Analytics Primer

An guide to the quantitative models across WoSo.Live.

Soccer is a fluid, low-scoring game where traditional counting statistics - such as goals, assists, and clean sheets - routinely tell misleading stories.

A striker might score a hat trick of simple tap-ins created entirely by her teammates, while an elite playmaker creates five clear-cut openings that her forwards fail to convert. Similarly, a goalkeeper might earn a clean sheet without facing a single difficult shot, while another concedes three times after facing ten point-blank strikes.

The analytics models across WoSo.Live look past surface results to measure what actually occurred on the pitch, operating across four distinct layers:

Layer	Question Answered	Core Metrics
1. Chance Quality	How dangerous was the scoring opportunity before the ball was struck?	xG (Expected Goals)
2. Shot Execution	Where did the ball go, and how difficult was it to save?	xGOT (Expected Goals on Target)
3. Goalkeeping	How many goals did the keeper prevent, how consistent is she, and what is her true talent?	Goals Prevented (GP), SAVE Profile, Bayesian Posteriors
4. On-Pitch Value	How much does a player improve her team’s goal differential and standings points?	RAPM, GAA, GAR, WAR

1. Expected Goals (xG): Evaluating Chance Creation

Expected Goals (xG) measures the quality of a scoring chance. It assigns a probability between 0.00 (impossible to score) and 1.00 (a guaranteed goal) to every attempt taken.

An xG value of 0.25 indicates that, based on historical shots taken under identical circumstances, an average professional scores that chance 25% of the time (or 1 in every 4 attempts).

Opportunity	Match Scenario	Historical Frequency	Expected Goals (xG)
Low-Threat Attempt	30-yard shot taken through defensive traffic	Converted in ~3% of attempts	0.03 xG
Medium-Threat Attempt	Header from an outswinging cross near the edge of the 18-yard box	Converted in ~12% of attempts	0.12 xG
High-Threat Attempt	Central penalty kick or uncontested back-post tap-in	Converted in ~78% of attempts	0.78 xG

What Factors Shape xG?

Distance to Goal: Closer attempts convert at significantly higher baseline rates.
Shooting Angle: Central attempts facing an open goal frame carry far more danger than tight-angle shots near the endline.
Striking Mechanism: Foot strikes convert at higher baseline rates than headers from the exact same pitch coordinates.
Phase of Play: Open-play counter-attacks against disorganized defenses yield higher probabilities than set-piece deliveries into crowded penalty boxes.

Key Takeaway: xG evaluates the chance creator. It answers: Did the team generate dangerous scoring positions, regardless of whether the final touch found the net?

2. Expected Goals on Target (xGOT): Evaluating Shot Placement

While xG measures chance quality before the shot is taken, Expected Goals on Target (xGOT) - frequently called Post-Shot xG - evaluates the shot after it leaves the player’s boot or head.

Once a strike occurs, its trajectory, velocity, and landing destination inside the goal frame are known:

Phase	Metric Value	Event Detail	Practical Interpretation
Chance Opening	0.35 xG	Open look from 12 yards out	An above-average opportunity created by the attacking team.
Scenario A	0.00 xGOT	Attempt flies over crossbar or hits a blocking defender	Threat ends immediately; zero probability of beating the goalkeeper.
Scenario B	0.15 xGOT	Shot struck weakly toward the center of the goal frame	Poor placement reduces chance quality, making the save routine.
Scenario C	0.85 xGOT	Shot driven with pace into the upper side netting	Elite placement converts an average chance into a near-certain goal.

Key Takeaway: Comparing a player’s total xGOT to xG isolates finishing execution. Elite finishers consistently turn modest opportunities into difficult-to-save placements.

3. The SAVE Profile: Advanced Goalkeeper Evaluation

Evaluating a goalkeeper by raw goals conceded or clean sheets primarily reflects team defensive structure rather than individual goalkeeping skill. Even raw save percentage can be misleading: a keeper who faces 20 weak, rolling shots from 30 yards will post an artificially high save percentage, while a keeper who faces five uncontested point-blank breakaways will post a low save percentage despite making exceptional stops.

