PP\%} + \text{PK\%}\)

Example:

22% PP + 82% PK = 104% STI (above average)

Offensive Zone Start Percentage

OZS%

basic Zone

Hockey

Percentage of faceoffs in offensive zone. High OZS% = easier deployment. Variables: OZ = Offensive Zone faceoffs, DZ = Defensive Zone faceoffs

Formula:

\(\text{OZS\%} = \frac{\text{OZ Faceoffs}}{\text{OZ} + \text{DZ Faceoffs}} \times 100\)

Example:

300 OZ, 200 DZ faceoffs: OZS% = 300/500 × 100 = 60%

Zone Entry Success Rate

Entry%

intermediate Zone

Hockey

Percentage of zone entry attempts that are successful. Measures transition ability. Variables: Successful Entries = Entries maintaining possession, Entry Attempts = All attempts to enter offensive zone

Formula:

\(\text{Entry\%} = \frac{\text{Successful Entries}}{\text{Entry Attempts}} \times 100\)

Example:

80 successful entries of 100 attempts: Entry% = 80%

Zone Entry With Control

Carry-In%

intermediate Zone

Hockey

Percentage of entries via carry or pass (vs dump-in). Controlled entries create more offense. Variables: Controlled Entries = Carry-in or pass-in, Total Entries = All zone entries

Formula:

\(\text{Carry-In\%} = \frac{\text{Controlled Entries}}{\text{Total Entries}} \times 100\)

Example:

60 controlled of 100 entries: Carry-In% = 60%

Greens in Regulation

GIR

basic Approach

Golf

Percentage of greens reached in regulation (par - 2 strokes). Key scoring indicator. Variables: Regulation = Par 3 in 1, Par 4 in 2, Par 5 in 3

Formula:

\(\text{GIR\%} = \frac{\text{Greens Hit in Regulation}}{18} \times 100\)

Example:

13 GIR in a round: GIR% = 72.2%

Proximity To Hole

Prox

basic Approach

Golf

Average distance to hole after approach shots. Better than GIR for approach quality. Variables: Measured for approach shots hitting the green

Formula:

\(\text{Prox} = \frac{\sum \text{Distance to Hole After Approach}}{\text{Approach Shots}}\)

Example:

Average 28 feet from hole after approaches

Driving Accuracy

DA%

basic Driving

Golf

Percentage of fairways hit. Less predictive than distance for scoring. Variables: Fairways Hit = Tee shots on fairway, excludes par 3s

Formula:

\(\text{DA\%} = \frac{\text{Fairways Hit}}{\text{Fairways Possible}} \times 100\)

Example:

9 of 14 fairways: DA% = 64.3%

Driving Distance

basic Driving

Golf

Average driving distance. Measured on specific holes each round. Variables: Average distance of tee shots on measured holes

Formula:

\(\text{DD} = \frac{\sum \text{Drive Distances}}{\text{Measured Drives}}\)

Example:

Average 305 yards (Tour avg ~295-300 yards)

One-Putt Percentage

1-Putt%

basic Putting

Golf

Percentage of greens one-putted. Combines putting skill and approach quality. Variables: Greens with one putt divided by total greens putted

Formula:

\(\text{1-Putt\%} = \frac{\text{One-Putt Greens}}{\text{Total Greens}} \times 100\)

Example:

35% one-putt percentage is very good

Putts Per Round

PPR

basic Putting

Golf

Average putts per round. Misleading because fewer GIR = fewer putts needed. Variables: Total putts divided by rounds played

Formula:

\(\text{PPR} = \frac{\sum \text{Putts}}{\text{Rounds}}\)

Example:

29.5 putts per round (Tour avg ~29)

Three-Putt Avoidance

3-Putt%

basic Putting

Golf

Percentage of greens with three or more putts. Lower is better. Variables: Greens with 3+ putts divided by total greens

Formula:

\(\text{3-Putt\%} = \frac{\text{Three-Putt Greens}}{\text{Total Greens}} \times 100\)

Example:

2.5% three-putt rate is excellent (Tour avg ~3%)

Make Percentage from Distance

Make%

intermediate Putting

Golf

Putting make rate from specific distances. Foundation of strokes gained putting. Variables: d = distance (e.g., 5ft, 10ft, 15ft, 20ft)

Formula:

\(\text{Make\%}_d = \frac{\text{Putts Made from } d}{\text{Attempts from } d} \times 100\)

