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Tuesday, July 28, 2009

Responses to responses about David and Goliath Strategies

Tomahawk Nation responds to my earlier post on David & Goliath Strategies. See parts one and two of TN's responses. (See also my post on conservative and risky strategies and kurtosis.) Both pieces are well worth the read (I am a supporter of anything that combines football and six sigma). But a couple basic thoughts:

First, I completely agree with the idea of reducing variation, particularly negative variation. That really is the genius of Bill Walsh's passing game: what he brought to the game was a reduction of risk related to passing. Passing had been the quintessential "underdog" or David strategy; he reduced risk so much it arguably stopped being a David strategy and became a dominant one.

But I'm not sure if I agree with this:

Think of UF. To me, the Urban Meyer offense at Utah is a prime example of a David strategy. As he moved to Florida, he helped a Goliath school with Goliath resources begin to think like a David. People said that his offense would never work in the SEC, the QB would get killed, defenses were too fast, etc. But Meyer knew that his approach took advantage of a weakness in defenses, and if executed properly wouldn't be nearly as risky as people thought. Think back to the Ole Miss game from 2 years ago (the game that might have won Tim Tebow the Heisman). When the basic structures of the Meyer offense failed to work against the Ole Miss defense (Goliath being unable to hit David with his sling), and Ole Miss still allowed UF to stay in the game (Goliath managing to fight to a draw with David in a slingshot battle), UF was able to run Tim Tebow left/Tim Tebow right to win the game (Goliath is able to fall back on his superior size and strength combination to win the battle). . . .

...Gladwell highlighted the press in basketball as an example of a David strategy. Why is this a David strategy? Because Goliath doesn't focus on beating the press as much as David focuses on executing it. Because it takes Goliath out of his comfort zone. And honestly, because frequently the top point guards in the country have a certain level of confidence/cockiness in themselves that makes them want to beat the press by themselves and not rely on their teammates. The goal of the press is also to force the ball into someone's hands who is not used to handling the ball-- an inefficiency in Goliath's approach. This is how a team can use the David strategy to capitalize on an advantage. It's a risk, but if executed correctly it's not just a risk for the sake of being risky.

But is that really a David, or underdog strategy? Or is it a dominant strategy? I.e. better no matter who you are? One of the reasons I wrote my post was that I thought Gladwell confuses this point too, and I also concede at the end of the post that one conceptual difficulty is that some strategies are better for favorites (Goliaths conservative, low variance strategies), some solely for underdogs (risky David strategies), but some strategies are simply better no matter who you are (dominant), or inferior (punting on first down).

The things Tomahawk Nation is focusing on are, to me at least, dominant: better matchups, an unusual strategy the favorite is not ready for, etc. Admittedly, Gladwell confuses these two concepts -- or at least doesn't tease them out -- but I do think it's important.

To better illustrate what I mean, Advanced NFL stats showed that David strategies are often beneficial for underdogs even when they are basically inferior overall. In other words, even if a strategy would result in fewer expected points, it still would benefit the underdog because it still could get lucky. As ANFL explains:

Here’s why underdogs should play aggressive and risky gameplans. Take an example where one team is a 7-point favorite over its underdog opponent. Say the favorite would average 24 points and the underdog would average 17 points. With a SD of 10 points for each team, the underdog upsets the favorite 31.5% of the time. The favorite’s scoring distribution is blue and the underdog’s is red.

But if the underdog plays a more aggressive high-variance strategy, increasing its SD to 15 points, it would upset the favorite 35.3% of the time.

Note that I haven’t increased the underdog’s average score in any way, just its variance. The increase in its chance of winning results due to more of its probability mass moving to the right of the favorite’s mean score of 24. In fact, the higher the variance, the wider the probability mass will be spread. Consequently, more mass will be to right side of the favorite’s average score. But more mass will also be to the left, meaning there is a higher risk of an embarrassing blowout.

Even if employing a high-variance strategy is non-optimum, it can still help an underdog. In other words, even if an aggressive gameplan results in an overall reduction in average points scored, it often still results in a better chance of winning.

Yet would there be any reason for a Goliath to use this strategy? No, not at all. All it would be doing is inviting variance that would result in a few more upsets, and in fact might make the team worse (though could give the illusion of success because, again, of its high variance, resulting in a few high-scoring output games).

This is the biggest problem with the example TN uses:

Goliath University believes in the old Big Ten philosophy, 3 yards and a cloud of dust. Let's say they've even perfected their approach to the point that they can get exactly 3.3333 yards every time without ever turning the ball over. There is no risk involved and they know exactly what they are going to get with every play. Per play, they expect to get around .23 points. In true Goliath fashion, however, they run a quick, no-huddle offense in order to maximize the number of trials on the field. Over the course of the game this translates (assuming about 100 plays per game) to about 23 points and let's say a little over 30 minutes T.O.P. They'd win most of their games, but they'd lose any game where their defense gave up 24 or more due to random variation in the amount of time their opponent held the ball.

Goliath State University instead takes a more wide open approach, similar to Tulsa's offense. They throw the ball a lot more often, and go downfield more frequently as well. There is a lot more uncertainty associated with this approach, as there are many possible outcomes to their plays. However, through the strength of their preparation, they have a 50% chance of completing any given pass. Each of their 5 options (4 receivers and a QB run) has a 10% chance of success.