To isolate true shot-stopping skill, WoSo.Live evaluates goalkeepers across three core dimensions: Workload, Shot-Stopping Efficiency, and Game-to-Game Reliability.

Goals Prevented (GP)

The foundation of shot-stopping evaluation begins with Goals Prevented:

Goals Prevented = Total xGOT Faced − Goals Conceded

What it Means: If a goalkeeper faces 20.0 xGOT across a season and concedes only 15 goals, she has prevented +5.0 goals above what an average professional goalkeeper would have allowed facing those identical shots.
Positive Goals Prevented (+GP): The goalkeeper is outperforming expectation and rescuing her team through elite shot-stopping.
Negative Goals Prevented (−GP): The goalkeeper is allowing routine, savable attempts to enter the net.

Chance Quality (CQ) Tiers & Shot Diet

Every on-target attempt is classified into a Chance Quality (CQ) tier based on its Post-Shot Expected Goals (xGOT):

Danger Tier	xGOT Range	Opportunity Type	Pro Baseline Save Rate	Evaluation Focus
Low Danger (LD)	≤ 0.10 xGOT	Speculative long-distance strikes, weak headers, central rolling balls	~96% to 98%	Routine ball handling; allowing a goal here is a severe blunder.
Medium Danger (MD)	0.11 to 0.35 xGOT	Contested in-box strikes, angled drives, partially screened shots	~75% to 80%	Baseline professional competence; solid positioning and footwork prevail.
High Danger (HD)	> 0.35 xGOT	1v1 breakaways, point-blank rebounds, strikes into the upper-90 corners	~30% to 45%	Pure shot-stopping talent; where elite athleticism and reflex saves separate keepers.

The CQ Mix per 90 A goalkeeper’s workload is defined not only by the total shots she faces, but by the composition of those shots. A keeper with a high High-Danger Mix is under constant pressure from defensive breakdowns, while one with a heavy Low-Danger Mix is shielded by her backline.

Danger-Specific Save Rates (LDSv%, MDSv%, HDSv%)

Rather than evaluating goalkeepers on an aggregate save percentage, WoSo.Live measures save percentages within each individual danger tier against league and global benchmarks:

Low-Danger Save Percentage (LDSv%): The measure of baseline reliability. Elite goalkeepers rarely allow soft goals, maintaining an LDSv% above 98%.
Medium-Danger Save Percentage (MDSv%): Demonstrates consistency on standard in-box chances.
High-Danger Save Percentage (HDSv%): The separator for elite talent. Top-tier goalkeepers stop 40% to 50% of high-danger chances, whereas below-replacement keepers stop fewer than 25%.

Standardized Value & Consistency Metrics

To compare keepers playing behind airtight defenses with those playing behind leaky backlines, the SAVE dashboard introduces two standardized metrics:

Goals Prevented per 10 xGOT (GP/10xGOT) Raw Goals Prevented accumulates with playing time and shot volume. A keeper who faces 60 xGOT will naturally accumulate more raw Goals Prevented than a keeper who faces only 20 xGOT.

GP/10xGOT = (Total Goals Prevented / Total xGOT Faced) × 10

What it Means: For every 10 expected goals on target a keeper faces, how many did she prevent from crossing the line?
Baseline: A league-average goalkeeper sits at 0.00.
Elite Level: Ratings of +1.50 to +2.50 GP/10xGOT indicate a keeper who consistently stops 15% to 25% more goal threat than an average professional.

Above Expected Appearance Percentage (AxA%) Cumulative season totals can hide erratic form. A goalkeeper could compile +5.0 Goals Prevented on the season by posting a single miracle +6.0 performance, while playing below average in every other fixture.