Example:

3ft: ~99%, 6ft: ~70%, 10ft: ~40%, 20ft: ~15%

Putts Per GIR

P/GIR

intermediate Putting

Golf

Putts per green hit in regulation. Better putting measure than PPR. Variables: Putts counted only on holes where green was hit in regulation

Formula:

\(\text{P/GIR} = \frac{\text{Putts on GIR Holes}}{\text{GIR}}\)

Example:

1.75 P/GIR is excellent (Tour avg ~1.77)

Birdie Average

Bird Avg

basic Scoring

Golf

Average birdies or better per round. Measures scoring ability. Variables: Total birdies and eagles divided by rounds

Formula:

\(\text{Bird Avg} = \frac{\text{Birdies (or better)}}{\text{Rounds}}\)

Example:

4.2 birdies per round is excellent

Bogey Avoidance

basic Scoring

Golf

Percentage of holes played at par or better. Measures consistency. Variables: Holes without bogey or worse divided by total holes

Formula:

\(\text{BA} = \frac{\text{Par or Better}}{\text{Total Holes}} \times 100\)

Example:

14 pars/birdies in 18 holes: BA = 77.8%

Par 5 Scoring Average

Par 5 Avg

basic Scoring

Golf

Average score on par 5s. Should be under 5.0 (birdie opportunities). Variables: Total strokes on par 5s divided by par 5s played

Formula:

\(\text{Par 5 Avg} = \frac{\sum \text{Par 5 Scores}}{\text{Par 5s Played}}\)

Example:

4.55 Par 5 avg is elite

Scoring Average

Avg

basic Scoring

Golf

Average score per round. Simple but affected by course difficulty. Tour avg ~70-71. Variables: Sum of all round scores divided by number of rounds

Formula:

\(\text{Avg} = \frac{\sum \text{Scores}}{\text{Rounds}}\)

Example:

280 total in 4 rounds: Avg = 70.0

Adjusted Scoring Average

Adj Avg

intermediate Scoring

Golf

Scoring average adjusted for field strength and course difficulty. Variables: Field Avg = Average score of field, 71.67 = PGA Tour baseline

Formula:

\(\text{Adj Avg} = \text{Scoring Avg} - (\text{Field Avg} - 71.67)\)

Example:

69.5 avg when field avg is 72.5: Adj Avg = 69.5 - 0.83 = 68.67

Sand Save Percentage

Sand%

basic Short Game

Golf

Percentage of successful up-and-downs from greenside bunkers. Variables: Saves from greenside sand divided by attempts

Formula:

\(\text{Sand\%} = \frac{\text{Up-and-Down from Sand}}{\text{Greenside Bunker Shots}} \times 100\)

Example:

50% sand save is solid (Tour avg ~50%)

Scrambling Percentage

Scramble%

basic Short Game

Golf

Percentage of pars or better when missing green in regulation. Measures short game. Variables: Successful scrambles divided by opportunities (non-GIR holes)

Formula:

\(\text{Scramble\%} = \frac{\text{Pars or Better (missed GIR)}}{\text{Missed GIR}} \times 100\)

Example:

5 pars from 8 missed greens: Scramble% = 62.5%

Strokes Gained Tee To Green

SG:T2G

intermediate Strokes Gained

Golf

Total ball-striking strokes gained. Everything except putting. Variables: Sum of OTT, Approach, and Around The Green

Formula:

\(\text{SG:T2G} = \text{SG:OTT} + \text{SG:APP} + \text{SG:ATG}\)

Example:

Elite ball strikers are +1.5 to +2.0 SG:T2G per round

Strokes Gained Total

SG:T

intermediate Strokes Gained

Golf

Total strokes gained versus field. Sum of all strokes gained categories. Revolutionary metric that changed golf analytics. Variables: OTT = Off The Tee, APP = Approach, ATG = Around The Green, P = Putting

Formula:

\(\text{SG:Total} = \text{SG:OTT} + \text{SG:APP} + \text{SG:ATG} + \text{SG:P}\)

Example:

SG:OTT +0.5, APP +1.2, ATG +0.3, P -0.2 = SG:Total +1.8

Strokes Gained Approach

SG:APP

advanced Strokes Gained

Golf

Strokes gained on approach shots (75-200 yards). Often the most predictive category for scoring. Variables: Calculated from expected strokes before and after approach shot

Formula:

\(\text{SG:APP} = E[\text{Strokes}]_{\text{before}} - E[\text{Strokes}]_{\text{after}} - 1\)

Example:

Approach from 150y to 10 feet vs avg to 25 feet: SG:APP ≈ +0.4

Strokes Gained Around The Green

SG:ATG

advanced Strokes Gained

Golf

Strokes gained within 30 yards of green (excluding putting). Measures short game skill. Variables: Includes chips, pitches, bunker shots. Before and after expected strokes comparison.

