When estimating the probability of a successful fourth down the data we use are conditional on teams attempting to go-for-it. We expect better teams to go-for-it more often in a given situation, and worse teams to be put in must-go situations more often. Correlation between the decision to go-for-it and the outcome can lead to biased probability estimates when the decision mechanism is not accounted for. To correct for this we treat it as a missing data problem, fitting a generalized Heckman selection model to all fourth-down plays from the 2014-2021 NFL seasons. We find a positive correlation between the decision to go-for-it and success probability when there are multiple viable choices for teams, and a negative correlation when teams are forced to go-for-it by the game situation. This causes fourth down probabilities estimated using only plays where teams go-for-it to be biased high in fourth-and-short scenarios, and biased low in fourth-and-long scenarios.