The following is a list of definitions of many of the concepts and statistics found throughout Advanced Football Analytics.

Air Yards (AY) - The passing yards forward of the line of scrimmage in which the ball travels through the air. In other words, it is total passing yards minus any yards after catch (YAC) gained by the receiver.

Air Yards Per Attempt (Air YPA) - The average air yards (AY) gained per pass attempt. Note that this does not include any sack yards.

Win Probability (WP) – The probability that a team will win a game in progress, given a particular combination of circumstances including score, time remaining, field position, down, and to go distance. WP is based on a model built on actual outcomes of NFL games from recent seasons that featured similar circumstances.

Win Probability Added (WPA) – The difference between a team’s Win Probability (WP) at the start of a play and the WP at the end of the play. WPA is the measure of a play’s impact on the outcome of a game. An individual player’s WPA is the sum of the WPA of the plays in which that player was directly involved. Being directly involved is defined as an offensive player who ran, threw, or kicked the ball, was targeted by a pass, or flagged for a penalty. Defensive players are credited for WPA when they tackle or sack the ball carrier, are credited with an assisted tackle or sack, cause a fumble, defend a pass, or are flagged for a penalty.

Expected Points (EP) – The value of the current down, distance, and field position situation in terms of future expected net point advantage. In other words, it is the net point value a team can expect given a particular combination of down, distance, and field position. First and goal at the one represents an EP near 6, while 3rd and 20 at a team’s own one yard line represents an EP of about -2. EP differs from Win Probability (WP) in that it does not take into account the game score and time remaining.

Expected Points Added (EPA) – The difference between the Expected Points (EP) at the start of a play and the EP at the end of they play. EPA is the measure of a play’s impact on the score of the game. An individual player’s EPA is the sum of the EPA of the plays in which that player was directly involved. Being directly involved is defined as an offensive player who ran, threw, or kicked the ball, was targeted by a pass, or flagged for a penalty.

Win Probability Added per Play (WPA/P) – The average Win Probability Added per play in which an offensive player is directly involved. WPA/P is a measure of an individual player’s impact on the outcome of his games, on a per play basis.

First Down Probability (P(1D)) – The probability that the offense will earn a new series of downs (or score a TD if it's goal-to-go) based on the current down and distance.

Expected Points Added per Play (EPA/P) – The average Expected Points Added per play in which an offensive player is directly involved. EPA/P is a measure of an individual player’s impact on the scores of his games, on a per play basis. EPA/P differs from WPA/P in that it is not as context-sensitive because it does not consider game score and time remaining.

Positive Win Probability Added (+WPA) – The Win Probability Added attributed to a defensive player, limited to only the plays that are net positives for his team. It is a measure of a defender’s impact on the outcome of games in terms of play-making ability. Only positive plays are considered for individual defenders because very good individual plays can still result in net losses in WPA. For example, a safety who makes a shoe-string tackle to stop a TD would be a great individual play, but the play as a whole would still be a net negative outcome for his team. However, overall individual WPA likely correlates well with +WPA.

Positive Expected Points Added (+EPA) -- The Expected Points Added attributed to a defensive player, limited to only the plays that are net positives for his team. It is a measure of a defender’s impact on the game score in terms of play-making ability. Like for +WPA, only positive plays are considered for individual defenders because very good individual defensive plays can still result in net losses in EPA. However, overall individual EPA likely correlates well with +EPA.

Positive Win Probability Added per Game (+WPA/G) – The measure of a defender’s impact on the outcome of his team’s games, on a per-game basis. Like +WPA, +WPA/G is limited to positive plays for individual defensive players.

Positive Expected Points Added per Game (+EPA/G) – The measure of a defender’s impact on the outcome of his team’s games on a per-game basis. Like +EPA, +EPA/G is limited to positive plays for individual players.

Tackle Factor (TF) – The ratio of a player’s proportion of his team’s tackles compared to what is expected at his position. For example, middle linebackers in a 4-3 typically make 11.9% of their team's tackles. A MLB who made 12.6% of his team's tackles would have a TF of 11.9/12.6 = 1.06. TF is adjusted for a full 16-game season.

Success Rate (SR) – The proportion of plays in which a player was directly involved that would typically be considered successful. Specifically, SR is the percentage of plays resulting in positive Expected Points Added (EPA).

Success Count (SC) – The number of plays in which a player was directly involved that would typically be considered successful. Specifically, SC is the number of plays resulting in positive Expected Points Added (EPA). SC is used primarily for individual defenders, because they should not be penalized for making tackles even if the offense has improved it's EP.

