In the game of cricket, the decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big target for the opponent. However, the opponen...

/pdf/a-probabilistic-approach-to-identifying-run-scoring-3sufdblx3a.pdf

A probabilistic approach to identifying run scoring advantage in the order of playing cricket

In the game of cricket, the result of coin toss is assumed to be one of the determinants of match outcome. The decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big target for the opponent. However, the opponent may fail to show their natural batting performance in the second innings due to a number of factors, including deteriorated pitch conditions and excessive pressure of chasing a high target score. The advantage of batting first has been highlighted in the literature and expert opinions, however, the effect of batting and bowling order on match outcome has not been investigated well enough to recommend a solution to any potential bias. This study proposes a probability theory-based model to study venue-specific scoring and chasing characteristics of teams under different match outcomes. A total of 1117 one-day international matches held in ten popular venues are analyzed to show substantially high scoring advantage and likelihood when the winning team bat in the first innings. Results suggest that the same 'bat-first' winning team is very unlikely to score or chase such a high score if they were to bat in the second innings. Therefore, the coin toss decision may favor one team over the other. A Bayesian model is proposed to revise the target score for each venue such that the winning and scoring likelihood is equal regardless of the toss decision. The data and source codes have been shared publicly for future research in creating competitive match outcomes by eliminating the advantage of batting order in run scoring.

A Probabilistic Approach to Identifying Run Scoring Advantage in the Order of Playing Cricket

In the sport of cricket, as with any other sport, spectators and officials would like the games to be as fair as possible. To this end, we evaluate methods used to determine the winner of interrupted games using statistical accuracy. In the traditional One Day International cricket matches, the current Duckworth‐Lewis (DL) method and the discounted most productive overs (DMPO) method are each used for predicting the winner. However, with the growing popularity of shorter Twenty20 matches, a new Bhattacharya‐Gill‐Swartz (BGS) method has also been introduced. We created both classical and Bayesian intervals to estimate the true accuracy of each. Using past game data from 2005‐2010, we compared the DL, DMPO and BGS methods using the new accuracy intervals and receiver operating characteristic (ROC) curves.

/pdf/statistical-analysis-of-diagnostic-accuracy-with-3bto6d4t1r.pdf

Statistical analysis of diagnostic accuracy with applications to cricket

in Diagnostic Testing with Three Outcomes Scott Clark, Lauren Mondin, Courtney Weber and Jessica Winborn Advisor: Melinda Miller Holt Abstract: In disease testing, patients and doctors are interested in estimates for positive predictive value (PPV) and negative predictive value (NPV). The PPV of a test is the probability that a patient actually has the disease, given a positive test result. The NPV is the probability that a patient actually does not have the disease, given a negative test result. Here we consider diagnostic tests in which the disease state remains uncertain, so the uncertain predictive value (UPV) is also of interest. UPV is the probability that, given an uncertain test result, follow-up testing will remain inconclusive. We derive classical Wald-type and Bayesian interval estimates of PPV, NPV, and UPV. Performance of these intervals is compared through simulation studies of interval coverage and width.

/pdf/interval-estimates-for-predictive-values-in-diagnostic-3dwef3u1jy.pdf

Interval Estimates for Predictive Values in Diagnostic Testing with Three Outcomes

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Statistical analysis of diagnostic accuracy with applications to cricket

Interval Estimates for Predictive Values in Diagnostic Testing with Three Outcomes