I've expanded the Stats pages on Turnovers. In addition to turnover margin I've split out interceptions thrown, interceptions gained ("picks"), and fumble margin (fumbles gained - fumbles lost), all corrected for opposition (that is, the corresponding tendency of the other teams they've played). I don't update these pages except late in the season since they deal with very small numbers and thus aren't reliable until enough data is available.
While doing so I had a question: How many points is a turnover worth, on average? I figured that there are a few relevant issues, namely, how many points is the lost opportunity for the offense worth? And how many additional points does the defensive team gain due to the turnover?
I roughly decided that apart from the turnover, since the offense may have scored a touchdown, or field goal, but might not have, then at most the offense loses 3.5 points (a high estimate of 50% chance of scoring a touchdown). The defense gains that much on average, so at the very most it should be a 7 point swing. That seemed high and I wasn't sure how far to back off; maybe it's only a 3 point swing, maybe even less. I had no idea how often a team scores on an average drive, etc., so I searched the web for some answers to the turnover question, thinking there would be some complex and well-grounded statistics to determine the answer.
It turns out that the most famous solution is from The Hidden Game of Football by Pete Palmer and Bob Carroll, and has a rather simple solution: The turnover can happen anywhere on the field, and the offense's loss and the defense's gain add up to roughly the same amount in lost and new opportunity totalled. A fumble at the 10 yard line is either a huge offensive mistake (but a minor gift to the other side), or (on your own 10 yard line) it costs the offense very little but gives the other team a huge opportunity.
They used 1969 field-position data compiled in a 1971 paper by Carter and Machol. This data suggested that field position is worth anywhere from -1.79 points (at your own goal line) to +5.91 points (the opponent's goal line). The relationship was very linear, with the 23 yard line as a neutral location. These numbers conveniently jibed with some common sense: having the ball on your own goal line is worth -2 points (the amount of a safety) and having it on your opponent's goal line is worth 6 points (a touchdown). The linear average—the 50 yard line—is worth 2 points to either team. Palmer and Carroll used the idealized numbers to conclude that a turnover anywhere is a 4-point swing.
Over at FootballOutsiders.com, they revisited this issue and in particular, ran some newer data (from 2002) to see if there really was a linear relationship. It turns out that a turnover in either red zone is slightly worse—about a 4.25 point mistake—than a turnover anywhere else, with a turnover at the 50-yard-line being a 3.75 point mistake. This is also intuitive, as it seems to be the effect of field goals which are taken out of the equation in the middle of the field. But still, it seems that the average turnover, which is what I was looking for, is still worth around 4 points.
But then SportsQuant.com has this article, which seeks to differentiate between fumbles and interceptions. At first blush, revisiting the old data and analyzing new data (from 2003), they come up with a 4.2 point penalty for fumbling and a 4.4 point penalty for interceptions. But then they dig deeper and postulate that the "return" stats for fumbles are incomplete, not accounting for the yards gained before the fumble, which means the offense's field position was actually better than stated, and fumbling's penalty must be increased to 4.65 points (with interceptions at 4.35). This increases the average turnover penalty to about 4.5 points.
But wait, there's more! Mathletics chimes in with an estimate of 3.4 (on offense) vs. 3.7 (on defense), and an average of 3.55, based on other methodologies. Who is right, SportsQuant.com or Mathletics? What's interesting is that if we average their estimates—4.5 and 3.55—we're back to almost exactly 4 points yet again, which was the result of the original, idealized data set from 1971.
So I'm using 4 points, and treating all turnovers as the same. In other words, keeping it simple.
Other thoughts on turnovers
I'm of the mind that fumbles are mostly random; that teams aren't really "good" at holding onto the ball or stripping the ball. And certainly teams aren't better at "recovering" fumbles—it's just random chance. So while I use data only on fumbles that are lost (from cbbstats.com) it would be better to use ALL fumbles, and then cut that by whatever overall percentage of fumbles are recovered by the defense (probably just under 50%, since some fumbles the QB just falls on, but other than that it's random). This would give bigger numbers to work with and be more instructive than fumbles-lost.
Interceptions, on the other hand, are a product of a quarterback on offense, and some skill (and intent) on defense. While the numbers are again small enough to largely be random—especially game by game—I think there's enough evidence that certain quarterbacks are more prone to interceptions and that certain defenses are better at picking off passes, and may style their defense around it (going for the pick rather than the tackle). So there's a lot less randomness concerning interceptions than fumbles, and there is some evidence to back this up.
The fumble data can be useful on a per-game basis since teams that run the ball more often will naturally have more fumbles, and teams that pass a lot will have somewhat fewer. And intent on defense can make a difference, such as deliberately making "stripping the ball" part of the gang-tackling concept. But in general fumbles are more unpredictable and random, so I only list a "Fumble Margin" chart rather than separating out each side of the ball, which I do for the passing game.