David strategies and Goliath strategies

Malcolm Gladwell's new New Yorker piece is called "How David Beats Goliath," and professes to describe what strategies underdogs -- or "Davids" -- can use to defeat Goliaths. His basic premise is that Davids all too often fall into the trap of playing Goliath's game, which is rarely going to lead them to victory: there's a reason that Goliaths are Goliaths and Davids are Davids. Instead, they should do something unique (the article's subtitle is "When underdogs break the rules") and risky:

The political scientist Ivan Arreguín-Toft recently looked at every war fought in the past two hundred years between strong and weak combatants. The Goliaths, he found, won in 71.5 per cent of the cases. That is a remarkable fact. Arreguín-Toft was analyzing conflicts in which one side was at least ten times as powerful — in terms of armed might and population — as its opponent, and even in those lopsided contests the underdog won almost a third of the time. . . .

What happened, Arreguín-Toft wondered, when the underdogs likewise acknowledged their weakness and chose an unconventional strategy? He went back and re-analyzed his data. In those cases, David’s winning percentage went from 28.5 to 63.6. When underdogs choose not to play by Goliath’s rules, they win, Arreguín-Toft concluded, “even when everything we think we know about power says they shouldn’t.”

So far so good. This is consistent with what I wrote in my post, "Conservative and Risky Strategies (and Kurtosis)." The problem with Gladwell's argument, however, is that although he recognizes that Davids ought not to employ Goliath strategies because it is a game they can't win -- "Arreguín-Toft found the same puzzling pattern. When an underdog fought like David, he usually won. But most of the time underdogs didn’t fight like David. . . ." -- he nevertheless assumes that Goliaths should all be using these David strategies as well, and can't understand why they don't.

This is incorrect. Just as Goliath strategies are often sub-optimal for Davids, David strategies are often sub-optimal for Goliaths. The reason Gladwell seems to miss it is because he doesn't have a broad theory for what makes a strategy appropriate for an underdog. His primary example is of the decision of a basketball team composed of twelve-year girls to use the full-court press in basketball the entire game. He also cites Rick Pitino as an example of a coach who has successfully used a David strategy at various stops, and as further counterfactual to the unsuccessful coaches who forgo using the press. This example has been much discussed and even derided as a descriptive matter in basketball, though Gladwell responds to the basketball points here.

More importantly though, Gladwell is actually right in a sense: the press (in basketball at least), is a pretty decent example of an underdog strategy. He fails to recognize that what makes it as a good underdog strategy is also what likely makes it inappropriate for Goliaths -- it is a high risk, high reward, high variance strategy. One reason it works for underdogs may have little to do with how good it is on absolute terms; the fact that there is increased variance by itself has value for underdogs because it might give the underdog a chance of actually winning. On the flipside, however, while a full-time press strategy might increase a Goliath's chance of blowing out an underdog, it also might result in them losing a game they shouldn't. I described all this previously, but the WSJ Daily Fix (Carl Bialik) does a nice job summarizing it:

To understand why, imagine that the Goliaths — the nickname of Philistine State’s basketball team — typically beat opponents by 10 points. They’re playing an average opponent in their next game. Strategy A, a low-variance strategy will, two out of three times, yield a Goliaths victory between 5 and 15 points (with the rest of hypothetical games played with that strategy falling outside that range, including a very small number of losses). But a high-variance strategy has a much wider range of outcomes, with two thirds of games ending somewhere between a five-point Goliaths loss and a 25-point rout. The second strategy, then, will lead to more games where the Goliaths lose. And that’s particularly costly in single-game-elimination competitions such as the NCAA tournament.

For true Davids, the full-court press might help, particularly if it’s not always expected so opposing Goliaths can’t know whether to prepare for it.

I used this image to visually represent the higher-variance, flattened bell curve of expected results from an underdog strategy. (I also assumed that the higher risk strategy increased the overall expected points too, though, as stated earlier, we need not make that assumption.)



I previously explained this trade-off for underdogs and favorites. For Davids:

It's a well-worn belief that underdogs -- i.e. the kind of severely outmatched opponent that cannot win without some good luck -- must employ some risky strategies to succeed. This has long been believed but now we have a reason, though it also teaches us that there is a price to this bargain. The underdog absolutely must take the riskier strategy, whether by throwing more and more aggressively, by onside kicking, or doing flea-flickers and trick plays. They have to get lucky. In the process, however, they also increase the chance that they will get blown out, possibly quite badly. But isn't that worth the price of a shot at winning? Florida might pick off the pass and run it back for a touchdown; they might sack the quarterback and make him fumble; they might blow up the double-reverse pass. If so, then things look grim. But what if they didn't? And if the team didn't do those things, how can it beat them by being conservative? By waiting for Florida to make mistakes?

And Goliaths:

Think about when Florida plays the Citadel. The Gators have a massive talent advantage compared with the Bulldogs. As a result, what is the only way they can lose? You guessed it: by blowing it. They can really only lose if they go out and throw lots of interceptions, gamble on defense and give up unnecessary big plays, or just stink it up.

A fan or some uninitiated coach might see this as a lack of effort, but another view might be that Florida used an unnecessarily risky gameplan that cost them a victory. And since we know that they would win almost every time, what did they gain by being more aggressive? Even if they gained in expected points, this is something like the difference between a forty-point and sixty-point victory, which ought to be irrelevant.

