Analysis

When teams should go for two (and why Jack Del Rio was right)

When is going for two not that risky?

In the offseason, Steelers quarterback Ben Roethlisbergerexpressed a desire to go for two after every touchdown in 2016, following unprecedented conversion success in 2015. Then, in Week 1, Oakland Raiders coach Jack Del Rio demonstrated his affinity for the two-point try with a bold, last-second conversion to seal a win against the Saints.

Though analysis by Sridutt Nimmagadda on this site last week suggested the Steelers should follow through on Big Ben's promise to up the two-point tries in 2016, Pittsburgh has yet to attempt a conversion in this young season. Del Rio similarly stuck to the point-after kick in Oakland's Week 2 loss to the Falcons. But the question remains: Should the Steelers, Raiders and other teams throughout the NFL consider going for two more often?

Many analysts have discussed certain late-game situations in which going for two can be advantageous, even for teams with low conversion rates. There are also some obvious scenarios that call for the strategy, such as when a team down by 8 or 11 late in the fourth quarter has just scored a touchdown. But are there other circumstances in which teams should regularly go for two instead of the PAT?

Some may suggest that any team that can score on two-point conversions over 50 percent of the time should be going for two, since even if said team were perfect at PATs (which are, of course, worth one point), they will score more points in the long run. While this might add to the chance of winning a given game, it can also increase the chance of losing against opponents opting for the more reliable PAT. Since most NFL teams prefer to avoid such risks (volatility or variance), are there scenarios where going for two can increase a team's chance of winning without also increasing its risk of losing?

The short answer is yes, for teams facing the right circumstances:

» They have a struggling kicker.

» They have better-than-average success at two-point conversions.

» They're in a game in which both teams score two or more touchdowns.

OR:

» They have better-than-average success at two-point conversions.

» They're underdogs.

Let's dig deeper.

The "struggling kicker" factor

Until 2015, extra-point kicks were practically a sure thing; consider that between 2010 and 2014, the extra-point success rate across the league was greater than 99 percent each season. However, for the 2015 season, the NFL moved the distance for extra-point attempts back to the 15-yard line, to make PATs less routine. For that season, the PAT success rate subsequently dropped to 94.1 percent. Through the first two weeks of 2016, the success rate has been similar (94.4 percent). That might not seem like a big change -- few people fret over the small gap between an A+ and an A. But in the NFL, a single point can make a world of difference. At least one postseason game in each of the past five years (seven in total) was tied or decided by one point at the end of regulation.

Perhaps more relevant to our discussion are the five teams that posted a PAT success rate below the 90 percent mark in 2015. That's more than the total number of teams to share that unglamorous trait in the 25-year span before the rule change. When such teams score two touchdowns in one game, the chance of making both extra-point kicks is less than 80 percent. Consider that, on average, each team scored about 2.6 touchdowns per game last season. (Furthermore, through two weeks in 2016, 21 games (or 66 percent) have involved both teams scoring at least two touchdowns.) Thus, teams with PAT success rates below 90 percent are estimated to find themselves slipping behind their more proficient PAT-making opponents approximately two to three times in the regular season based on missed PATs alone.

Given what has happened around the NFL thus far this season, it looks like PAT struggles will continue in 2016. At least one PAT was missed each week in the preseason. In Week 1, there were five missed PATs, including one that contributed to a 1-point loss for the Jets. In Week 2, four more PATs were missed. Going forward, I'd estimate about two to seven missed PATs on most weeks across the NFL (though this should dip slightly once bye weeks begin) based on recent averages of TDs and PAT success.

Teams that get two when they go for two

The only alternative to attempting a PAT is to go for a two-point conversion after a touchdown. The success rate is much lower in comparison to PATs -- the average across the league in 2015 was 49.5 percent. Thus, even teams with relatively poor-performing kickers (say, with a PAT accuracy rate of 90 percent) and an average two-point conversion rate (49.5 percent) typically prefer the prudent option to kick the PAT, forgoing the opportunity to pad their point total because the chance of missing and potentially falling behind their opponent is much higher than going for one. But when does it make sense for teams that struggle to convert PATs to go for two after the first touchdown scored?

