Submission declined on 31 May 2026 by EatingCarBatteries (talk). This draft appears to contain text generated by a large language model (such as ChatGPT). You cannot use LLMs to generate article content. LLM-generated pages with certain obvious signs of being machine generated may be deleted without notice. These tools are prone to specific issues that violate our policies: hallucinations: they often invent false information and cite non-existent references. unencyclopedic tone: they tend to be vague, promotional, or essay-like, rather than neutral and factual. copyright issues: they may closely paraphrase existing text, leading to copyright violations. Instead, only summarize in your own words a range of independent, reliable, published sources that discuss the subject. See the advice page on large language models for more information. This draft appears to be a duplicate of an existing article. Wikipedia does not permit multiple articles on the same topic. To improve the existing article, please edit it directly at Cumulative accuracy profile. If the article is protected and you cannot edit it, propose your changes on the article's talk page. If you are writing about a different subject with the same name, ask the reviewer to rename your draft to distinguish it. If you would like to continue working on the submission, click on the "Edit" tab at the top of the window. If you have not resolved the issues listed above, your draft will be declined again and potentially deleted. If you need extra help, please ask us a question at the AfC Help Desk or get live help from experienced editors. Please do not remove reviewer comments or this notice until the submission is accepted. Where to get help If you need help editing or submitting your draft, please ask us a question at the AfC Help Desk or get live help from experienced editors. These venues are only for help with editing and the submission process, not to get reviews. If you need feedback on your draft, or if the review is taking a lot of time, you can try asking for help on the talk page of a relevant WikiProject. Some WikiProjects are more active than others so a speedy reply is not guaranteed. How to improve a draft Wikipedia:Contributing to Wikipedia – a basic overview on how to edit Wikipedia. Help:Wikitext – how to use the markup Help:Referencing for beginners – how to include references Wikipedia:Article development – how to develop your article Wikipedia:Writing better articles – how to improve your article Wikipedia:Verifiability – make sure your article includes reliable third-party sources You can also browse Wikipedia:Featured articles and Wikipedia:Good articles to find examples of Wikipedia's best writing on topics similar to your proposed article. Improving your odds of a speedy review To improve your odds of a faster review, tag your draft with relevant WikiProject tags using the button below. This will let reviewers know a new draft has been submitted in their area of interest. For instance, if you wrote about a female astronomer, you would want to add the Biography, Astronomy, and Women scientists tags. Add tags to your draft Editor resources Easy tools: Citation bot (help) | Advanced: Fix bare URLs Declined by EatingCarBatteries 7 days ago. Last edited by EatingCarBatteries 7 days ago. Reviewer: Inform author. Resubmit Please note that if the issues are not fixed, the draft will be declined again.

The Cumulative Accuracy Profile (CAP) is a graphical tool used in statistics and machine learning to evaluate the discriminatory power of binary classification models. It is widely utilized in fields such as credit risk modeling, fraud detection, and direct marketing to assess how effectively a predictive model can distinguish between two classes (e.g., "default" vs. "non-default", "fraud" vs. "legitimate").^[1]

The CAP curve illustrates the cumulative percentage of positive outcomes captured as a function of the cumulative percentage of the total population, sorted by their model-predicted risk score.

A standard CAP diagram consists of three distinct curves plotted on a coordinate system where both the X and Y axes range from 0 to 100%.

• The X-Axis (Population): Represents the cumulative percentage of the population, sorted from the highest predicted probability of the target outcome to the lowest.
• The Y-Axis (Positives): Represents the cumulative percentage of actual positive outcomes (e.g., actual defaults) captured by selecting the given percentage of the population.
• The Random Model: Represented by a diagonal line extending from (0,0) to (100,100). This represents a model with zero predictive power, where the probability of selecting a positive outcome is the same as picking at random.
• The Perfect Model: Represented by a line that rises steeply from (0,0) to 100% of the positive outcomes, and then travels horizontally to (100,100). This represents a hypothetical model that identifies every positive outcome immediately, capturing 100% of the events using the minimum possible number of cases.
• The Proposed Model: The actual performance curve of the model being evaluated. It lies between the Random Model and the Perfect Model. A model with higher predictive power will have a curve that bows further toward the top-left corner of the graph.^[2]

The effectiveness of a model is quantified by the Accuracy Ratio (AR), often referred to in the context of credit risk as the Gini Coefficient. The AR measures the area between the proposed model curve and the random model line, normalized by the maximum possible area (the area between the perfect model and the random model).^[3]

The formula for the Accuracy Ratio is defined as:

${\displaystyle AR={\frac {Area_{Proposed}-Area_{Random}}{Area_{Perfect}-Area_{Random}}}}$

• AR = 0: The model has no discriminatory power (the model curve coincides with the random diagonal).
• AR = 1: The model is perfect (the model curve coincides with the perfect model line).

The CAP curve is frequently compared to the Receiver operating characteristic (ROC) curve. While both are used for model validation, they differ in their construction and utility:

• ROC Curve: Plots the True Positive Rate (Sensitivity) against the False Positive Rate (1 - Specificity). It is generally independent of the prevalence (the proportion of positive cases in the population).
• CAP Curve: Plots the cumulative percentage of positive outcomes against the cumulative percentage of the population. Because it is sensitive to the population distribution, it is often more intuitive for business applications where the focus is on "how many positive cases do we catch if we target the top X% of our population?"^[4]

• Credit Scoring: Banks use CAP curves to determine the percentage of loan defaults captured by reviewing a specific percentage of their highest-risk-score applicants.
• Fraud Detection: Financial institutions use the curve to decide what proportion of transactions to investigate to catch the majority of fraudulent activities.
• Direct Marketing: Businesses use the curve to identify the percentage of their customer base that should be targeted to maximize the conversion rate (capture the highest percentage of total buyers).