All metrics control for opponent, field position, tempo, game state (garbage time), and recency
Drive Efficiency: the offensive or defensive residual of what is explained by a team control, but not by the yards metrics. In simplified terms controlling for explosives, yards per play, and 3 and outs & turnover; how well do you put up points? Teams that score well here are able to sustain drives through playcalling and execution.
Explosive Drives: drives that average more than ~7.5 yards per play. This controls for big plays and how they relate to scoring. Big plays are not really all random and teams will be better at creating/preventing them than others.
Negative Drives: a little bit of a catchall for the defense doing bad things to the offense. Turnovers, 3 and outs, drives that average less than 3.333 yards per play are all contained here. Some teams excel at creating or avoiding these.
Play Efficiency: controlling for Explosive Drives and Negative Drives; how well do you generate yards per play. This is the least important of the core 4 Beta_Rank metrics, but still matters.
Other Stats
Post-Model Points: the predicted points based on the Beta_Rank models and the actual data from the game. This is an excellent stat to isolate the luck component of football; turnovers, special teams touchdowns, etc. I prefer this metric over Post Game Win Expectancy.
Win Probability: Beta_Rank maps teams into model space or Beta_Rank space; basically the team scores themselves. Bucketing the distance between teams for all the games that we have data on (teams about this far apart); how often did the higher Beta_Rank score team win?
Naive Spread: basically the same concept as Win Probability, but this time for the team with the higher Beta_Rank score; how much did similar rated teams against similar rated opponents win by? Its a team characteristic agnostic spread, but it still performs well.
Predicted Points: a predicted team score that takes into account the characteristics of team and opponent. It does not include any Vegas spread information in the prediction.