When to Go for 2

by: Harold Sackrowitz
Professor of Statistics, Rutgers University
© More from this issue

          
The two-point conversion adds an interesting strategy option to the game of football. Its frequency of use is usually related to the level of play and, in particular, the quality of place kickers. At the high school and recreation level one sees many two-point attempts, while in the NFL there tends to be less than one attempt for every two games played. Even when its use is slight, its impact is often great. The decision to "go for two" is peculiar in that it is not really a "football" decision. By that, I mean that one cannot confidently rely solely on the gut feeling of an experienced football person. Except for obvious situations very late in a game, there are subtle probabilistic issues of a technical nature involved here.

Not Always in the Cards

Many coaches have a card based only on the point differential immediately following a touchdown to assist them with the decision. These cards are inadequate and may even be detrimental for a number of reasons:

1) It doesn't make sense for all teams to have the identical card. Different teams have different scoring characteristics. Some teams are higher scoring than others, some are better at picking up short yardage, some have weaker place kickers, etc.

2) Furthermore, it doesn't even make sense for any one team to be using the same card for every game. The scoring characteristics of your particular opponent as well as your own scoring characteristics against that opponent should be factored in.

3) An extremely important issue, ignored by these cards, is the time remaining in the game. Probably the most perplexing problem for coaches is when it is safe to use their card. Unfortunately, decisions that are correct near the end of a game need not be correct earlier in the game.

As will be seen, it is possible to construct more sophisticated tables that are easy to read and much more informative. Such tables would give a coach a more realistic assessment of any situation.

The correctness of a decision is determined not only by the current point differential, but also on the probabilities of converting both a one and two-point conversion, the scoring (TD and FG) abilities of both teams, the time remaining, AND what is likely to happen during that time. A weekly review of game summaries indicated that there are mistakes (going against the percentages) made almost every week although very few games are close enough that the outcome is affected. However, those few games can be very significant. Because a football schedule is relatively short, a single unnecessary loss can destroy an entire season. This season's most striking NFL example occurred in the Lions - Cardinals (11/14/99) game.

Some Examples

With 5:26 left in the game, the Lions scored a TD to pull within 23-19 of Arizona. To everyone's surprise, they went for two and missed. Coach Bobby Ross had been hoping for one more possession and for an outright win. Due to injuries, he said he did not want to play in overtime. As a result, the Lions could not go for a field goal when they got to the Cardinal 10-yard line with less than two minutes remaining.

Although severely criticized, Ross may have been correct about that decision. In effect, he had determined that his team's probability of a two-point conversion was greater than his team's probability of winning in overtime. However, to find the real transgression (which went unnoticed) we have to go back to the third quarter. With 10:51 remaining in the third quarter, the Lions scored a TD to cut the Arizona lead to 23-13. With a 10-point deficit naïve tables would tell you to go for two-points. This would be the proper action near the end of a game. However, it is not the percentage play early in the second half. Had they kicked an extra point after that TD, they also would have simply kicked again after the fourth quarter touchdown, and they likely would have won the game with a last-minute chip shot field goal.

A common situation that seems to tempt a coach to try for two points is when his team scores a touchdown to go up 12-0 early in a game. Jacksonville tried and failed in last season's wildcard game vs. New England with 5:58 remaining in the first half. Although they went on to win easily with an explosive fourth quarter, the needless danger became clear when the Patriots pulled to 12 - 10 with almost a full quarter to go.

In 1997 Oakland lost a game to the Jets by one point after making the same decision very early in the game.

Another familiar setting deals with a team trying to recover from a 14-point deficit towards the end of the game. In this situation teams hope to score two quick touchdowns with extra points and force overtime. However, the calculations show that many teams would be better off going for two points after the first TD. Some appreciation of this strategy can be obtained by looking at the famous 1984 Orange Bowl game between Nebraska and Miami. Although there was no overtime back then, it is still informative.

