Written by Adam Tucker (@adamtb182)
- Expected point gain of going for it on fourth down gives key insights as to why Mike Tomlin chose not to kick a field goal at the end of the half of yesterday’s game.
- Under the lens of expected point gain, are NFL coaches really acting rationally to maximize points scored?
There are very few moments that bring a football fan to the edge of his or her seat like when a team goes for it on fourth down. The coach often gets praise for when this gutsy call pays off, but the same people who would praise the coach are also ready to lambast him for when it fails. Pittsburgh Steelers fans are no stranger to these feelings; Coach Mike Tomlin often goes for it on fourth down and attempts many two-point conversions. Although his decision yesterday to go for the touchdown twice at the end of the second quarter was not on fourth down, he still had to make many of the same considerations as a fourth down play because the drive would have been over if the play was unsuccessful.
Tomlin’s two options to score were to either attempt a field goal or go for it. In order to evaluate his decision making, I will use data from 2009-2015 NFL season and figures calculated by Konstantinos Pelechrinis in his paper “Decision Making in American Football: Evidence from 7 Years of NFL Data” to evaluate success rates of field goals and attempted fourth down conversions, the costs of failing to convert and turning the ball over, and using the previous two metrics to calculate the net gain (or loss) of going for it on fourth down. Let us examine the effectiveness of a field goal first.
Field Goal Success Rate
As you can see in Figure 1, the success rate of a field goal decreases as distance increases. Not controlling for distance, the average success rate of a field goal attempt is 85.5%.[i] However, one can also observe that, for attempts near the goal line, the success rate is very close to 100% according to Figure 1, as was the case for the Steelers.
FIGURE 1: Probability of a successful field goal given distance (credit to Konstantinos Pelechrinis)
Fourth Down Conversion Success Rate
Likewise, fourth down conversion success rate decreases as yards to go increases as seen in Figure 2. The overall success rate of fourth down conversion is 73% when controlling for yards to go.[ii] However, 55% of the dataset for these situations occurs when the offense only has one yard to go, which was the case for the Steelers, and this success rate figure jumps up to an 89% in this situation.[iii]
FIGURE 2: Probability of a fourth down conversion given yards to go (credit to Konstantinos Pelechrinis)
Cost of Turning the Ball Over
The biggest downside of going for it on fourth down instead of attempting a field goal or punt is turning the ball over to the opponent and risking giving them a scoring drive. The following figure illustrates the probability of a drive ending in a TD, field goal, or a failure to score points as a function of drive starting position. These probabilities are important in the final calculation for the expected gain of going for it on fourth down.
FIGURE 3: Probability of the result of a drive given the beginning yard line (credit to Konstantinos Pelechrinis)
Expected Benefit of Going for It on Fourth and Conclusion
Using the above data, expected point gain of going for it on fourth down (E[P]) is calculated by E[P] = E[P+] - E[P-], where E[P+] is the expected point benefit of a successful fourth down conversion and E[P-] is the expected point cost of a failed fourth down conversion.[iv] E[P+] is a function of the fourth down conversion rate given a yard line, and E[P-] is a function of the success rate of a field goal and probability of an opponent’s drive leading to a touchdown or field goal given a yard line.[v] A more rigorous derivation can be found here. Using the above, a graph for E[P] can be created, as seen in Figure 4. In conclusion, at the goal line the value of E[P] is over 3, which is greater than the expected points from a field goal at the same yard line. Therefore, Mike Tomlin made the correct call twice yesterday (11/20/16) to attempt to convert for a touchdown instead of opting for an attempted field goal. However, more broadly, one can see that E[P] is positive for a majority of the field and leads to questions as to why coaches don’t go for it on fourth more often. The rationality of coaches and whether they seek to be averse to risk or maximize expected points is outside the scope of this paper, but something that could be researched further.
FIGURE 4: E[P] given distance to goal line when 4th down (credit to Konstantinos Pelechrinis)
Fellow TSAC member and President Arvind Pendurthi defends Tomlin’s actions further: http://www.post-gazette.com/sports/steelers/2016/11/19/The-sports-analytics-community-has-Steelers-coach-Mike-Tomlin-s-back.html
[i] Konstantinos Pelechrinis, “Decision Making in American Football: Evidence from 7 Years of NFL Data”
[ii] Konstantinos Pelechrinis, “Decision Making in American Football: Evidence from 7 Years of NFL Data”
[iii] Konstantinos Pelechrinis, “Decision Making in American Football: Evidence from 7 Years of NFL Data”
[iv] Konstantinos Pelechrinis, “Decision Making in American Football: Evidence from 7 Years of NFL Data”
[v] Konstantinos Pelechrinis, “Decision Making in American Football: Evidence from 7 Years of NFL Data”