CTI Model

Understanding the Model Variables

The Corner Threat Index (CTI) captures multiple aspects of corner kick danger. Each component measures a different dimension of set-piece effectiveness.

y₁: Shot Probability

P(Shot within 10 seconds)

Predicts whether the attacking team will take a shot within 10 seconds of the corner kick. Binary outcome (yes/no) converted to a probability. Higher values indicate more immediate offensive threat.

y₂: Expected Goals (xG)

Max xG gain in sequence

Estimates shot quality using Expected Goals (xG) when a shot occurs. This continuous value represents the likelihood that the shot will result in a goal. Tap-ins from 5 yards have high xG, while long-range efforts have low xG.

y₃: Counter-Attack Risk

P(Counter-attack shot by opponent)

Tracks the probability that the defending team will launch a counter-attack and take a shot. Captures the defensive vulnerability that comes with committing players forward for corner kicks.

y₄: Counter xG

xG of counter-attack if it occurs

Measures the quality of the opponent's scoring chance when a counter-attack happens. Fast breaks often lead to high-quality chances, so this risk must be factored into the overall corner assessment.

y₅: Territorial Gain (ΔxT)

Expected Threat change

Uses Expected Threat (xT) grids to measure how much the attacking team improves their field position. Even without a shot, advancing the ball into dangerous areas creates value. Positive values indicate successful territory gain.

CTI: Corner Threat Index

CTI = y₁ × y₂ - 0.5 × y₃ × y₄ + 1.0 × y₅

Combines all components into a single metric representing the overall value of a corner. The formula rewards offensive threat (y₁ × y₂) and territorial gains (y₅), while penalizing counter-attack risk (y₃ × y₄). The coefficients (0.5 and 1.0) are tuned weights to balance these competing factors. Higher CTI = more dangerous corner.

Overall Model Performance

Total Corners

2,243

Teams Analyzed

20

y₁ ECE

0.0806

y₃ ECE

0.0997

CTI Correlation

0.172

Interpreting the Metrics

Expected Calibration Error (ECE): Primary reliability metric. Values below 0.05 are excellent, below 0.10 are acceptable. Shows how well probability estimates match reality.
Correlation: Measures how well predicted values align with actual outcomes. Values above 0.7 indicate strong predictive power, while values above 0.5 are moderate.
Coverage: Analysis covers 2,243 corners across 20 teams, providing a robust sample for model evaluation.

Calibration & Reliability Analysis

Understanding Reliability Curves

Reliability curves show whether the model's confidence matches reality. The dashed diagonal line represents perfect calibration. If the model predicts 70% probability, that outcome should occur 70% of the time. Deviations from this line indicate over-confidence (above the line) or under-confidence (below the line).

y₁: Shot Probability

y₃: Counter-Attack Risk

Prediction vs Reality: Scatter Analysis

Understanding the Scatter Plots

Scatter plots show individual predictions (x-axis) against actual outcomes (y-axis). Points close to the diagonal line indicate accurate predictions. The density of points reveals where the model is most confident and where it struggles. These visualizations help identify systematic biases and improvement opportunities.

y₂: xG Prediction

y₅: Territorial Gain (ΔxT)

CTI: Overall Index

Distribution: CTI Values

Interactive Team Analysis

Select a Team to Analyze Their Corner Patterns

Side-by-side comparison:
Left: NMF tactical pattern showing player movement from initial zones (blue dots) to target areas (red arrows).
Right: Model predictions visualized - green zone shows shot danger, red zone shows counter-attack risk, yellow arrow shows territorial gain.

CTI Score

Shot Prob

Counter Risk

Δx Threat

Teams in This Analysis

This analysis covers all 20 Premier League teams from the 2024/25 season. Each team's corner patterns, tactical approaches, and defensive vulnerabilities contribute to the model's comprehensive understanding of set-piece dynamics.

Team Tactical Patterns - NMF Feature Analysis

Understanding NMF Features

Using Non-negative Matrix Factorization (NMF), 30 distinct tactical patterns have been identified in corner kick execution across all teams. Each team has a dominant pattern (top feature) that characterizes their most common corner strategy. The "Top Weight" shows how strongly a team relies on this particular pattern, while "xT Total" and "xT Avg" measure the territorial threat generated using this approach.

Rank	Team	Corners	Top Feature ID	Top Weight	xT Total	xT Avg
1	Arsenal	59	#12	0.0628	9.36	0.1586
2	Manchester City	58	#11	0.0704	12.85	0.2215
3	Tottenham Hotspur	57	#4	0.0686	14.00	0.2456
4	Newcastle United	55	#12	0.0595	9.13	0.1660
5	Fulham	54	#15	0.0853	8.05	0.1490
6	Brighton	54	#15	0.0698	10.04	0.1859
7	Chelsea	52	#15	0.0794	12.51	0.2406
8	Brentford FC	49	#3	0.0649	7.28	0.1485
9	Leicester City	46	#3	0.1222	2.22	0.0483
10	Southampton	44	#6	0.0633	4.40	0.1000
11	Wolverhampton Wanderers	43	#4	0.0896	2.76	0.0643
12	Bournemouth	43	#3	0.0843	6.84	0.1591
13	Nottingham Forest	42	#3	0.1198	3.80	0.0904
14	Ipswich Town	42	#6	0.0880	5.40	0.1287
15	Crystal Palace	41	#23	0.0768	6.53	0.1591
16	Everton	41	#15	0.0681	3.10	0.0755
17	Aston Villa	40	#3	0.0919	4.23	0.1058
18	West Ham United	37	#3	0.0795	2.89	0.0780
19	Manchester United	36	#3	0.0809	6.45	0.1793
20	Liverpool	34	#15	0.0935	4.62	0.1359

How to Read This Table

Rank: Teams ordered by total number of corners analyzed
Top Feature ID: The dominant tactical pattern (1-30) used by this team
Top Weight: Strength of association with this pattern (higher = more consistent)
xT Total: Cumulative Expected Threat generated from corners
xT Avg: Average Expected Threat per corner (efficiency metric)

Team Corner Performance Analysis

CTI Rankings & Metrics

This section presents comprehensive team rankings based on Corner Threat Index (CTI) averages. The table includes key performance indicators: shot probability, counter-attack risk, and territorial gain. Hover over team logos to see detailed statistics. CTI badges are color-coded: Green (Excellent ≥4.5), Blue (Good ≥3.5), Orange (Average ≥2.5), Red (Poor <2.5).