Let's consider different outcomes between Team A and Team B, where each team scores two touchdowns (a scenario that is likely to occur, given touchdown-per-game averages). Say Team B has an average kicker and elects to kick PATs after each score. If we know the PAT success rate for both teams, we can calculate the minimum two-point conversion rate necessary to increase Team A's chance of taking the lead without increasing its chances of falling behind, as compared to attempting PATs.

The chart below illustrates a decision boundary relating two-point conversion success vs. PAT success in a two-touchdown scenario, and how different teams performed in their post-touchdown scoring attempts in 2015. Teams above the line would benefit from going for two without increasing their chances of losing, while those below the line are better off kicking the PAT. This analysis simply assumes both teams score two touchdowns and the order of the scores does not matter. Since teams with low PAT accuracy are likely to fall behind simply because of missed PATs, they require lower two-point conversion rates to ensure their chances of losing are no worse than they would be with the PAT-only strategy. Notably, for many of the teams, the number of two-point attempts was quite small, so the two-point success rate could be a bit misleading, as there were too few attempts for a confident estimate of long-term success to be made. That said, if teams had been able to maintain success rates similar to their performance in 2015, six teams would have stood to benefit from more two-point conversion attempts, including the Steelers, who seemingly came to a similar conclusion, as they attempted a record-tying 11 two-point attempts.

Note that for reference, teams that did not attempt any two-point conversions in the 2015 regular season have two-point conversion rates below 0 on the chart.

Here is a detailed breakdown using statistics from the 2015 Steelers' season to illustrate the point:

Consider the probabilities of the Chargers, who were worse at both PATs (with an 88 percent success rate) and at two-point conversions (67 percent) in 2015. With the PAT-only strategy, the Chargers win 9 percent of the time, tie 71 percent of the time and lose 20 percent of the time. With the two-point-only strategy, the Bolts win 50 percent of the time, tie 39 percent of the time and lose 11 percent of the time. By contrast, the Jaguars, who fared exceptionally poorly with two-point tries in 2015 (20 percent success rate) and performed below average at PATs (82 percent), would lose much more often when going for two (8 percent chance of winning versus a 28 percent chance of tying and a 64 percent chance of losing) than kicking the PAT (with an 8 percent chance of winning, a 63 percent chance of tying and a 29 percent chance of losing).

Underdogs benefit from riskier decisions

The above analysis is for situations where the chances of winning can increase without increasing the risk of losing, which should appeal to many NFL coaches who have demonstrated that style of decision-making. However, others have written in depth about the fact that in order to maximize chances of winning, teams that are favored should reduce risky decisions while underdogs should increase them, as volatility favors the weaker team. In brief, underdogs can increase their chances of winning by playing a risky style, which would lead to either winning slightly more often by a small margin or getting blown out by the better team more often.

When it comes specifically to the decision of going for two versus a PAT, as long as an underdog has a greater than 50 percent chance of making a two-point conversion, it's in the team's benefit to do so, since it increases the volatility without decreasing the team's expected points. (Technically, as long as the team's two-point conversion rate is greater than half the PAT rate, going for two would lead to more victories for the underdog.)

Caveats

Certainly, football games are more complicated than the simplified two-touchdown situation we've discussed. What if we think there's a greater chance that each team scores three touchdowns instead of two? Should that alter the decision?

The three-touchdown scenario makes going for two a bit riskier, because ties are less likely to occur when there are an odd number of touchdowns. For teams that convert PATs between 85 percent and 90 percent of the time, the required break-even two-point conversion rate increases by about 10 percent (from about 50-60 percent to 60-70 percent). Of course, in any particular game, a team's PAT rate and two-point conversion rate will depend on game-specific factors, such as the opponent's defense, the weather, changes in personnel, etc. Note that this simplified analysis is meant to highlight how certain teams may improve their strategy for scoring points after touchdowns, with other scoring being equal. Thus, other score combinations including field goals and safeties were ignored. Another note worth mentioning is that this analysis does not take into account the unlikely chance that the defense scores two points on a turnover during a conversion attempt. Due to their rare occurrence, defensive two-point scores would not alter the decision curve by much.

