## Comparing The 3-4 And 4-3 Defenses Part 2

In a previous post, I detailed how the 3-4 defenses over the past 10 seasons have, on average, outperformed 4-3 defenses. However, it’s possible that those 3-4 defenses simply had better players and that the 3-4 only appears to be the better scheme.

This time around, to account for each individual defense’s strength, I used a multivariate regression. The dependent variable in each model was a measure of success—EPA, WPA, and Success Rate (SR). The variable of interest was whether or not the defense was a 3-4 (a 1 if it was and a 0 if it wasn’t). The resulting coefficient of this variable represents the advantage of the 3-4 over the 4-3.

Each individual team was also assigned a dummy variable intended to capture the team-specific strength of their defense. Conveniently, this technique also accounts for the general year-by-year improvement in the effectiveness of NFL offenses.

There were 318 cases (team-years), from the 2000 Arizona Cardinals...to the 2009 Washington Redskins.

The results of the regressions indicated that the advantage of the 3-4 was not due to a coincidence of exceptionally talented players who happen to play in 3-4 schemes. In fact, the advantage of the 3-4 is even larger when individual team strength is accounted for.

This time, in addition to comparing WPA and EPA, I compared the 3-4 and 4-3 in terms of Success Rate (SR). SR is defined as the proportion of plays that result in positive EPA. Although it is a simple derivative of EPA, it is important in how the teams themselves perceive the game, a concept I'll explain in a later post.

Here are the key results of the regressions. Like before, negative numbers are better. Spikes, kneel downs, and aborted plays are excluded. The resulting coefficients for the 3-4 defenses were significant at the 0.05 level, except those noted by an asterisk, which were significant at the 0.10 level.)

 Advantage of 3-4 In: Per Play Per Game SR Overall -1.4% - SR vs. Pass -1.5% - SR vs. Run -1.4% - EPA Overall -0.038 -2.48 EPA vs. Pass* -0.041 -1.50 EPA vs. Run -0.036 -0.98 WPA Overall -0.00103 -0.066 WPA vs. Pass* -0.00109 -0.040 WPA vs. Run -0.00095 -0.026

According to the regression results, defenses employing the 3-4 tend to yield 1.4% fewer successful plays than 4-3 defenses. They tend to allow 2.5 fewer EPA per game, giving their teams an additional 6.6% greater chance of winning each game. This would roughly be the equivalent of home field advantage.

Contrary to the results seen in part 1, the regression results suggest the strength of the 3-4 is against the pass, although not by much.

Teams all around the league are switching to the 3-4 for a reason, and the stats appear to back up the belief that it's a better scheme against the modern NFL offense.

### 22 Responses to “Comparing The 3-4 And 4-3 Defenses Part 2”

1. Anonymous says:

Can you tell if this advantage has widened, narrowed or remained the same over the last ten years? Is it possible that the 3-4's advantage is that teams see it less often and as more teams switch to that alignment its advantage will disappear? I just stumbled across this site, so I apologize if you have addressed this elsewhere.

2. Brian Burke says:

That's a good question. It's hard to answer definitively because so few teams ran the 3-4 in the early 2000s. Your point is important. As offenses become more familiar with the 3-4, they should improve, and the advantage disappears.

We're probably approaching what game theorists call an Evolutionary Stable Strategy (ESS) mix. Suppose the 3-4 really is better. Most teams will become 3-4s, and the minority will be 4-3. Now, offenses would be less familiar with 4-3s. At some point, the overall average effectiveness of each strategy would equalize at an equilibrium.

3. James says:

Okay Brian, I'm trying to work out the Texans OT punt/FG/go-for-it probabilities but having trouble with the WP calculator. Is there some way you could add an option or list the different WPs depending on whether the offense kicks, punts or attempts to convert?

4. Brian Burke says:

James-I'll have a full analysis on that shortly. It's probably going to end up at the Wash Post.

The bottom line is that the FG from the 34 is generally better than the punt.

5. Anonymous says:

One note about pass vs. run effectiveness from a Steelers fan: effectively handling the run game from "base" packages (which seems to be something 3-4 defenses are adept at) allows a team to be better against the pass.

6. Anonymous says:

I know this isn't really related to this post but are you going to do an article on the Saint's decision to kick the field goal that gave them an 8 point lead rather then go for it on 4th down? Thanks and great work as always.

7. Anonymous says:

Are 3-4 defenses more "expensive" than 4-3 defenses? My perception is that they are and therefore teams who use the 3-4 have to give up something with their the offensive unit. Could you compare the offenses of this same data set to see if the teams with the 4-3 defenses have better offenses? If so, does the offensive improvement exceed the EPA they are giving up by using the 4-3?

8. JURI says:

Wow - this was unexpected. I certainly thought that 3-4 defenses were better because the teams running 3-4 were "defense first" kind of teams. (Pit Bal NE)

I do wonder what the explanation is - having one more guy standing up is better - why?

9. Unknown says:

If it's true that the main thing NFL defenses do very well, and differently than college defenses) is disguise coverages, 3-4 defenses give teams more options to overload one side of the offensive formation by only adding one blitzer. 4-3 defenses I think accomplish the same feat by employing tactics that take longer to develop (e.g. lineman stunts). The Tampa-2 and its' progeny are somewhat unique here as they rely on getting single blocking for one dominant lineman, and very rarely blitz linebackers or DBs.

I also have the impression that 3-4 defenses ask less of each position than 4-3 defenses, perhaps it is easier to identify talent and to teach.

10. skyjo says:

"Each individual team was also assigned a dummy variable intended to capture the team-specific strength of their defense."

