*This article is co-authored with Tyler Hickey, a senior math major at Davidson College.*

In Monday night's championship game, a team will reach the other team's 20-yard line. At that moment, they are in the red zone and with it come the stats. The announcers will talk about the offense's red zone scoring percentage, which is the percentage in which a team converts their presence in their opponent's red zone into some form of points.

What if your team has the ball on the other team's 21- or 22-yard line? Should you be excited? If so, then why not the 23- or 24 yard line? Asked another way, where on the field is a position where an offensive score is imminent, where is this red zone, really?

### Scoring and Equivalent Points

To begin, let's determine the value of an offense's position. We will do this through Equivalent Points (or EqPts), which is a statistic used most popularly by the sports analyst and writer Bill Connelly. At the most basic level, Equivalent Points are the average number of points that a team scores from any position on the field. For this analysis we will use the most complete version of EqPts called Third-Level Equivalent Points, which take into account down, distance, and field position in determining EqPts values.

Let's take a look at a small data set to help better understand this concept.

From this very small data set of five plays, we can see that the EqPts (or average points scored) given 1st and 10 at your own 45-yard line = 5: (7+3)/2 = 5. If we were to use three new variables and had the situation of 2nd and 5 from your opponent's 35 yard line, EqPts = 1.5: (3+0)/2 = 1.5.

Now, instead of a sample size of 5 plays, lets look at a graph of Third-Level EqPts that uses 16,658 plays generated from 1st and 10 and 1st and Goal situations from 300 FBS games this season.

As expected, as one gets closer to their opponent's goal line, the higher the EqPts at that position. Interestingly enough, the shape of the curve demonstrates the commonly held notion that "yards are harder to get in the red zone, and therefore more valuable" (obviously in terms of previous definitions of the red zone). Before we go too much into the significance of EqPts in terms of redefining the red zone, let's look at some other historical data that will aid us in our new definition.

### Drive Results by Yard line

We can see the ways in which EqPts were calculated by observing the number of occurrences of Touchdowns, Field Goals and Non-Scoring drives and their contribution to the averages or EqPts. The following graph shows the number of drives that led to the various types of scoring outcomes, given 1st and 10 or 1st and goal from varying positions on the field.

One of the first things you might notice is the tremendous spike occurring at an offenses 25-yard line. This is to be expected due to the NCAA's new rule that repositions touchbacks to the 25-yard line. The old rule positioned touchbacks at the offenses 20-yard line. In addition, one can see that non-scoring drives decrease steadily as 1st down field position approaches the opponent's goal line. If we look even further into this graph, our first glimpse of a new red zone will appear.

By adding two new measures, Non-Touchdown and Score, we can visually see two things: where scoring drives start to occur more often than non-scoring drives, and where touchdowns begin to occur more often than non-touchdowns. From this data the yard line in which the percentage of scoring drives is equal to the percentage of non-scoring drives is roughly at the 50-48 yard line (on the opponent's side of the field). Thus, if an offense achieves a 1st down on their opponent's side of the field, the odds would say that they score! In addition, the yard line in which the percentage of touchdowns is equal to the percentage of non-touchdowns is at the opponent's 22-20 yard line. A first down at this field position or better is indicative of a touchdown! The basis for our definition of a new red zone, potentially TWO new red zones, is now taking form.

### Another Look at EqPts

Before we go about defining this new red zone, another look at EqPts is in order. From the EqPts graph, there are two critical points that should be recognized: where EqPts = 3, and where EqPts = 5. The point where EqPts = 3 is crucial to our understanding of this data because it is the point where an offense's position on the field is equal to or better than a field goal in terms of averages. Shockingly, that point occurs right where we hoped it would - at the 50-yard line.

Not only does one's chances of scoring outweigh one's chances of not scoring with a 1st down from the 50-yard line to an opponent's goal line, but also a study of EqPts suggests that a 1st down from these field positions is greater than or equal to the value of a field goal.

Looking at the case where EqPts = 5 is even more interesting. First, we should recognize why this position is so important. For EqPts to be greater than or equal to 5 indicates that touchdowns must be scored more than field goals and non-scores. Additionally, it means that the weight of a field goal becomes a sub-par scoring result in comparison to the weight of a touchdown. So, where is EqPts greater than or equal to 5? The answer is the 15-yard line.

### The Hot Zone: inside the 15 or the 20?

From both an analysis of scoring occurrences and scoring averages we have determined that there is an area of the field where a touchdown not only becomes probable, but also becomes the only truly successful result, on average, in terms of value. While there is a variance of roughly five yards between the two field positions we calculated, it is important to recognize the circumstances. Points are points, and either a field goal or touchdown is an acceptable score for a majority of drives. Therefore, one might be more liberal toward the acceptance of a field goal should one achieve a 1st down between the opponent's 20 and 15 yard line. Not only from the standpoint of the circumstances of the game, but also from the indication provided by our study on EqPts that a field goal is not quite inadequate in terms of value. On the other hand, a drive that achieves a field goal, given a 1st down between the opponent's 15-yard line and goal line, is both underachieving in terms of probability and in terms of value of the score.

### A New Gridiron: the Orange Zone and the Hot Zone

Given the above analysis it is now time to propose a new definition of scoring success and the football field, as we know it.

The Orange Zone - When a team achieves a 1st down from midfield to their opponent's 15-yard line, they are considered to be in the Orange Zone. Not only is the offense in a position where the probability of scoring is greater than 50%, but also the value of their position in terms of EqPts is greater than that of a field goal.

Orange Zone Scoring Percentage (OZSP) - The percentage of drives, who's final 1st down is between midfield and the opponents 15-yard line, that leads to either a field goal or a touchdown.

The Hot Zone - When a team achieves a 1st down from their opponent's 15-yard line to their opponent's goal line, they are considered to be in the Hot Zone.. Given these 1st down field positions, a team's probability of scoring a touchdown is greater than 50%, and the value of their position is closer in magnitude to that of a touchdown than a field goal.

Hot Zone Scoring Percentage (HZSP) - The percentage of drives, who's final 1st down is between the opponent's 15-yardline and the opponent's goal line, that leads to a touchdown.

Through an analysis of various scoring occurrences and Third-Level Equivalent Points, given 1st and 10 and 1st and Goal scenarios, a new perspective on the game of football should be considered; a perspective that not only redefines scoring statistics, but the field as a whole. From this new information we can create models that quantify and determine success, measurements of explosiveness, and fresh characterizations of teams and players.

So, on Monday night, want to know how the game is going? You might just want to keep track of how the teams are doing in these two new zones. It might just give you a handle on who is doing the best job towards holding the trophy above their heads by night's end!