The numbers that back Del Rio's bold move

Through two weeks of 2016 NFL action, PAT accuracy (94.4 percent) has been very similar to last year, while the average number of two-point attempts per week (4.5) is slightly lower than last year's average of 5.5. One Week 1 outcome in particular sparked a bit of discussion regarding post-touchdown decisions.

Jack Del Rio and the Raiders went for two after three out of four TDs in their game against the Saints and won in dramatic fashion on a two-point conversion that put them up by 1 in the game's closing moments. The decision to go for two has been publicly debated from a mathematical perspective, with ESPN's probability model opposing the decision, as explained by Sharon Katz and Brian Burke, with Neil Paine of FiveThirtyEight offering some additional analysis. Del Rio even took a moment to respond to his analytical critics.

While Del Rio's decision was not supported by kicker inefficiency (Sebastian Janikowski made over 97 percent of his PATs last year, which is above the league averages used by the aforementioned analyses), the Raiders were a slight underdog going into the game, according to ESPN's win probability and FiveThirtyEight's Elo Predictions, and thus stood to benefit from a riskier overall strategy, as explained above.

Regarding the specific decision to go for two with 47 seconds left, what was actually more relevant than PAT percentage was the Saints' ability to score with that much time remaining in the game, even if the Raiders converted the two-point try. This is a difficult number to estimate, but -- given that the Saints accumulated over 500 yards in the game -- the possibility was not trivial. Still, the necessary two-point conversion rate can be calculated if we know (1) the chance of winning when going for a PAT and (2) the chance of a Saints comeback.

Let's assume that, at best, the Raiders had a 51 percent chance of winning had the Raiders gone for a PAT, as computed by the ESPN model (though Paine provides evidence for a smaller number). If we estimate the Saints to have had a 9 percent chance of mounting a comeback, as estimated by the ESPN model, then, as Katz and Burke mentioned, the Raiders needed a two-point conversion rate of at least 56 percent to justify the attempt. If we give the Saints a 15-20 percent chance -- not unreasonable, given Drew Brees' knack for late-game heroics and the Raiders' difficulty stopping the Saints' offense for the first 59 minutes of the game -- then the break-even two-point conversion rate increases to 60-64 percent. Going into the game, Del Rio-coached teams with Bill Musgrave as offensive coordinator (the Raiders in 2015 and the Jaguars in 2003 and '04) had a combined two-point conversion success rate of 63 percent (five of eight). Meanwhile, from 2013 to 2015, the Saints' defense allowed 67 percent (six of nine) of two-point tries against it to be converted. Yes, these rates are calculated from a small number of attempts, but perhaps Del Rio's decisions were based on these factors rather than the recent league average of 48 percent.

Of course, the debate is not easily settled, since many assumptions go into all of these different analytical approaches and there doesn't seem to be an obvious choice. But in my opinion, Del Rio made the right move, and he and Musgrave have had the type of success that encourages going for two when the Raiders are underdogs.

Let's get practical

Though it's not an uncommon occurrence, I will admit that the two-touchdown scenario is a bit contrived, and there's obviously no way of knowing early in a game how many TDs an opponent will score, let alone how many other points will come by virtue of field goals and safeties. Thus, the charts above are not meant to determine a guaranteed optimal after-touchdown strategy before each game. Rather, they are meant to highlight that teams with poor PAT accuracy should consider going for two more often, especially if they are underdogs.

In practical terms, after Week 5 or 6, teams that struggle to convert PATs may have scored enough TDs, missed enough kicks and attempted enough PATs to roughly estimate where they are on the chart. Based on last year, I'd estimate that three to five teams will find themselves in a place where they should seriously consider going for two after early-quarter TDs. It won't necessarily be because they match the offensive firepower of the Steelers, but rather, because they need an alternative to a subpar kicking game against a favored opponent. Also, if the weather is adverse for kickers and the opponent's goal-line defense has shown vulnerabilities, the balance may tip in favor of a two-point conversion attempt.

Nasir Bhanpuri, PhD, is a data scientist based in San Francisco. He has been applying analytics and modeling techniques to address challenges in a wide range of fields, including sports, healthcare, fitness, wearables, education, neuroscience, robotics and music. He would like to thank Justin Lakeman and Jordan Hupp for inspiration and feedback on the article.

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