This study proposes a statistical measure and a stochastic optimization model for generating risk-seeking wind power offering strategies in electricity markets. Inspired by the value at risk (VaR) to quantify risks in the worst-case scenarios of a profit distribution, a statistical measure is proposed to quantify potential high profits in the best-case scenarios of a profit distribution， which is referred to as value at best (VaB) in the best-case scenarios. Then, a stochastic optimization model based on VaB is developed for a risk-seeking wind power producer, which is formulated as a mixed-integer linear programming problem. By adjusting the parameters in the proposed model, the wind power producer can flexibly manage the potential high profits in the best-case scenarios from the probabilistic perspective. Finally, the proposed statistical measure and risk-seeking stochastic optimization model are verified through case studies.