Can you further explain what these dummy vars were and how they were derived?

11. Anonymous says:

You should post all the statistics of your regression. For example, you can't tell if the difference in the pass and run coefficients are significantly different. My guess is no, they aren't significantly different. The only thing I can tell because of different signficance levels is that the standard error for the pass coefficient is probably larger than the standard error for the run coefficient.

I'd like to see the r-squared, too.

Finally, I thought that another argument for the 3-4 was that down linemen were hard to find: getting good down linemen is harder than getting good linebackers.

12. Ralph Hickok says:

Is this a play-by-play or a game-by-game analysis? I think that's an important question because many teams that use the 3-4 as a base defense use a 4-3 in some situations. In fact, I believe the Patriots last season actually used the 4-3 more than 3-4, though I may be wrong about that.

13. Brian Burke says:

Most "3-4" teams run 4-3 fronts in varying ways. They just do it with 3 lineman and 4 LBs.

There's "3-4" the front, and "3-4" the baseline personnel package.

14. Anonymous says:

But what you aren't taking into account is how changes in the front dictate changes in the strategy of the Defense -- specifically the differences between teams that one gap and teams that two-gap.

15. Anonymous says:

This can't be taken seriously unless you share the data so that this study can be replicated.

16. Brian Burke says:

Yes it can.

By the way, here you go. Get crackin'! Let me know your results. You can publish them here.

17. Anonymous says:

Hmm, I can't seem to find the defensive formation listed in your play-by-play data.

Nor can I find the source code for WPA. Oh wait, I forgot, it's all done by hand.

18. Brian Burke says:

Hey, jerk. That's not how it works. Replicating research doesn't mean you get spoon fed all the analysis and then you press print.

WP is a regressed average of how often teams have won given particular game states from all actual games from 2000-2009. You want my source code? Right! Build your own model. I've given you all the data you need, for free.

Nice try. Buzz off.

19. Anonymous says:

Just pointing out that your WP implementation is a proprietary black box. Fair enough, but it would be hypocritical to imply otherwise.

There have been many other football WP models published (with varying degrees of openness), yet you come across as having invented the concept, unwilling to cite or even acknowledge your predecessors in this area of research.

And the name-calling exposes you as having the maturity of a seven year old.

20. Brian Burke says:

Why do people with personality disorders always end up at my site? "Oh wait, I forgot, it's all done by hand." Who's the 7-yr old, loser? You're a hater with an agenda, and it's transparent.

Show me another WP model that's more open.

-Does it provide its full methodology, like ours?

-Does it provide a calculator for determining the WP at any game state, like ours?

-Does it provide graphs and play-by-play of a decade of games?

-Does it provide free and full data to anyone who would like to replicate it, or even build their own?

I thought so.

For those without severe personality disorders who are interested, the WP model is not a black box. It is primarily based on several dozen LOESS regressions. There is no magic formula or code. LOESS regressions produce tables of data. The WP uses a combination of multi-dimensional look-up tables and Markov models to interpolate game states to estimate WP.

21. Anonymous says:

Actually, I'm not a hater. I love your research, but I think it would be more eagerly accepted if it didn't come with such a pretentious attitude and unwillingness to accept criticism. And I know others associated with the league feel the same way, FYI.

FootballCommentary published the full source code for its WP model. And SportsQuant and GridIronMine have also had WP calculators on their sites in the past. GIM also lists WP changes on a play-by-play basis. Not necessarily saying their implementations are more accurate, but then again, how would we know?

Clearly you have the best presentation (although the GIM charts were nice too) and apparently the most time to devote to spreading the word and keeping things up-to-date. I just think you need to be more careful when nearly every research article is now based on EP or WP, which are very powerful concepts, but very difficult to implement correctly. If you can't show the accuracy of the base estimates, I think it reduces the effectiveness of all the other studies you do.

BTW, your description of your WP methodology matches almost exactly how ProTrade described theirs a couple years ago ("regression with Markov chains"). Yet there are game situations with very different estimations. So again, how does one determine which number is better? Without looking into the black box, we'll never know.

22. Michael L says:

- How are you counting so-called hybrid defenses? What about the teams that had a transitional year where they played 3-4 only part-time while staying mostly 4-3?

- It seems fairly commonly believed around the league that a big advantage of the 3-4 earlier in the decade was a Moneyball-type cost of talent one. Attributes and body types needed/not needed for the 3-4 were not in high demand and competed for, so players that could be effective in a 3-4 but not so much in a 4-3 were comparatively plentiful and cheap. With the fast-rising popularity of the 3-4, this advantage is now disappearing (or gone). I.e. perhaps it wasn't _better_ personnel but rather leveraging under-utilized personnel that explains part of the discrepancy?

- Furthermore, the AFC turned to the 3-4 much earlier and in greater numbers, thus familiarity (i.e. preparation) was high in the AFC for years before the NFC. Can the 3-4 advantage be fully accounted for simply by inter-conference games? How different is the advantage if you limit analysis to only intra-conference AFC games?

- I wonder what a similar analysis of the shift from majority 3-4 to ubiquitous 4-3 in the 80s would show... I realize you don't have play-by-play for games back then, but it makes me curious.

- Lastly, I think it makes sense to include spikes and maybe aborted plays. A defense may be willing to give up a bigger play that keeps the clock running. Likewise, a defense that gives up the same play but lets an offense get out of bounds should be punished. Perhaps it makes sense to combine the previous play and the spike as a single "play" for EPA purposes. As for aborted plays, at least some of them are caused by the defense (if indirectly via confusion or rattling). Probably too infrequent to affect the final results, but worth noting anyway.