David,

First of all a clarification: Price was outnumbered, not the other way around. He had around 3200 while Rosecrans fielded between 4000 and 4500. If Ord had joined in as ordered, the Union forces would have been more than 3 to 4 times the size of Price's. After the late afternoon and evening action, Price was prepared to have another go at it the next morning, but was convinced by his subordinates to go with an earlier plan to rendevous with Van Dorn. By abandoning the field he is considered to have lost while he actually probably got the best of Rosecrans during the actual fighting.