Rank	Logo	Team	CTI Avg	Shot Prob	Counter Risk	ΔxT	Corners
1	West Ham United Corners: 22751 Shot Prob: 51.6% Counter Risk: 25.84% ΔxT: -0.0012	West Ham United	5.09084	51.6%	25.84%	-0.0012	22751
2	Tottenham Hotspur Corners: 35648 Shot Prob: 47.4% Counter Risk: 20.45% ΔxT: -0.0006	Tottenham Hotspur	5.01205	47.4%	20.45%	-0.0006	35648
3	Arsenal Corners: 36121 Shot Prob: 55.0% Counter Risk: 40.01% ΔxT: -0.0021	Arsenal	4.14177	55.0%	40.01%	-0.0021	36121
4	Aston Villa Corners: 38568 Shot Prob: 46.5% Counter Risk: 56.87% ΔxT: -0.0004	Aston Villa	4.01466	46.5%	56.87%	-0.0004	38568
5	Manchester United Corners: 34133 Shot Prob: 51.1% Counter Risk: 34.04% ΔxT: -0.0009	Manchester United	3.78636	51.1%	34.04%	-0.0009	34133
6	Liverpool Corners: 30129 Shot Prob: 50.0% Counter Risk: 23.95% ΔxT: -0.0014	Liverpool	3.69204	50.0%	23.95%	-0.0014	30129
7	Bournemouth Corners: 31193 Shot Prob: 48.1% Counter Risk: 15.80% ΔxT: -0.0009	Bournemouth	3.50581	48.1%	15.80%	-0.0009	31193
8	Crystal Palace Corners: 33780 Shot Prob: 49.5% Counter Risk: 20.05% ΔxT: -0.0010	Crystal Palace	3.30844	49.5%	20.05%	-0.0010	33780
9	Nottingham Forest Corners: 27586 Shot Prob: 51.5% Counter Risk: 40.89% ΔxT: -0.0012	Nottingham Forest	3.24925	51.5%	40.89%	-0.0012	27586
10	Newcastle United Corners: 34352 Shot Prob: 47.0% Counter Risk: 14.91% ΔxT: -0.0004	Newcastle United	2.90825	47.0%	14.91%	-0.0004	34352
11	Brighton Corners: 31817 Shot Prob: 47.8% Counter Risk: 22.10% ΔxT: -0.0003	Brighton	2.78844	47.8%	22.10%	-0.0003	31817
12	Brentford FC Corners: 34411 Shot Prob: 50.5% Counter Risk: 32.76% ΔxT: -0.0010	Brentford FC	2.73994	50.5%	32.76%	-0.0010	34411
13	Chelsea Corners: 33696 Shot Prob: 46.6% Counter Risk: 27.61% ΔxT: -0.0003	Chelsea	2.65940	46.6%	27.61%	-0.0003	33696
14	Everton Corners: 31316 Shot Prob: 51.9% Counter Risk: 19.91% ΔxT: -0.0011	Everton	2.59257	51.9%	19.91%	-0.0011	31316
15	Manchester City Corners: 37232 Shot Prob: 49.3% Counter Risk: 20.61% ΔxT: -0.0003	Manchester City	2.42928	49.3%	20.61%	-0.0003	37232
16	Ipswich Town Corners: 29208 Shot Prob: 51.6% Counter Risk: 28.91% ΔxT: -0.0010	Ipswich Town	2.08796	51.6%	28.91%	-0.0010	29208
17	Fulham Corners: 33148 Shot Prob: 46.0% Counter Risk: 21.37% ΔxT: -0.0005	Fulham	1.66287	46.0%	21.37%	-0.0005	33148
18	Leicester City Corners: 29558 Shot Prob: 49.0% Counter Risk: 29.28% ΔxT: -0.0011	Leicester City	1.59469	49.0%	29.28%	-0.0011	29558
19	Southampton Corners: 28965 Shot Prob: 49.3% Counter Risk: 20.52% ΔxT: -0.0011	Southampton	1.48950	49.3%	20.52%	-0.0011	28965
20	Wolverhampton Wanderers Corners: 26871 Shot Prob: 46.4% Counter Risk: 20.49% ΔxT: -0.0009	Wolverhampton Wanderers	1.13869	46.4%	20.49%	-0.0009	26871

Offense vs Counter Risk Quadrants

This scatter plot visualizes the trade-off between offensive threat (shot probability) and defensive vulnerability (counter-attack risk). Teams in the top-right quadrant combine high attacking output with elevated counter risk, while bottom-left teams are more conservative. Badge positions reflect each team's tactical approach to corner kicks.

Understanding the Metrics

CTI Avg: Average Corner Threat Index across all corners taken by the team
Shot Prob: Probability of generating a shot within 10 seconds of the corner
Counter Risk: Probability of conceding a counter-attack shot opportunity
ΔxT: Average territorial gain measured by Expected Threat change
Corners: Total number of corners analyzed for this team