A win would definitely have given Nebraska the national championship and a tie would likely have done the same. Unfortunately they trailed Miami by 14 points in the middle of the fourth quarter. Remarkably they pulled to 31-30 with 48 seconds left to play. Coach Osborne wanted a definitive title and went for two. It failed, and Miami became No. 1 and Nebraska No. 2.

Now look at the added insurance going for two after the first TD would have given them. If they make it, they can win outright after the next TD. If they fail, they are still playing for a tie game and the national championship.

Another Approach

How do we determine which decision gives the best probability of winning? First we look at the time remaining in the game. Then we must enumerate every possible set of outcomes than can occur during that time and compute the probability of each possibility. This is not difficult near the very end of the game when not much can happen within the time remaining. Otherwise it can be quite complicated.

A method called dynamic programming and the use of a computer makes all these calculations possible. The technical details, as well as other examples, will appear in Chance magazine (published by the American Statistical Association).

The two tables below are examples of what a (probability-based) time dependent strategy table would look like. They do not correspond exactly to any real teams. Similar tables can (and should) be constructed for particular matchups involving specified teams once their scoring characteristics are known and the probabilities are recalculated.

Table I was developed for two hypothetical "NFL league average" 1998 teams playing against one another. That is they roughly, each score 2.41 touchdowns per game, make 1.475 field goals per game, and convert 98% of their one-point conversion attempts and 39% of their two-point attempts.

Table II demonstrates the affect of a much weaker place kicker. The scoring characteristics of Table I are used except that only 70% of one-point conversions are converted and the number of field goals per game is only 0.5. Thus Table II might be representative of a good high school team.

These are essentially the two ends of the spectrum. Looking at the tables, we can see that in the NFL the question is "when to go for two," while in high school the question is "when to go for one."

STRATEGY TABLE I
(best for college and pro football teams):

Gives conversion (one- or two-point) to be attempted. Blank indicates it doesn't matter.

Note 1: The status is immediately after the TD but before any conversion is attempted.

Note 2: To improve intuition, we point out that a typical NFL game has approximately six possessions in each quarter.

status after
scoring TD total number of possessions remaining in the game for both teams combined
0123456789101112131415161718
behind by
15 22222111111111
14 11111111111111
13 22222212111111
12 2222222111111
11 111111111111111
10 22221111111111111
9 222212111111111
8 22222221111111111
7 111111111111111111
6 111111111111111
5 22222222222221111
4 11111111111111111
3 11111111111111111
22222222222222222111
11111111111111111111
ahead by
01111111111111111111
1222222211111111111
2 111212221211111111
3 111111111111111111
4 11111111111111111
5 222222222222222111
6 111111111111111111
7 111111111111111111
8 111111111111111111
9 1111111111111111
10 1111111111111111
11 1111111111111111
12 2222222222211111

STRATEGY TABLE II
(best for a good high school team):

Gives conversion (one- or two-point) to be attempted. Blank indicates it doesn't matter.

Note: The status is immediately after the TD but before any conversion is attempted.

status after
scoring TD total number of possessions remaining in the game for both teams combined
0123456789101112131415161718
behind by
15 22222222222222
14 22222222222222
13 111222222222222
12 111222222222221
11 222222222222222
10 22222222222222222
9 22222222222222222
8 22222222222222222
7 11111111111112222
6 11111111111112222
5 22222222222222222
4 22222222222222212
3 11111222222222222
22222222222222222222
12222222222222222222
ahead by
01111111111111111112
1 222222222222222222
2 222222222222222222
3 111111111111112222
4 22222222222222222
5 222222222222222222
6 111111111111111112
7 222222222222222222
8 111111111111112222
9 1111111111111222
10 2222222222222222
11 2222222222222222
12 2222222222222222

| Current Issue | Back Issues | March 2000

NEW BOOK!

Digital Download - 304 Pages of Football Forms for the Winning Coach