Formula:

\(\text{SG:ATG} = E[\text{Strokes}]_{\text{before}} - E[\text{Strokes}]_{\text{after}} - 1\)

Example:

Chip from 20y to 3 feet vs avg to 8 feet: SG:ATG ≈ +0.3

Strokes Gained Off The Tee

SG:OTT

advanced Strokes Gained

Golf

Strokes gained on tee shots compared to field. Measures driving quality combining distance and accuracy. Variables: Expected strokes based on lie after tee shot vs average. Applied on par 4s and 5s.

Formula:

\(\text{SG:OTT} = E[\text{Strokes from lie}]_{\text{before}} - E[\text{Strokes from lie}]_{\text{after}} - 1\)

Example:

Drive to fairway at 280y vs avg position at 260y rough: SG:OTT ≈ +0.25

Strokes Gained Putting

SG:P

advanced Strokes Gained

Golf

Strokes gained putting versus field. Based on make percentage from each distance. Variables: Expected putts from starting distance minus actual putts taken

Formula:

\(\text{SG:P} = \sum_{\text{putts}}(E[\text{Putts}]_{\text{start}} - \text{Actual Putts})\)

Example:

Make 15-footer (E[1.8]) in one putt: SG:P = +0.8

Net Points Won

Net%

basic Net

Tennis

Points won when approaching the net. Good volleyers are 65%+. Variables: Points won at net divided by net approaches

Formula:

\(\text{Net\%} = \frac{\text{Points Won at Net}}{\text{Net Approaches}} \times 100\)

Example:

20 points won from 28 net approaches: Net% = 71.4%

Performance Index

basic Overall

Tennis

Simple sum of serve and return winning percentages minus 100. Positive is winning. Variables: SPW% = Service Points Won %, RPW% = Return Points Won %

Formula:

\(\text{PI} = \text{SPW\%} + \text{RPW\%} - 100\)

Example:

65% SPW + 40% RPW = 105 - 100 = +5 (positive margin)

Total Points Won

TPW%

basic Overall

Tennis

Overall point-winning percentage. 52%+ usually wins the match. Variables: All points won divided by all points played

Formula:

\(\text{TPW\%} = \frac{\text{Total Points Won}}{\text{Total Points Played}} \times 100\)

Example:

110 points won of 200: TPW% = 55%

Dominance Ratio

intermediate Overall

Tennis

Ratio of serve points won to serve points conceded. Above 1.0 is winning. Variables: SPW% = Service Points Won, RPW% = Return Points Won

Formula:

\(\text{DR} = \frac{\text{SPW\%}}{100 - \text{RPW\%}}\)

Example:

SPW% 65%, RPW% 40% (opponent SPW 60%): DR = 65/60 = 1.08

Unforced Errors

basic Rally

Tennis

Errors made without significant pressure. Lower is better. Variables: Errors not attributed to opponent pressure

Formula:

\(\text{UE} = \text{Errors not forced by opponent}\)

Example:

20 unforced errors in a match

Winner to Unforced Error Ratio

W/UE

basic Rally

Tennis

Ratio of winners to unforced errors. Above 1.0 is positive, 1.5+ is excellent. Variables: Winners divided by Unforced Errors

Formula:

\(\text{W/UE} = \frac{\text{Winners}}{\text{Unforced Errors}}\)

Example:

35 winners, 25 UE: W/UE = 1.40

Winners

basic Rally

Tennis

Outright winning shots the opponent cannot touch. Measures offensive firepower. Variables: Count of unreturnable shots (excluding aces)

Formula:

\(\text{W} = \text{Shots opponent cannot reach}\)

Example:

30 winners in a match

Forced Error Percentage

FE%

intermediate Rally

Tennis

Errors forced from opponent through pressure. Measures offensive pressure. Variables: Forced errors by opponent divided by total points

Formula:

