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I keep seeing 49ers linebacker Patrick Willis' name listed at the top of defensive player statistics the last few years. He led the league in tackles in 2009 and 2007, and was second in 2008, but does this mean that Willis is really a top player?

Most fans understand that the tackle statistic is not a very good way to measure a defender. Weaker defenses tend to give up longer drives, giving players more opportunities to make tackles. So in a perverse way, more tackles can be a bad thing. If a defensive back has a lot of tackles, it may be because he's being thrown on successfully. Plus, certain positions get more tackles by the nature of team defense. Middle and inside linebackers will naturally have the most tackles by virtue of their role and where they are at the snap. If you scan down the list of the season leaders in tackles, you're likely to see a simple list of each team's central linebacker, assuming he was healthy most of the year. So how can we tell if Patrick Willis is really that good using just tackle information?

An Idea from Baseball

Baseball faced similar problems with defensive statistics. Until recent years, fielding skill was measured solely by the Fielding Percentage stat, which is a player’s number of put-outs and assists divided by his total of put-outs, assists, and errors. It’s basically a player’s “non-error rate.” This is a flawed way of looking at fielding for many reasons. For one thing, you can't make an error if you can't get to the ball.

In 1977 Bill James revolutionized fielding stats with the invention of Range Factor (RF). Say that for the major leagues as a whole, the shortstop position typically accounts for 20% of its team's putouts and assists. Assuming a relatively even distribution of fielding opportunities, a shortstop who creates significantly more than 20% of his team's outs could be considered to have better than average range and skill. And a shortstop who has significantly fewer than 20% could be considered to have below average range and skill. It’s elegantly simple and compellingly useful.

Tackle Factor

(I bet you know where I'm going with this.) What if we looked at the proportion of all 49ers tackles for which Patrick Willis was given credit? San Francisco logged a total of 832 tackles in the 2009 regular season, and Willis got credit for 114, a proportion of 13.7%. Willis is an ILB in a 3-4 scheme, and in 2009 the ILB position in all the NFL’s 3-4 schemes accounted for 21.5% of a team's tackle total. Because there are two ILBs on the field at once, a single ILB could be expected to average half that, or 10.7% of a team's total.

Willis' 13.7% compares very well with his position’s expected tackle rate. His ratio of tackle percentage compared to the expected percentage for his position is 13.7/10.7, or 1.23. In other words, Patrick Willis has a 'Tackle Factor' of 1.23; he makes 23% more tackles than you'd expect from his position, which tells us a lot about his ability to shed blocks, get to a ball carrier, and make a tackle.

To compare Willis to other players we can follow the same process. Redskins MLB London Fletcher notched 95 of Washington's 804 tackles in 15 games last season. Over a full season we could estimate he would have 16/15 * 95 = 101 'season-adjusted' tackles. Fletcher's adjusted share of the Redskin's tackles would be 101/804, or 12.6%. The MLB position in a 4-3 defense averages 11.9% of a team's tackles, making Fletcher's Tackle Factor 1.06.

Shortcomings

There are a number of shortcomings with TF. For starters, it tells us something very different about defensive backs than for linemen and linebackers. Just like total tackles, a weak pass defense would increase the proportion of tackles in the secondary. It still may tell us something about safeties, however. If a safety is making a very high proportion of his team’s tackles it may mean he’s a standout in an otherwise weak defense. We could also modify the stat to count only run plays, which might be even more illuminating.

TF penalizes players who are not every-down defenders. For now, it is adjusted for games played, but not for snaps on the field. Ideally, if we knew how many snaps each player was on the field we’d get a more reliable stat. Because so many players are not every-down defenders, the average TF is not 1.0. But on the other hand, if a player is not worthy of playing every down, that alone tells us something about his ability.

Baseball’s Range Factor suffers from many of the same issues, but it was nevertheless considered a quantum leap forward in defensive statistics. I think TF could also be a step forward despite its flaws. Defensive baseball stats have evolved significantly in the generation since RF was invented, and the concepts Bill James set forth underlie each new development.

Applications

So what can TF tell us now? The other night I came across a post at Pro Football Talk that ranked the free agent LBs available this year. Here are the available players and their 2009 TF numbers:


Free Agent TF
Karlos Dansby 1.01
Gary Brackett 0.84
Jason Taylor 0.68
Keith Bulluck 1.12
Scott Fujita 1.07
Joey Porter 0.82
Tully Banta-Cain 0.70
Larry Foote 0.86
Antonio Pierce 0.74

In this group, Keith Bulluck looks like the better tackler according to TF, followed by Karlos Dansby. Jason Taylor is not an every-down guy anymore, and that’s reflected in his tackle numbers.

Tackle Factor: the ratio of a player’s proportion of his team’s tackles compared to what is expected at his position. Pretty simple. We can improve it by putting it on a per-snap basis and possibly by limiting it to run plays. One obvious improvement I’ve already made is to count assists as half a tackle. (The free agent TF numbers above include assists.) We can do much more too, such as giving extra credit when a tackle was for a loss or whether the play was a “success” (defined by whether it resulted in a positive or negative change in Expected Points (EP). There could be opponent adjustments or adjustments for a defenses' overall strength. This would reward the best players on the best defenses and not penalize good players surrounded by better players. It's really just a matter of the getting good data.

For reference, here are the proportions of tackles (plus one half for every assist) that each defensive position garnered in 2009.


Position 3-4 DEF 4-3 DEF
CB 9.3% 9.5%
DE 6.0% 6.6%
DT - 5.6%
ILB 11.0% -
MLB - 11.9%
NT 6.4% -
OLB 7.0% 9.9%
S 10.5% 10.0%

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