1 – Abstract
An examination of the existing scholarship of First Down Probability (P(1D)) in American football. A fairly unambiguous question, this work reviews ten studies over the past 45 years, albeit mostly in the last decade. Results are generally consistent across sources that P(1D) decreases in linear proportion to distance-to-gain for 1st and 2nd downs, while different sources model 3rd down as being either a weakly fit linear relationship or a slight exponential fit.
4th down was not examined fully by any source because of insufficient data. What data points can be confidently placed seem very close to 3rd down, leading to discussion over whether 3rd down data can serve as a proxy for 4th down in decision-making models.