Yards per Attempt (YPA) – Yards gained per pass attempt.

Adjusted Yards per Attempt (AYPA) – A quarterback’s Yards per Attempt (YPA) minus sack yards, adjusted by a 45-yard penalty for each interception thrown. 45 yards is chosen because it is approximately equivalent to the Expected Point (EP) value of an interception.

Target Percentage (Tgt%) – A receiver’s proportion of his team’s pass attempts targeted to him. Tgt% excludes passes thrown away, passes not intended for any particular receiver, and spikes.

Catch Rate (CR) – The proportion of passes targeted to a receiver that are caught.

Yards per Reception (YPR) – The average yards a receiver gains per reception, including Air Yards (AY) and Yards After Catch (YAC).

Targets (Tgts) – The number of pass attempts directed at a particular receiver.

Yards per Target (YPT) – A receiver’s average yards gained per pass attempted to him.

Interception Rate (Int%) – The proportion of passes attempted that result in interceptions.

Fumble Rate (Fum%) – The proportion of carries that running back fumbles the ball. Yards per Rush (YPR) – Yards gained per rush attempt.

Games Played (G) – The number of games in which a player appeared.

Deep Pass Percentage (Deep%) – The proportion of pass targets in which a receiver is greater than 15 yards beyond the line of scrimmage.

Quarterback Hits (QBHits) – The number of times a defender is able to hit the quarterback who is in the process of throwing the ball or immediately following a throw.

Passes Defended (PD) – The number of passes successfully deflected by a defender.

Excitement Index (EI) – The measure of how exciting a game is. EI measures the total movement of the Win Probability (WP) line during a game. The more that WP fluctuates, the more dramatic, uncertain, and exciting a game is.

Comeback Factor (CBF) – The measure of how big a comeback is in a game. CBF is defined as the inverse of the winning team’s lowest Win Probability (WP) during a game. For example, if a winning team’s lowest point in a game is 0.10 WP, its CBF would be 10, which is 1 / 0.10. The higher the CBF, the bigger the comeback.

Leverage Index (LI) – The measure of how critical a play is in potentially determining the outcome of a game. Specifically, LI is based on the difference between the Win Probability Added (WPA) of a potential “good” outcome and the WPA of a “bad” outcome. The LI is the ratio of the potential good WPA to an NFL-average typical WPA.Plays in the final minutes of a close game will have very high LIs, while plays toward the end of blowout games will have very low LIs.

Generic Win Probability (GWP) – The probability that a team would win a game against a notional league-average opponent at a neutral site. GWP is based on actual NFL game outcomes from recent seasons. GWP considers each team’s offensive and defensive running and passing efficiency, turnover rates, and penalty rates, weighted according to how predictive each stat is in determining winners. Adjusted GWP (AdjGWP) is corrected for the strength of a team’s past opponents.

Offensive Generic Win Probability (OGWP) – The probability that a team would win a game against a notional league-average opponent at neutral site, assuming the team in question had a league-average defense. Adjusted OGWP (AdjOGWP) is corrected for the strength of a team’s past opponent defenses.

Defensive Generic Win Probability (DGWP) – The probability that a team would win a game against a notional league-average opponent at neutral site, assuming the team in question had a league-average offense. Adjusted DGWP (AdjDGWP) is corrected for the strength of a team’s past opponent offenses.

Yards After Catch (YAC) - The yards gained by a receiver after catching a pass.

Is there somewhere that explains the methodology behind the ratios and statistics more in depth? For example, which variables are used in calculating win percentage or what the model looks like? Would you be willing to disclose more information?

Jason - the main difference between WPA and EPA is that WPA takes into account the score and time remaining. In a sense, it adds "clutch" factor so to speak. EPA measures the "points" value of particular plays, but WPA takes this and adds to it the game situation. So it is possible that there will be a low correlation between the two, i.e. if some particular player can't get it done when games are close, but for some reason plays really well when games are already out of reach. As far as which one is more useful from a fantasy perspective, I would say EPA. Because in fantasy, you don't really care what the game situation is, you just want raw stats.

These plottings are very interesting but unless they can assess the purely human factors of the game, they merely describe the difference between uphill and downhill. What matters when a team has only, say, a 26% chance of winning, is how much fortitude do they have. If the other team has seized the momentum in the game, how ready are they mentally to get it back?
By the way, if the analysts producing these graphs really believe in the validity of the grammar algorithms that are trying to "correct" my English as I write this, it makes me wonder about their fitness for this kind of project.

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