| Summary: | In this thesis, we focus on decision problems in test cricket. Initially, we address declaration and follow-on decision problems. We then investigate session by session batting and bowling strategy. Later, we extend our analysis to the rating of test cricket players. We also study how the nature and strength of the covariate effects in our match outcome models vary as a match progresses. We model the match outcome given the end of first, second and third innings positions and then use this for decision making. Our declaration models provide a decision support tool to a batting team captain and management to consider the best timing of declarations in the first three innings. Match outcome probabilities (win,draw, loss) are calculated using nominal multinomial logistic regression models. We also propose quantitative decision support for batting strategy in the third innings. We approach the statistical problem by supposing that the third innings run-rate and the target that the side batting third aims to set its opponent are decision variables. The follow-on decision problem is also briefly considered: should a captain enforce the follow-on or not? Surprisingly, we find that the decision to enforce the follow-on or otherwise has no effect on the match outcome. We forecast match outcomes in test cricket in play, session by session. Match outcome probabilities are modelled using multinomial regression, with a win, draw, or loss response, and explanatory variables or covariates relating to match state at the start of each session. These probabilities can facilitate a team captain or management to decide on an aggressive or defensive batting strategy for the coming session. These covariates include the lead, wicket resources used, run-rate, a home advantage factor, and surrogates for the state of the pitch (ground effect) and the pre-match strengths of teams. We attempt to compare our results with bookmakers' odds by means of examples. This thesis also investigates how the covariate effects vary from innings to innings and session to session. The nature of the covariates that influence the match outcome changes as the match progresses. Early in the match, pre-match team strengths have a large effect. This reduces as the match progresses. Home advantage and ground effect appear small and exist only early on. We also extend our analysis to the rating of test cricket players. The rating system is based on player contributions session by session in a test match. This rating system evaluates the performance of the players taking into account the stage of match in which runs and wickets are earned and conceded and the influence of the runs and wickets earned on the match outcome.
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