It's notoriously hard to quantify the defensive efforts of a single players from stats alone, but I like a good challenge, and I didn't have anything else to do this weekend, so I decided to give it a shot. If you don't want to know the mathematical details that went into the calculation, just scroll a bit until you see the tables.
Because I used Yards Above Average Player as my metric for offensive players, I decided I was going to develop a metric called Yards Below Average Player (as in, yards prevented that an average DIII player wouldn't have prevented) for defense. The counting stats that went into the calculation were
-- Tackles for loss
-- Forced fumbles
-- Fumbles recovered
-- Blocks (even though they're technically occurring on special teams)
-- Pass breakups
-- Defensive touchdowns
Each stat was given a weight based on their importance in determining the defense's Adjusted Net Yards per Attempt (ANY/A) allowed. The average offensive play goes for 5.1 ANY, turnovers count for 45 yards, and a touchdown counts for 20. So the easiest weights to determine were interceptions (x45), defensive TDs (x20), and FF/FRs (x15 apiece). On average, every two forced fumbles results in a turnover, because the offense and defense are equally likely to recover a fumble. So the combined value of two forced fumbles and one recovery should amount to the same equivalent yardage as an interception.
The weight for a pass breakups, sacks, and tackles for loss are also pretty easy to understand. The average pass completion goes for around 11-12 yards, and around 1-in-3 PBUs results in an interception, so I used a weight of x15 for PBUs. The average sack occurs between 6 & 7 yards yards in the backfield, so resulting yards prevented of a sack are just over 15 yards. Because sacks are highly correlated to turnovers (more so than any other quality-based defensive statistic), I decided to bump that up to 20. The average TFL occurs 4 yards in the backfield, and with the average offensive play going for 5 yards, I used a weight of x10 for TFLs.
The only other stats left without weights at this point are tackles and safeties. A safety is already going to be credited as a TFL, and their weight should be the resultant of the yardage value of 2 points, which is a third of a touchdown (which are x20), so around x7 for safeties. Because I like round numbers (and because a safety is less indicative of performance/outcome than any other stat), I used x5.
To determine the weight to use for tackles, I took the rate of all of the aforementioned stats multiplied by their weights, and subtracted the results from an average result. This means that your run-of the-mill tackle ends up being worth about 3 yards prevented.
So add up every player's weighted stats and divide by the total number of plays, and you end up with their Net Yards Prevented per Attempt (NYP/A). The amount over/under the average result (5.1 yards) is each players' Efficiency Below Average (EBA). Multiply EBA by the total number of team plays, and you get each player's Yards Below Average Player.
A few things in the calculation also needed to be accounted for that are much harder for defensive players than offensive players, first of which is the number of plays participated in. This was an easy (and pretty unscientific) fix. I assumed every player played in about 3/4 of their team's plays.
To account for players who impact plays but don't rack up as many stats, I also gave credit to each player for one-eleventh of their defense's average ANY/A. So if a defense's average ANY/A is one yard below the national average, every player on that team's individual Net Yards Prevented is increased by 1/11 of a yard. The result is then adjusted for strength of opponents faced and pace of play.
The nifty thing about these results is that the top performers at each position end up having around the same Yards Below Average Player. Defensive lineman, linebackers, and defensive backs all ended up having approximately equal statistical contributions to the games. Below are the top 28 performers in each position group. Why 28? Because that's now may rows fit onto my laptop, and because there were a few big names (Baylor Mullins & Teidrick Smith) landed in the 25-28 range.
Later in the week, once I finish performing analysis on special teams, I'll put together an "official" All-American Team for the 2016 DIII season.