What Should XFL Teams do on Point(s) After Touchdown Attempts?

The new football league XFL started play this past weekend. In an effort to create a more exciting play style compared to the NFL, the XFL has implemented some unique rules. One of the more notable rules is that after a touchdown, the team that scored the touchdown must run an offense play from the 2, 5, or 10-yard line, and a successful play is worth 1, 2, or 3 points respectively. What is the optimal strategy for the point(s) after attempts? Using available NFL play-by-play data from 2013 to 2019, the value for attempts from the 2, 5, and 10-yard lines can be estimated. XFL players certainly are not as talented as NFL players; however, the NFL serves as a better proxy for these values than NCAA football players would due to the larger talent differential between the XFL and NCAA.

Although the majority of the two-point conversion attempts that are attempted in the NFL occur at the 1 or 2-yard line, fourth and goal attempts can be used as a stand-in for attempts at other distances. All-in, there were 1,025 fourth and goal or two-point conversion attempts in the seven seasons spanning 2013-2019, 1,018 which were from the 15-yard line or closer. Conversions from the two-yard line succeed at roughly a rate of 50% rate, which, in the XFL would have an expected value of half a point.

It gets trickier to estimate the success rate from the 5 and 10-yard lines due to the significantly less amount of attempts. Given that a 5-yard conversion is worth two points, the 5-yard conversion rate would only have to be higher than 25% to yield a higher amount of expected points than the 2-yard conversion. Considering the rates at the 4, 5, 6, and 7-yard lines are all over 25% and that the combined success rate between 4 and 7 yards is 39%, going for the two-point attempt from the 5-yard line appears to be a superior strategy than going for the one-point attempt at the 2-yard line. Attempting the two-point conversion would yield .78 points on average compared to .5 points for the one-point conversion. 

Estimating the true success rate for the three-point conversion from the 10-yard line is significantly more difficult given the much lower number of attempts. In order for the three-point conversion to be worth more points as the two-point conversion, it must have a success rate greater than 26%, which would yield .78 expect points. Using the 33% success rate at the 10-yard line would not be optimal way to infer the overall success rate given that there were only six attempts. There were twelve combined attempts from the 9-11 yard lines, which were converted at a combined rate of 25%. Likewise, using the local polynomial regression line (a generalization of moving average and polynomial regression) line in the plot below, the estimated success rate is a bit under 25%. All things being equal, it would appear that the optimal strategy for point(s) after attempts in the XFL is to attempt the two-point conversion from the 5-yard line. 

One obvious thought that comes to mind when looking at NFL teams that attempted to go for a two-point conversion or for a fourth and goal situation is that the team may have been forced to because they were losing. If a team was losing, then that team is more likely to be an inferior team to the team that they are playing. To see if there was a selection bias in the plays included in the sample, the efficiency rating for each offense and defense in the sample can be used. The efficiency rating, or DVOA, is calculated by Football Outsiders to determine the quality of each offense, defense, and team overall. A positive difference in DVOA means that the offense was better and a negative difference means that the defense was better, so a .98% difference in DVOA means that the offense was .98% better than the defense in that play. It is not a surprise that teams that had attempts at the one or two-yard line had a positive differential, because these teams might go for it when they are not forced to because of confidence in their offense. Likewise, teams that have attempts of greater yardage tend to be worse, likely as a result of the team being more likely to be a desperate situation. While the difference in DVOA does not easily allow for any sort of handicapping of success rate, it can be used to give context to the success rate. 

The success rates and expected point totals at the 2, 5, and 10-yard lines indicate that XFL teams should avoid attempting one-point conversions from the 2-yard line and should either attempt two-point or three-point conversions from the 5 or 10-yard lines respectively. Although the true success rates are not know, it is likely that two-point conversion attempts from the 5-yard line will produce the highest number of expected points in a given situation in the XFL.

The code and files used for this analysis can be accessed here: https://github.com/pfmccull/Football-Point-s-After-Attempts