Using data from 1,199 matches containing 10,933 ends in the Canadian Men`s Curling Championships, we developed both a three-dimensional empirical state space model and three-dimensional homogeneous and heterogeneous Markov models to estimate win probabilities throughout a curling match. The Markovian win probabilities were derived from the observed scoring probabilities using recursive logic. These win probabilities allowed us to answer questions regarding optimal curling strategy. When presented with the choice to score 1 point or blanking an end, we conclude that teams holding the hammer should choose to blank the end in most situations. Looking at empirical results of conceded matches, we conclude that concession behavior is consistent with a psychological win probability threshold of 2.57%. However, we also find that teams frequently concede when their win probability at time of concession is, in fact, much higher than this threshold. This is true particularly after the 9th end, suggesting that teams are conceding matches when they have up to a 15% chance of winning.
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