The accuracy paradox for predictive analytics states that predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. It may be better to avoid the accuracy metric in favor of other metrics such as precision and recall.

Accuracy is often the starting point for analyzing the quality of a predictive model, as well as an obvious criterion for prediction. Accuracy measures the ratio of correct predictions to the total number of cases evaluated. It may seem obvious that the ratio of correct predictions to cases should be a key metric. A predictive model may have high accuracy, but be useless.

In an example predictive model for an insurance fraud application, all cases that are predicted as high-risk by the model will be investigated. To evaluate the performance of the model, the insurance company has created a sample data set of 10,000 claims. All 10,000 cases in the validation sample have been carefully checked and it is known which cases are fraudulent. To analyze the quality of the model, the insurance uses the table of confusion. The definition of accuracy, the table of confusion for model M1Fraud, and the calculation of accuracy for model M1Fraud is shown below.

$\mathrm{A}(M) = \frac{TN + TP}{TN + FP + FN + TP}$ where

TN is the number of true negative cases
FP is the number of false positive cases
FN is the number of false negative cases
TP is the number of true positive cases

Formula 1: Definition of Accuracy

Predicted Negative Predicted Positive
Negative Cases 9,700 150
Positive Cases 50 100

Table 1: Table of Confusion for Fraud Model M1Fraud.

$\mathrm A (M) = \frac{9,700 + 100}{9,700 + 150 + 50 + 100} = 98.0%$

Formula 2: Accuracy for model M1Fraud

With an accuracy of 98.0% model M1Fraud appears to perform fairly well. The paradox lies in the fact that accuracy can be easily improved to 98.5% by always predicting "no fraud". The table of confusion and the accuracy for this trivial “always predict negative” model M2Fraud and the accuracy of this model are shown below.

Predicted Negative Predicted Positive
Negative Cases 9,850 0
Positive Cases 150 0

Table 2: Table of Confusion for Fraud Model M2Fraud.

$\mathrm{A}(M) = \frac{9,850 + 0}{9,850 + 150 + 0 + 0} = 98.5%$

Formula 3: Accuracy for model M2Fraud

Model M2Fraudreduces the rate of inaccurate predictions from 2% to 1.5%. This is an apparent improvement of 25%. The new model M2Fraud shows fewer incorrect predictions and markedly improved accuracy, as compared to the original model M1Fraud, but is obviously useless.

The alternative model M2Fraud does not offer any value to the company for preventing fraud. The less accurate model is more useful than the more accurate model.

Model improvements should not be measured in terms of accuracy gains. It may be going too far to say that accuracy is irrelevant, but caution is advised when using accuracy in the evaluation of predictive models.