* If the QB runs, there is a 70% chance he will gain 4 yards, a 25% chance he will gain 14, and a 5% chance he scores
* Receiver A is running our deep fly, and there is a 50% chance he gets a 40 yard completion and a 50% chance he scores
* Receiver B is running the post, and there is a 80% chance he will get a 14 yard completion and a 20% chance he scores
* Receiver C is running the out, there is a 95% chance he gets 7 yards and a 5% chance he scores
* Receiver D is running the drag, there is a 95% chance he gets 4 yards and a 5% chance he scores

The expected point value of this play is:

.5*.1*((.7*.23+.25*1+.05*7)+(.5*3+.5*7)+(.8*1+.2*7)+(.95*.5+.05*7)+(.95*.23+.05*7)) = .468 expected points per play

Again, this is simply a better strategy, which is different than being a David strategy. Risk does not automatically equal David, and very conservative does not equal Goliath. Sometimes there is still better or worse.

To be fair, there is some indication in the TN pieces that this comes through. It repeatedly discusses the need to reduce the riskiness of these strategies "through film study, personnel decisions, and practice." Again though, I would argue that (a) these extra resources are themselves often a Goliath strategy (this becomes evident at high school for sure, but also in college with big differentials in resources, film equipment, practice materials, etc), and (b) practice and preparation is the quintessential dominant strategy -- it neither favors the underdog nor favorite, it's just a good idea!

The upshot is that these are two very good pieces, and well worth the read. I just want to emphasize my earlier point that I am using David and Goliath strategies in a very specific way, and one that differs slightly from Gladwell (it may not even be correct, it's just how I am using it). A true "David strategy" is one that, by definition, would not be good for a Goliath, because it is riskier. I used the example of extra fake punts, onside kicks, going for it on fourth, trick plays, etc. Relatedly, some Goliath strategies are low variance but that doesn't mean they have to be literally three-yards and a cloud of dust.

But the important point that TN clearly does get is that, Goliaths may nevertheless act suboptimally, and it is the underdogs and Davids that might discover the better, dominant strategies. The dominant ones will be adopted by those Goliaths (think of the spread of the spread, with its ability to push boundaries while keeping risk low), and others, though derided mightily as "gimmicks," simply might be appropriate for an underdog. It's not always easy to tell the difference, but this is an idea definitely worth continued exploration.


War Eagle AC-47 said...

I think Les Miles benefits from the trickeration aspect of what you mention. He benefits because he has a strong team, but he also does the unexpected. He might use fake punts that end with a pass. He has used an on-side kick in the third quarter just for the hell of it. But he has the players to pull it off.

The element of surprise is powerful.

Utah vs Alabama. Surprise.

Just doing the unexpected can result in big gains. But a one trick pony will lose his head. You must have strong players to make the sneaky stuff work more than once.

Jon said...

Chris, speaking of Gladwell, he mentioned this book in jis latest New Yorker article. Football isn't really war, but I wonder if any lessons can be gleaned from it.

MattDNole said...

And this is why you are the pro and I am still getting there. It was my original intent to respond to both yours and Gladwell's piece together, and neglected to differentiate between your definitions of true "David" and "Goliath" strategies.

I think overall we are just dealing with a difference in terminology. When I was trying to develop a working definition of a "David strategy," it ended up being a lot like the old court case on adult materials. "I don't know how to define it, but I know it when I see it."

You are correct, most of the approaches in the article actually relate to Gladwell's definition.

I think the point I am eventually trying to make is that a lot of these times, these approaches are created to give smaller schools a competitive advantage and when they are co-opted by bigger schools they morph into a Goliath approach.

It could just be that smaller schools are more likely to try something new and discover a dominant strategy.

I appreciate the feedback though, and I've definitely got some more things to think about before Part 3 (basically just looking at how a gain in margin of victory can offset the increased variance and reduce the probability of losing).

MattDNole said...


Obviously no one would run the proposed offenses I suggested, I just wanted to cite an example where "no risk" did not mean "best."

I also wanted to make my math calculations as easy as possible.

Chris said...


Thanks for the comments. I do want to be clear that I really enjoyed your pieces, they just got me thinking. The original works I did were an example of me working through many of these issues myself; this was another opportunity.

(Also, I'm not an academic, but I read a thing about high-level philosophy departments I agreed with: There, it is not uncommon for a speaker to give a long presentation, and then as soon as he is done someone else begins, "All that is interest, but doesn't all of that rest on an assumption that is demonstrably false because of X, Y, Z, etc?" And then from there the discussion merely begins. I'm a believer in that model for ideas.)

Anyway, I look forward to Part III. Keep up the great work.

Anonymous said...

Two good examples of "David" strategies are Hal Mumme's go-for-it on 4th down and Jeff Fisher's onside kicks after every score vs. Indy a few years ago.

In both situations, the coach concludes that his defense is very unlikely to stop the opponent. Thus, field position has very little value. Trading worthless yards of field position for a valuable chance to retain possession is a smart "David" strategy.