Hack 58. Go for Two

In football, when is the two-point conversion attempt the right choice? Regardless of which "chart" you're using, the problem gets even more complicated when statisticians enter the debate.

A few years back, I was enjoying watching my local professional football team as they were losing a close game. I wasn't entertained by my team's dismal performance as much as I was delighted by my team's befuddled coach as he attempted to read and understand a two-point conversion chart.

In football, after a touchdown is scored (the touchdown itself is worth six points), the scoring team has two options for scoring an "extra point" or two. Usually, the team chooses to kick a single extra point through the uprights (like a short-distance field goal), but they might also choose to "go for two" points (known as the two-point conversion), which involves the offense rushing or passing for another trip into the end zone.

At the time, as was later "confirmed" by sportswriters, it was clear that he wasn't sure how to read the chart. Specifically, when interpreting the column on the chart that listed how many points behind or ahead a team was, he thought this meant how many points ahead or behind a team would be if they made the point-after conversion.

As I mused about how an NFL head coach might never have learned to read such a chart, I began to wonder who produced this "chart" and what principles it was based on. Later, as I searched for the "official chart," I found two "official" charts, and they didn't always agree.

More recently, I ran across a chart based on a statistical analysis of the probability of possible outcomes and on the amount of time remaining (as indicated by the number of possessions remaining). This chart didn't agree with either of the earlier charts I discovered.

This hack is for you, Coach. It examines from a statistical perspective when to go for two points and when to settle for one.

Traditional Two-Point Conversion Charts

When you see a coach on TV holding a plastic laminated card and studying it before deciding whether to go for two, sportscasters like to refer to the card as the chart, though, as mentioned in the previous section, there's more than one chart in use. The slight differences might be due to the fact that one is identified as being used in the NFL and the other is identified as a classic set of standard decisions used in college football.

The differences might also be based on the fact that the college chart was produced for a certain team that may have had a more aggressive or confident style. The college chart seems to play for a victory, not a tie. Though college ball now has overtime rules, they are a fairly recent development, whereas the pros have had overtime for a while.

The NFL chart is provided on Norm Hitzges' web site (Norm is a broadcaster in Dallas and an all-around sports guru) at http://www.normhitzges.com/thechart.htm. The college chart (found at http://www.NFL.com/fans/twopointconv.html) is identified as the one used in the 1970s and developed at the University of California, Los Angeles (UCLA). Table 5-14 provides the suggested decisions from both charts and is condensed a bit.

Table Classic decision making for two-point attempts

	Points behind or ahead
	0	1	2	3	4	5	6	7	8	9	10	11	12
Behind (NFL)	1	1	2	1	1	2	1	1	1	1	2	1	1
Behind (College)		2	2	1		2	1	1	1	2	1	2	2
	0	1	2	3	4	5	6	7	8	9	10	11	12
Ahead (NFL)	1	2	1	1	2	2	1	1	1	1	1	2	2
Ahead (College)		2	1	1	2	2	1	1	1	1	1	1	2

The UCLA chart does not provide suggestions for when the score is tied or when your team is behind by four points. The NFL chart, on the other hand, is full of advice for all occasions. As discussed, the primary difference seems to be whether you're willing to play for the tie or not. UCLA clearly did not wish to play for the tie, while the NFL chart has no such hesitancy.

Modern Super-Scientific Chart

In the real world, a set of statistical probabilities controls the outcome of a sporting event, and the decision about whether to go for two or take the extra point should be based on more information than just the score and whether your team is winning or losing. In actual game situations, smart coaches take the following additional factors into account:

• The likelihood that their field goal kicker will make the field goal

• The likelihood that their team will score on a given two-point conversion play

• The current health, attitude, and skill of their players

• How many more possessions their team will receive

Past statistics show that the average NFL football team makes about 98 percent of its extra points and about 40 percent of its two-point attempts. Coaches must use their experience and intuition to gauge their players' current ability level, and a chart isn't much help on that score.

As for possessions left, however, this is exactly the type of information that decision systems based on probability need to take into account. Based on a process of working backward from the ending of a hypothetical football game that takes the probability of success on either option (98 percent for one-point plays and 40 percent for two-point plays) into account, statisticians have produced a chart based on not only on the current score, but also on the total number of possessions remaining for both teams.

In a 2000 issue of Chance magazine (Vol. 13, No. 3), Harold Sackrowitz presented the results of such an analysis using a process called dynamic programming. Table 5-15 shows a portion of Dr. Sackrowitz's chart.

Table Modern decision making for two-point attempts

		Points behind or ahead
		0	1	2	3	4	5	6	7	8	9	10	11	12
Possessions remaining
1	Behind	1	1	2					1
	Ahead	1	2	1	1		2	1	1	1
2	Behind	1	1	2	1	1	2		1	2		2
	Ahead	1	2	1	1	1	2	1	1	1
3	Behind	1	1	2	1	1	2		1	2		2
	Ahead	1	2	1	1	1	2	1	1	1	1	1	1	2
4	Behind	1	1	2	1	1	2	1	1	2	2	2	1
	Ahead	1	2	2	1	1	2	1	1	1	1	1	1	2
5	Behind	1	1	2	1	1	2	1	1	2	2	2	1
	Ahead	1	2	1	1	1	2	1	1	1	1	1	1	2
6	Behind	1	1	2	1	1	2	1	1	2	2	2	1	2
	Ahead	1	2	2	1	1	2	1	1	1	1	1	1	2

This two-point conversion chart is based on the branching possibilities starting at different points in the game and assuming basic probabilities of success for either an extra point or a two-point conversion. An average NFL quarter sees six possessions in total, so think of this chart as being most useful in the fourth quarter. Sackrowitz also assumes a 50 percent chance for overtime victories.

How It Works

The calculations for Table 5-15 work something like this simple example:

1. Imagine you are down by one point without much chance of getting the ball again.

2. You have a 98 percent chance of making an extra point kick and a 50 percent chance of winning in overtime. Going for the extra point results in a victory 49 percent of the time (.98 x .50 = .49).

3. You have a 40 percent chance of converting a two-point play, so going for two points results in a victory 40 percent of the time. Failure ends the game, and success wins the game.

4. 49 percent is better than 40 percent, so you should elect to go for the extra point. Notice that if you believe your team's chances of converting the two-point play are better than 49 percent, you should go for it. Calculations like these, but over a longer series of possessions, result in the decision tree reflected in Table 5-15.

Which chart should you use the next time you find yourself coaching in a crucial football game with a key decision to make? That's up to you, but just remember that befuddled football coach I watched on TV a few years ago. Not only was he replaced the next year by Dick Vermeil, considered one of the brighter football coaches around, but it was Vermeil who helped develop the UCLA two-point conversion chart shown in Table 5-14. Now you know the rest of the story!