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Life at the 1
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.
This entry was posted on Monday, September 29th, 2008 at 6:47 am and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.

"Five teams a team threw for a score;"
Sounds like poetry
So with those stats, you could assign a point value for 2nd and goal at the 1, or 3rd and goal, or 4th and goal... And with enough data, presumably you could do the same thing with every other down/yardline combination... yes? Though obviously 3rd and 26 at the 16 yard line or some such isn't going to occur enough to calculate directly. I wonder if the data would make some sort of pretty mathematical shape. . .
Maybe, Mattie.
But you would have to, in some way, take into account that outside the 10-yard line the object isn't always to score - but to get a first down.
Also, there might be a "bump" on the mathmatical shape around the 30-yard line - where a fieldgoal no longer is possible (likely).
Right?
Mattie already figured out tomorrow's post
.
Danish Denver-fan, Romer already derived a map for 1st and 10 in any situation and there's no bump -- http://www.pro-football-reference.com/blog/?p=41. I suspect you might be right if we're looking at say, 3rd and 10s. But in most situations, given a large enough sample, most curves will be pretty smooth.
Woo hoo, poetry tomorrow!
...
err, wait...
I think the object is to score no matter where you are on the field. There may just be some intermediate steps.
And once you know the value of 3rd and 10 at the 20 and 1st and 10 at the 30, you can assign a point value to that completion that got you the first down. Or the value of the incomplete pass that leaves you at 4th and 10 at the 20.
Well, I suppose late in the game with a lead, the object becomes "maintain possession" rather than score because it can ensure victory better than 7 points.
So once you have values for every down and yardage at every position on the field, you can assign a point value per play on non-scoring plays. Not only that, you can assign a more fair value to scoring plays -- If the QB/WRs drive the ball 79 yards with passes and the RB gets it in on first and goal and scores the TD... Clearly some of those 6/6.4/7/8 points should be assigned to the other players, eh?
Also, it might allow one to more fairly compare defenses -- A defense with a lousy offense is going to end up defending poor field positions and let up more points, but if we know the value that the opposing offense STARTED with due to field position, we could subtract it from the drive results. Ditto for special teams play.
For that matter, you could devise some sort of way of rating players based on their situational play -- A QB that can complete that 10 yard pass on 3rd and 10 and keep the drive moving may be more valuable than a QB with better overall stats that can't seem to get the first down in those tight situations.
You could also measure the risk/reward of going for it on fourth and short -- 1st and 10 at the X is worth N points, 1st and 10 at the X-1 for the opponents is worth M points...
You could probably also find some interesting things about teams -- 1st and 10 at the 20 may be worth more for the Colts than the Ravens, but 1st and 10 at the 50 might be worth more for the Ravens than the Colts. (or whatever)
Ooh, and if you've got per-play data, you can also assign more accurate +/- to TD/INT passes on a per-case basis -- An interception in the endzone hurts you more than an interception at midfield, and an intercepted screen returned for a TD is much worse than an intercepted 40 yard hail mary...
Chase--- How about sometime in the future, do this same study using 108 similar examples that happened IN THE PLAYOFFS. I think it would be interesting to compare the results. Just a thought. It would be even more interesting to use 108 in the Wildcard Round, then 108 in the Divisional Round, 108 in the Conf. Champ. Round, and finally 108 (if there were that many) in the S.B. I'm guessing that those results would show just what effect BIG GAME PRESSURE has on decisions and performance.
You shoulda mailed this article to the Eagles after the Bears game. They coulda told you the difference between a TD and the 1.