AxA% = (Matches with Goals Prevented > 0 / Total Matches Played) × 100

What it Means: The percentage of appearances in which the goalkeeper outperformed expectation (GP > 0).
Baseline: Average professional goalkeepers post an AxA% between 45% and 50%.
Elite Consistency: Goalkeepers with an AxA% above 65% are game-to-game stabilizers who rarely cost their team points.

Bayesian Shot-Stopping Posteriors

Goalkeeping sample sizes are notoriously volatile. If a backup saves the first four shots she faces in her debut, her raw save rate is 100%, but she is not necessarily the best keeper in the league.

WoSo.Live uses Conjugate Empirical Bayes modeling to estimate a goalkeeper’s true talent distribution:

The Baseline Prior: Every keeper begins anchored to the global professional baseline (a bell curve centered at 0.00 Goals Prevented per shot).
Live Posterior Updating: Each time a shot is faced, the model updates the curve based on the shot’s difficulty (xGOT) and the actual outcome (goal or save).
Curve Center (Peak): Represents the keeper’s most likely true shot-stopping talent. Shifted right = elite shot-stopper; shifted left = below average.
Curve Width (Spread): Represents statistical certainty. A wide, flat curve indicates high uncertainty (small sample size). As a goalkeeper faces 100, 200, and 300 shots, the curve narrows into a tall, sharp peak, confirming her established talent level.

Head-to-Head Probability of Superiority When comparing two goalkeepers, single-number averages ignore sample confidence. The Head-to-Head engine calculates the exact mathematical overlap of both full posterior curves:

Probability of Superiority = P(Talent of Keeper A > Talent of Keeper B)

This answers the scouting question directly: Accounting for sample size, shot difficulty, and historical variance, what is the exact probability that Goalkeeper A is genuinely a better shot-stopper than Goalkeeper B?

4. Regularized Adjusted Plus-Minus (RAPM): Complete On-Pitch Impact

Most decisive soccer contributions occur off the ball: opening passing lanes with an uncredited decoy run, applying a pressing angle that forces a hurried turnover, or tracking a runner to prevent a cutback cross. Traditional box-score tallies miss these events entirely.

Regularized Adjusted Plus-Minus (RAPM) isolates a player’s direct impact on her team’s goal differential per 90 minutes.

The Modeling Sequence

Stint-by-Stint Segmentation: Matches are divided into distinct stints whenever a substitution, goal, or red card alters on-pitch personnel or game state.
Context Residualization (Stage 1 OLS): The model strips away external noise unrelated to individual ability:
- Venue Advantage: Home teams generate higher threat on baseline expectation.
- Score Differential: Teams trailing by two attack aggressively, while teams defending a lead drop into low defensive blocks.
- Numerical Strength: Playing 11v11, 11v10, or 10v11 fundamentally alters baseline scoring rates.
- Schedule Load: 10-day rolling minutes played and cross-country travel mileage are explicitly accounted for.
Player Attribution (Stage 2 Ridge Regression): Simple plus-minus is biased if a player shares the pitch with superstars. RAPM applies Ridge regression to isolate an individual’s contribution independent of her 10 teammates and the 11 opponents on the pitch.

Reading RAPM Values

Offensive RAPM (xGF/90): Expected goals her team generates per 90 minutes driven by her presence on the pitch.
Defensive RAPM (xGA/90): Expected goals her team suppresses per 90 minutes. Positive numbers indicate stronger defensive suppression.
Net RAPM/90: Total isolated possession value (Offensive RAPM + Defensive RAPM). A rating of +0.25 means a player improves her team’s net goal differential by a quarter-goal every full match.

5. Spatial RAPM: Mapping Where Threat Occurs

While Net RAPM produces a single overall score, Spatial RAPM illustrates where on the pitch a player makes her impact.

WoSo.Live partitions the attacking half into 91 distinct zones (a Deep Zone plus a 90-hexagon grid in the final third). The model solves for a player’s isolated offensive creation and defensive suppression inside each individual zone.