\(\text{FE\%} = \frac{\text{Opponent Forced Errors}}{\text{Total Points}} \times 100\)

Example:

25 forced errors in 150 points: FE% = 16.7%

Break Points Converted

BP Conv%

basic Return

Tennis

Percentage of break points converted. 40%+ is excellent. Variables: Break points won divided by total break point opportunities

Formula:

\(\text{BP Conv\%} = \frac{\text{Break Points Won}}{\text{Break Point Opportunities}} \times 100\)

Example:

5 breaks from 12 opportunities: BP Conv% = 41.7%

First Serve Return Points Won

1st Ret%

basic Return

Tennis

Points won when facing first serve. Good returners are 30%+. Variables: Points won against opponent first serves divided by first serves faced

Formula:

\(\text{1st Ret\%} = \frac{\text{Points Won vs 1st Serve}}{\text{1st Serves Faced}} \times 100\)

Example:

21 points won vs 70 first serves: 1st Ret% = 30%

Return Points Won

RPW%

basic Return

Tennis

Points won on opponent's serve. Elite returners are 40%+. Variables: Points won while returning divided by total return points

Formula:

\(\text{RPW\%} = \frac{\text{Points Won Returning}}{\text{Total Return Points}} \times 100\)

Example:

40 points won returning of 100: RPW% = 40%

Second Serve Return Points Won

2nd Ret%

basic Return

Tennis

Points won when facing second serve. Elite returners are 55%+. Variables: Points won against opponent second serves divided by second serves faced

Formula:

\(\text{2nd Ret\%} = \frac{\text{Points Won vs 2nd Serve}}{\text{2nd Serves Faced}} \times 100\)

Example:

19 points won vs 30 second serves: 2nd Ret% = 63.3%

Ace Percentage

Ace%

basic Serve

Tennis

Percentage of service points that are aces. Big servers are 10%+. Variables: Aces = Unreturnable serves, Total Service Points = All points on serve

Formula:

\(\text{Ace\%} = \frac{\text{Aces}}{\text{Total Service Points}} \times 100\)

Example:

12 aces in 100 service points: Ace% = 12%

Break Points Saved

BPS%

basic Serve

Tennis

Percentage of break points saved on serve. 65%+ is excellent. Variables: Break points saved divided by total break points faced

Formula:

\(\text{BP Saved\%} = \frac{\text{Break Points Saved}}{\text{Break Points Faced}} \times 100\)

Example:

8 saved of 10 faced: BP Saved% = 80%

Double Fault Percentage

DF%

basic Serve

Tennis

Percentage of service points lost to double faults. Lower is better; under 3% is good. Variables: Double Faults = Points lost from two consecutive faults

Formula:

\(\text{DF\%} = \frac{\text{Double Faults}}{\text{Total Service Points}} \times 100\)

Example:

3 double faults in 100 service points: DF% = 3%

First Serve Percentage

1st%

basic Serve

Tennis

Percentage of first serves landing in. Higher is better but must balance with effectiveness. Variables: First Serves In = Successful first serves, Total First Serves = All first serve attempts

Formula:

\(\text{1st\%} = \frac{\text{First Serves In}}{\text{Total First Serves}} \times 100\)

Example:

60 of 100 first serves in: 1st% = 60%

First Serve Points Won

1st Won%

basic Serve

Tennis

Points won when first serve lands in. Elite servers are 75%+. Variables: Points won when 1st serve is in divided by 1st serves in

Formula:

\(\text{1st Won\%} = \frac{\text{Points Won on 1st Serve}}{\text{First Serves In}} \times 100\)

Example:

50 points won from 70 first serves in: 1st Won% = 71.4%

Second Serve Points Won

2nd Won%

basic Serve

Tennis

Points won when serving second serve. Top players are 50%+. Variables: Points won on second serve divided by second serves in play

Formula:

\(\text{2nd Won\%} = \frac{\text{Points Won on 2nd Serve}}{\text{Second Serves In}} \times 100\)

Example:

20 points won from 35 second serves: 2nd Won% = 57.1%

Service Games Won

SGW%

basic Serve

Tennis

Percentage of service games held. Top players on fast courts are 90%+. Variables: Service games won (held) divided by total service games

Formula:

\(\text{SGW\%} = \frac{\text{Service Games Won}}{\text{Service Games Played}} \times 100\)

Example:

18 holds in 20 service games: SGW% = 90%

Service Points Won

SPW%

basic Serve

Tennis

Overall percentage of service points won. Elite is 65%+. Variables: All points won while serving divided by all service points

Formula:

\(\text{SPW\%} = \frac{\text{Points Won on Serve}}{\text{Total Service Points}} \times 100\)

Example:

65 points won of 100 on serve: SPW% = 65%

Championship Rounds Win Rate

Champ Rd%

intermediate Durability

MMA

Performance in championship rounds. Measures cardio and deep water ability. Variables: Scoring in 4th and 5th rounds when applicable

Formula:

\(\text{Champ Rd\%} = \frac{\text{Points in Rounds 4-5}}{\text{Total Possible Points R4-5}} \times 100\)

Example:

Winning both championship rounds = strong cardio

Strikes Absorbed Per KO

SA/KO

intermediate Durability

MMA

Significant strikes absorbed per knockout loss. Higher = better chin. Variables: Total career sig strikes absorbed divided by KO/TKO losses

Formula:

\(\text{SA/KO} = \frac{\text{Total Sig Strikes Absorbed}}{\text{Times Knocked Out}}\)

Example:

500 strikes absorbed, 2 KO losses: SA/KO = 250

Output Efficiency

Eff

basic Efficiency

MMA

Ratio of strikes landed to strikes absorbed. Measures trading efficiency. Variables: Can use sig strikes landed vs absorbed, or weighted damage metrics

Formula:

\(\text{Eff} = \frac{\text{Damage Dealt}}{\text{Damage Received}}\)

Example:

150 landed, 75 absorbed: Eff = 2.0

Finish Rate

Fin%

basic Finishing

MMA

Percentage of wins that are finishes (KO/TKO/Sub). Measures finishing ability. Variables: KO/TKO/Submission wins divided by all wins

Formula:

\(\text{Fin\%} = \frac{\text{Wins by Finish}}{\text{Total Wins}} \times 100\)

Example:

10 finishes in 15 wins: Fin% = 66.7%

Knockdown Rate

KD/15

basic Finishing

MMA

Knockdowns per 15 minutes. Measures knockout power. Variables: Knockdowns scored normalized to 15 minutes

Formula:

\(\text{KD/15} = \frac{\text{Knockdowns}}{\text{Fight Time}} \times 15\)

Example:

2 knockdowns in 10 minutes: KD/15 = 3.0

KO/TKO Rate

KO%

basic Finishing

MMA

Percentage of wins by knockout or TKO. Measures striking power. Variables: KO and TKO wins divided by total wins

Formula:

\(\text{KO\%} = \frac{\text{KO/TKO Wins}}{\text{Total Wins}} \times 100\)

Example:

8 KO/TKOs in 15 wins: KO% = 53.3%

Submission Rate

Sub%

basic Finishing

MMA

Percentage of wins by submission. Measures grappling finishing ability. Variables: Submission wins divided by total wins

Formula:

\(\text{Sub\%} = \frac{\text{Submission Wins}}{\text{Total Wins}} \times 100\)

Example:

5 submissions in 15 wins: Sub% = 33.3%

Control Time Percentage

Ctrl%

basic Grappling

MMA

Percentage of fight spent in dominant control position. Key for decision wins. Variables: Time in top control or clinch control divided by fight time

Formula:

\(\text{Ctrl\%} = \frac{\text{Control Time}}{\text{Total Fight Time}} \times 100\)

Example:

6 minutes control in 15 minute fight: Ctrl% = 40%

Submission Attempts Per 15 Minutes

Sub/15

basic Grappling

MMA

Average submission attempts per 15 minutes. Measures ground attack. Variables: All submission attempts normalized to 15 minutes

Formula:

\(\text{Sub/15} = \frac{\text{Submission Attempts}}{\text{Fight Time}} \times 15\)

Example:

2 submission attempts in 10 minutes: Sub/15 = 3.0

Submission Average

SubAvg

basic Grappling

MMA

Average submission attempts per fight

Formula:

\(SubAvg = Submissions attempted per 15 minutes\)

Takedown Accuracy

TD%

basic Grappling

MMA

Percentage of takedown attempts that succeed. Elite wrestlers are 50%+. Variables: Successful takedowns divided by attempts

Formula:

\(\text{TD Acc\%} = \frac{\text{Takedowns Landed}}{\text{Takedowns Attempted}} \times 100\)

Example:

4 of 8 takedowns: TD Acc% = 50%

Takedown Defense

TD Def%

basic Grappling

MMA

Percentage of opponent takedowns defended. Elite is 85%+. Variables: Takedowns defended divided by opponent attempts

Formula:

\(\text{TD Def\%} = \left(1 - \frac{\text{Takedowns Conceded}}{\text{Takedowns Faced}}\right) \times 100\)

Example:

7 defended of 8 faced: TD Def% = 87.5%

Takedowns Per 15 Minutes

TD/15

basic Grappling

MMA

Average takedowns per 15-minute equivalent. Measures wrestling activity. Variables: Takedowns normalized to 15 minutes (standard 3-round fight)

Formula:

\(\text{TD/15} = \frac{\text{Total Takedowns}}{\text{Fight Time}} \times 15\)

Example:

4 takedowns in 10 minutes: TD/15 = 6.0

Guard Pass Rate

Pass%

intermediate Grappling

MMA

Guard passes per minute spent in opponent's guard. Measures top game. Variables: Guard passes divided by time in guard position

Formula:

\(\text{Pass\%} = \frac{\text{Guard Passes}}{\text{Time in Guard (min)}}\)

Example:

2 passes in 4 minutes in guard: Pass% = 0.5/min

Win Streak Average

WSA

basic Overall

MMA

Average length of win streaks. Measures consistency at high level. Variables: Total wins in streaks divided by number of separate streaks

Formula:

\(\text{WSA} = \frac{\text{Sum of Win Streak Lengths}}{\text{Number of Win Streaks}}\)

Example:

Streaks of 5, 3, 4: WSA = 12/3 = 4.0

Distance Strike Rate

Dist%

basic Striking

MMA

Percentage of strikes at distance (vs clinch/ground). Measures fighting style. Variables: Distance strikes divided by all significant strikes

Formula:

\(\text{Dist\%} = \frac{\text{Distance Strikes}}{\text{Total Strikes}} \times 100\)

Example:

100 distance of 150 total: Dist% = 66.7%

Head Strike Rate

Head%

basic Striking

MMA

Percentage of strikes targeting the head. Higher indicates finishing intent. Variables: Head strikes divided by total strikes

Formula:

\(\text{Head\%} = \frac{\text{Head Strikes Landed}}{\text{Total Strikes Landed}} \times 100\)

Example:

80 head strikes of 120 total: Head% = 66.7%

Significant Strike Accuracy

SigStr%

basic Striking

MMA

Percentage of significant strikes that land. Elite strikers are 50%+. Variables: Landed vs Attempted significant strikes

Formula:

\(\text{Str Acc\%} = \frac{\text{Significant Strikes Landed}}{\text{Significant Strikes Attempted}} \times 100\)

Example:

100 landed of 200 attempted: Str Acc% = 50%

Significant Strike Defense

Str Def%

basic Striking

MMA

Percentage of opponent significant strikes avoided/blocked. Higher is better defense. Variables: Strikes Absorbed = strikes that land, Strikes Faced = opponent attempts

Formula:

\(\text{Str Def\%} = \left(1 - \frac{\text{Strikes Absorbed}}{\text{Strikes Faced}}\right) \times 100\)

Example:

80 absorbed of 160 faced: Str Def% = 50%

Significant Strikes Absorbed Per Minute

SApM

basic Striking

MMA

Average significant strikes absorbed per minute. Measures defense and durability. Variables: Significant Strikes Absorbed = Power strikes taken

Formula:

\(\text{SApM} = \frac{\text{Significant Strikes Absorbed}}{\text{Total Fight Time (min)}}\)

Example:

75 sig strikes absorbed in 25 minutes: SApM = 3.0

Significant Strikes Landed Per Minute

SLpM

basic Striking

MMA

Average significant strikes landed per minute of fight time. Key offensive metric. Variables: Significant Strikes = Power strikes (not jabs/feints), Fight Time in minutes

Formula:

\(\text{SLpM} = \frac{\text{Significant Strikes Landed}}{\text{Total Fight Time (min)}}\)

Example:

150 sig strikes in 25 minutes: SLpM = 6.0

Striking Differential

Str Diff

basic Striking

MMA

Difference between strikes landed and absorbed per minute. Positive = winning exchanges. Variables: SLpM = Strikes Landed per Minute, SApM = Strikes Absorbed per Minute

Formula:

\(\text{Str Diff} = \text{SLpM} - \text{SApM}\)

Example:

6.0 SLpM - 3.0 SApM = +3.0 Str Diff

Attack Efficiency

Eff

basic Attacking

Volleyball

Net attacking efficiency accounting for errors. Elite is .350+, good is .250+. Variables: Kills = Points scored, Errors = Attack errors, Attempts = Total attacks

Formula:

\(\text{Eff} = \frac{\text{Kills} - \text{Errors}}{\text{Total Attempts}}\)

Example:

15 kills, 5 errors, 35 attempts: Eff = (15-5)/35 = .286

Attack Error Percentage

AE%

basic Attacking

Volleyball

Percentage of attacks resulting in errors. Lower is better; under 15% is good. Variables: Attack Errors = Attacks hit into net/out/blocked, Total Attempts = All attacks

Formula:

\(\text{AE\%} = \frac{\text{Attack Errors}}{\text{Total Attempts}} \times 100\)

Example:

5 errors in 35 attempts: AE% = 14.3%

Kill Percentage

Kill%

basic Attacking

Volleyball

Percentage of attack attempts resulting in kills. Elite hitters are 40%+. Variables: Kills = Attacks resulting in points, Total Attempts = All attack attempts

Formula:

\(\text{Kill\%} = \frac{\text{Kills}}{\text{Total Attempts}} \times 100\)

Example:

15 kills in 35 attempts: Kill% = 42.9%

Kills Per Set

K/S

basic Attacking

Volleyball

Average kills per set. Primary attacking volume metric. Variables: Total Kills = Attack points, Sets = Sets played

Formula:

\(\text{K/S} = \frac{\text{Total Kills}}{\text{Sets Played}}\)

Example:

50 kills in 15 sets: K/S = 3.33

Points Per Set

Pts/S

basic Attacking

Volleyball

Average points contributed per set. Includes kills, blocks, aces. Variables: Total Points = Kills + Blocks + Aces, Sets = Sets played

Formula:

\(\text{Pts/S} = \frac{\text{Total Points}}{\text{Sets Played}}\)

Example:

60 points in 15 sets: Pts/S = 4.0

Block Error Percentage

BE%

basic Blocking

Volleyball

Percentage of block attempts resulting in errors (net violations, etc.). Variables: Block Errors = Net touches, centerline, etc.

Formula:

\(\text{BE\%} = \frac{\text{Block Errors}}{\text{Block Attempts}} \times 100\)

Example:

3 errors in 40 block attempts: BE% = 7.5%

Blocks Per Set

B/S

basic Blocking

Volleyball

Average blocks (solo + assist) per set. Good blockers are 1.0+. Variables: Total Blocks = Block kills, Sets = Sets played

Formula:

\(\text{B/S} = \frac{\text{Total Blocks}}{\text{Sets Played}}\)

Example:

15 blocks in 15 sets: B/S = 1.0

Solo Blocks Per Set

SB/S

basic Blocking

Volleyball

Average solo blocks per set (no assist). Measures individual blocking. Variables: Solo Blocks = Single player blocks

Formula:

\(\text{SB/S} = \frac{\text{Solo Blocks}}{\text{Sets Played}}\)

Example:

6 solo blocks in 15 sets: SB/S = 0.4

Dig Percentage

Dig%

basic Defense

Volleyball

Success rate on digging attacks

Formula:

\(Dig% = Successful digs / Dig attempts\)

Digs Per Set

D/S

basic Defense

Volleyball

Average digs per set. Liberos typically have highest D/S. Variables: Total Digs = Successful defensive plays, Sets = Sets played

Formula:

\(\text{D/S} = \frac{\text{Total Digs}}{\text{Sets Played}}\)

Example:

45 digs in 15 sets: D/S = 3.0

Dig Efficiency

Dig Eff

intermediate Defense

Volleyball

Percentage of dig attempts that result in playable balls. Variables: Good Digs = Digs allowing offense, Dig Attempts = All defensive plays on attacks

Formula:

\(\text{Dig Eff} = \frac{\text{Good Digs}}{\text{Dig Attempts}}\)

Example:

40 good digs of 50 attempts: Dig Eff = 0.80

Reception Efficiency

Rec Eff

intermediate Passing

Volleyball

Net serve receive efficiency accounting for errors. Variables: Good Receptions = Passes allowing full offense, Errors = Aces/Bad passes

Formula:

\(\text{Rec Eff} = \frac{\text{Good Receptions} - \text{Errors}}{\text{Total Receptions}}\)

Example:

35 good, 5 errors, 50 attempts: Rec Eff = (35-5)/50 = 0.60

Serve Receive Rating

SRR

intermediate Passing

Volleyball

Weighted rating of serve receive quality. 2.0+ is excellent. Variables: Perfect (3) = Ball to setter in zone, Good (2) = Playable, OK (1) = Difficult, Bad (0) = Error/Ace

Formula:

\(\text{SRR} = \frac{3(\text{Perfect}) + 2(\text{Good}) + 1(\text{OK}) + 0(\text{Bad})}{\text{Total Passes}}\)

Example:

10 perfect, 15 good, 5 OK, 2 bad: SRR = (30+30+5+0)/32 = 2.03

Ace Percentage

Ace%

basic Serving

Volleyball

Percentage of serves resulting in aces. Good servers are 8-10%. Variables: Aces = Serves not returned, Total Serves = All serve attempts

Formula:

\(\text{Ace\%} = \frac{\text{Aces}}{\text{Total Serves}} \times 100\)

Example:

5 aces in 50 serves: Ace% = 10%

Aces Per Set

A/S

basic Serving

Volleyball

Average aces per set. Measures serving effectiveness. Variables: Total Aces = Service winners, Sets = Sets played

Formula:

\(\text{A/S} = \frac{\text{Total Aces}}{\text{Sets Played}}\)

Example:

8 aces in 16 sets: A/S = 0.5

Service Error Percentage

SE%

basic Serving

Volleyball

Percentage of serves resulting in errors. Under 10% is good. Variables: Service Errors = Serves into net/out, Total Serves = All serve attempts

Formula:

\(\text{SE\%} = \frac{\text{Service Errors}}{\text{Total Serves}} \times 100\)

Example:

4 errors in 50 serves: SE% = 8%

Assist Percentage

Ast%

basic Setting

Volleyball

Percentage of team kills assisted by setter. Measures setter involvement. Variables: Assists = Sets leading to kills, Team Kills = All team attack points

Formula:

\(\text{Ast\%} = \frac{\text{Assists}}{\text{Team Kills}} \times 100\)

Example:

140 assists, 160 team kills: Ast% = 87.5%

Assists Per Set

Ast/S

basic Setting

Volleyball

Average assists per set. Primary setter productivity metric. Variables: Total Assists = Sets leading to kills, Sets = Sets played

Formula:

\(\text{Ast/S} = \frac{\text{Total Assists}}{\text{Sets Played}}\)

Example:

150 assists in 15 sets: Ast/S = 10.0

Set Win Percentage

Set Win%

basic Team

Volleyball

Percentage of sets won. Measures overall team performance. Variables: Sets won divided by total sets played

Formula:

\(\text{Set Win\%} = \frac{\text{Sets Won}}{\text{Sets Played}} \times 100\)

Example:

42 sets won of 60 played: Set Win% = 70%

Point Scoring Percentage

PSP

intermediate Team

Volleyball

Percentage of your serves resulting in your point (break points). Variables: Points won while serving divided by your serve opportunities

Formula:

\(\text{PSP} = \frac{\text{Points Won Serving}}{\text{Your Service Points}} \times 100\)

Example:

25 points scored serving of 50 serves: PSP = 50%

Sideout Percentage

SO%

intermediate Team

Volleyball

Percentage of opponent serves resulting in your point. Key team metric. Variables: Points won while receiving serve divided by opponent serve opportunities

Formula:

\(\text{SO\%} = \frac{\text{Points Won Receiving}}{\text{Opponent Service Points}} \times 100\)

Example:

30 sideouts of 50 opponent serves: SO% = 60%

Understanding Sports Analytics Formulas

Learn how to interpret and apply these formulas in your analysis.

Formula Notation Guide

Basic symbols: +, −, ×, ÷ represent addition, subtraction, multiplication, and division

Fractions: Written as numerator over denominator

Summation (Σ): Indicates sum of multiple values

Variables: Abbreviations represent statistical categories (e.g., AB = At Bats)

Difficulty Levels

Basic Basic: Simple calculations using common statistics

Intermediate Intermediate: Combines multiple stats with moderate complexity

Advanced Advanced: Complex calculations often requiring league adjustments

Learn More in Tutorials View Glossary