What's the difference between a touchdown and the ball at the one yard line? A touchdown is worth either 6, 6.4, 7 or potentially 8 points, depending on who you ask. Sticklers for details will tell you that a touchdown is no guarantee of a successful extra point, and is only worth six points. Most people will say that a TD is worth seven points, as teams that score touchdowns almost always come away with seven points. A touchdown is worth potentially 8 points, of course, because if you're down by 8 you only need a touchdown to have a chance to tie.
And David Romer would tell you that a touchdown is worth 6.4 points -- just like a field goal is worth 2.4 points -- because following the mandatory kickoff the opposing team gets the ball at around the 27 yard line. And having the ball at around the 27 is worth about 0.6 points.
Arguments about the worth of a touchdown aside, the ball at the one is almost always going to be less valuable than a touchdown. But we know it's not much less valuable. So, in fact, how much less valuable is it?
Ignoring the final minute of each half, teams had first down at the one yard line about 108 times in 2007. (I say about, because while my data is as close to complete and as accurate as any I know of, it's certainly possible and even likely that I'm missing some specific plays.) What happened on those 108 "drives"?
On first down, 20 of the 108 teams threw the ball. Of those, 12 went for completions, and all twelve were touchdowns. Eight passes went incomplete, along with zero sacks and zero interceptions. Obviously 88 plays were rushes (although some may have been designed pass plays that turned into QB runs), with 38 of them going for touchdowns. Eight teams lost two, three or four yards. Eleven teams lost one yard (with one fumble lost) and 31 gained zero yards (with one holding penalty, meaning the team started at the 11 despite gaining zero yards on the rush).
To conclude, of the 108 plays in first and goal at the one situations (excluding those with one minute left in either half), 50* of them were touchdowns, 38 gained zero yards, one resulted in a fumble lost, and 19 left the teams with the ball and further away from the goal line. On second down, of the 38 plays from the one, 15 times the team ran for a touchdown and six times they threw for a score. Of 19 plays run from farther out, four times the team threw for a score and zero times the team ran for a score. One interception was thrown. That leaves 31 plays for third down.
Five teams a team threw for a score; six times a team ran for a score. Two times a team threw an interception. Once a team threw for a score, had the play nullified by a penalty, and then scored on the ensuring third down attempt. So what happened on 4th down?
On the 17 remaining plays, 11 times the team kicked a field goal and all eleven were successful. Six times the team went for it, resulting in two touchdowns and four turnovers on downs.
To sum, 108 teams last year had the ball at the opponent's one yard line on 1st down, with more than one minute to go in the half. 89 times (82.4%) the team scored a touchdown and 11 times the team scored a field goal. Four times the team turned the ball over, and four more times the team went for it and failed on fourth down.
It's not too difficult to value the touchdowns and the field goals. What about the turning the ball over and the failed fourth down conversions? The fumble was recovered at the four. Two of the interceptions were recovered in the end zone and downed there; one was returned to the six yard line. Obviously four isn't a large enough sample size to feel confident about anything, but the average field position the opponent took over the ball following the turnover was the 12.5 yard line.
The turnover on downs data are probably more reliable. The defenses took over at the two, five, twelve and fourteen yard lines -- on average, the 8.25 yard line. For all eight turnovers, the opposition took over at roughly the ten yard line.
We could re-look at the 2007 data as follows: 82.4% of the time teams facing 1st and goal from the one eventually score a touchdown; 10.2% of the time those teams settle for a field goal, and 7.4% of the time the defense ends up with the ball before any scores, at around the ten yard line.
Using Professor Romer's logic, this means 82.4% of the time a team scores 6.4 points, 10.2% of the time a team scores 2.4 points, and 7.4% of the time a team scores about +0.35 points. Where'd I get that last number from? According to Romer, 1st and 10 from your own 10 yard line is worth about -0.35 points. So our offense that fails to score still puts its team in a position where it's more likely to score than next. If we weight our averages, that means 1st and 10 at the one yard line is worth between 5.5 and 5.6 points. Since a touchdown is worth 6.4 points, this means 1st and goal at the one is about 86-87% as good as a touchdown. It's worth noting that Professor Romer reached the same exact result. According to his graph, 1st and goal at the one is worth 5.55 points. I wasn't sure if he was right or not, but my query today makes me feel very confident that he was.
*I'll be discussing more plays from the one yard line tomorrow, but it's worth noting that only 50 of the 108 rushes on 1st down scored touchdowns. That rate of 46% is pretty low -- on other downs and in general 3rd or 4th and 1 situations, teams convert at around a 55% clip. I checked the 2006 data (unfortunately, the rest of the data is too cumbersome to go back to '05 or '06 at this time) and the conversion rate was only 49%. But in 2005, the conversion rate was an incredible 65%. The weighted three year average was 54%, which is in line with what you'd expect.
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