These spatial vectors are smoothed using thin-plate splines and rendered via Tanaka shaded elevation contours:

Red and Orange Elevation Ridges: High-impact zones where a player generates significant offensive threat or concedes more threat than league average when the player is on the pitch.
Blue Depressions: Zones where the team produces less threat or delivers heavy defensive suppression.
Contour Peaks: Lighted from the upper-left to visually display the depth and sharpness of a player’s local territorial influence.

6. Wins Above Replacement (WAR): Converting Talent into Standings Value

A rate metric like Net RAPM/90 measures per-minute efficiency, but it does not account for availability. A substitute who plays 150 elite minutes off the bench provides less aggregate value to a club over a season than a reliable starter logging 2,500 minutes at an above-average level.

The Wins Above Replacement (WAR) framework connects per-minute performance with playing time to evaluate a player’s total contribution to her team’s standings position.

The Valuation Chain

Step	Metric	Mathematical Formula	Practical Meaning
1. Per-Minute Talent	Net RAPM / 90	Stage 2 Ridge Regression	Isolated player rate impact per 90 minutes.
2. Average Baseline	Goals Above Average (GAA)	(Net xG per 90 × Nineties) + Finishing Talent	Net goals produced relative to an average player over the same minutes.
3. Replacement Baseline	Goals Above Replacement (GAR)	GAA − (Replacement Floor × Nineties)	Net goals produced relative to an accessible bench or reserve replacement.
4. Standings Impact	Points Above Replacement (PAR)	GAR × 0.65	League table standings points delivered to the team.
5. Match Victories	Wins Above Replacement (WAR)	GAR / 3.65	Total match victories directly added by the player.
6. Season Efficiency	Paced WAR (WAR/30)	(WAR / Nineties) × 30	Value paced to a full 30-match season (minimum 450 minutes).

Core Valuation Concepts

The “Replacement Level” Benchmark

Average talent (GAA = 0.0) is not the baseline of value. If a starting central defender suffers an injury, her club cannot sign a league-average starter mid-season; they must rely on a replacement player - a reserve from the back end of the squad or a youth call-up.

Outfield Replacement Floors: Defined by the bottom 15th percentile of active rotation players in each position group (Center Back, Fullback, Midfielder, Forward), bounded between −0.25 and −0.12 goals per 90 minutes.
Goalkeeper Replacement Floor: Anchored to −0.104 goals per 90 minutes to prevent small backup samples from distorting starter ratings.

Goals to Points (PAR) and Wins (WAR)

Points Above Replacement (PAR): In professional soccer, each +1.0 in net goal differential historically yields approximately 0.65 standings points (PAR = GAR × 0.65).
Wins Above Replacement (WAR): It takes approximately 3.65 net goals above replacement to produce one additional team victory (WAR = GAR / 3.65).

WAR Range	Production Tier	Typical Profile
+3.0 to +4.5 WAR	MVP Contender	Dominant league leader responsible for 3 to 4 team victories over replacement.
+1.5 to +2.5 WAR	High-End Starter	All-League caliber player who consistently swings matches.
+0.8 to +1.4 WAR	Solid Starter	Dependable everyday starter playing above replacement level.
0.0 to +0.5 WAR	Rotational Depth	Bench contributor providing replacement-level support.
< 0.0 WAR	Below Replacement	Player performing below readily available reserve options.

Paced WAR (WAR/30)

Because injuries or transfers limit total minutes, Paced WAR (WAR/30) standardizes performance to a full 30-match season (2,700 minutes) to display per-game efficiency.

To prevent small-sample cameos from distorting the leaderboard, Paced WAR enforces a strict 450-minute qualification floor (five full matches). Players below 450 minutes receive an NA rating, preventing a player who logged 20 fortunate minutes from displaying an unearned 7.0 WAR pace.