So Gladwell accurately identifies the fact that Davids should use underdog strategies -- and thus avoid playing the favorite's game as so many do -- he fails to perceive that the corollary is also true: Goliaths shouldn't necessarily use David strategies, either.

Application to football

Basketball aficionados are all over Gladwell, trying to poke holes in his understanding of the press or basketball or whatever. With Gladwell, that's kind of beside the point. The basic premise is true: underdogs win when they make the game theirs, not the favorite's.

The question then is how to determine what are good underdog strategies. Year2 at TeamSpeedKills concludes:

"The challenges they both [full-court press and Malzahn's offense] present opponents are all the more challenging for their uniqueness."

He should have stopped there, because that's also where Gladwell's argument ends. It's solely about being different.

I disagree. I think being different is merely a dominant strategy: all else being equal, it is better for Goliaths and Davids alike to be be different. Year2 and Gladwell are correct that there are some dominant strategies that Goliaths merely overlook (and I think Gladwell may have assumed incorrectly that pressing the entire game was one of them rather than what it is, a good but high variance strategy).

Jerry of Joe Cribbs Car Wash tries to draw a direct parallel between the press Gladwell discusses and Gus Malzahn's up-tempo no-huddle offense. First, I'm not convinced that going no-huddle is a dominant strategy, better for all teams. A team definitely gains the advantage of endurance, and there is a psychological advantage and all that, but, overall it seems fairly value neutral: it's just the repetition of the same trials over and over again.

Except that it isn't, but in the exact opposite way you'd think. Going extreme hurry-up to get as many plays as possible -- other than endurance, I suppose -- is a Goliath strategy: it decreases variance by increasing the number of trials. The chance of getting only heads and no tails in five coin flips is much higher than it is in a hundred -- i.e. the impact of the law of large numbers or regression to the mean. If Oklahoma has significantly more talent, better schemes, and everything else than the underdog, then the more plays it run the more likely it is to exhibit its raw dominance over the underdog; the underdog is less likely to "steal" a few good plays and get the heck out of dodge. The principle is the same as the difference between an underdog winning a game in a single-elimination tournament and trying to win a seven-game series: the seven-game series is far less likely to produce upsets.

So mere up-tempo, no-huddle is not an underdog strategy (and may in fact be a better strategy for Goliaths).

But what strategies would be good underdog, high-variance strategies? Here are some possibilities.

• Passing. It's very clear that passing is a higher-variance (and higher reward) strategy than running. The nature of passing can vary (if you only throw bubble screens that does not entirely count) but passing repeatedly is an underdog strategy. Now, good passing teams can reduce risk, throw safer passes, and the like. All good. And there is an open question with what mix of passes: Deep ones? Short ones? What blend is correct? That can be sorted out later. The bottom line though is that passing is a high variance strategy that can give an underdog a better chance of winning -- and a better chance of messing up and getting creamed.
  
  
• Reducing the length of the game and the total number of plays. As explained above, the higher variance and thus David-favoring strategy is to reduce the number of "trials" -- i.e. plays. This is where a passing strategy and a strategy that involves "shortening the game and keeping it close" might run counter to each other. Incomplete passes typically stop the clock (I can't keep the college clock rules in my brain anymore), as do plays where the ballcarrier goes out of bounds, which is more common on passes (same with the clock rules). If an underdog were to get an early lead, they obviously would love it if the game effectively ended right there. Yes, there is much to say about the problems inherent in not playing to lose and all that, but those are means questions, not ends. And all can agree that an underdog would love to get an early lead in a game against a favorite and have the clock run out as fast as possible.
  
  
• High variance defense. This is a difficult question. On the one hand, the defense could go for a blitzing, press type defense that might grab turnovers and get opportune stops, on the theory that you only need a few of these to get an underdog advantage. On the other hand, to an underdog each touchdown given up could be backbreaking, and in any event shortening the game by forcing the offense to march the ball up the field methodically, using up the clock, might be better. Yes people like to talk about "if we have the ball, they can't score" but that mistakes time of possession with possessions. If the underdog can force the favorite to use up a lot of clock and, at minimum, not score a touchdown, and then the underdog can somehow pull of a touchdown itself, then huge advantage to the underdog. On the other hand, pressing defenses that give up big plays periodically might play right into the Goliath's hands because it can score without taking much time off the clock. There is more to this but that is enough for some preliminary thoughts. Likely some mixed strategy is best.
  
  
• Other high variance strategies. Although much of the focus is on offensive and defensive strategies, the best bet for the David strategies is likely in the realm of truly high-variance strategies like trick plays or onside kicks. Onside kicking is particularly promising, because it is something an underdog can get better at, would be unique, and can be disguised. There's at least a chance -- unless data proves that it remains a fool's strategy, like throwing lots of hail marys (high risk but not beneficial) -- that a high percentage of routine onside kicking can give underdogs a real chance. Because when it works, it both gives the offense decent field position and steals a possession. When it doesn't, that's bad, but hey, we're talking underdog strategies.

So those are some options. Interestingly, it could be argued that on offense, the best strategy might be something like the flexbone or another triple-option offense like Paul Johnson uses: it has big play potential (and thus can be a substitute for passing), yet carries the benefit of keeping the clock going, which works against pass-first underdogs.

In any event, it's an interesting discussion, and an eternal one: how do underdogs beat the big guys? How do the big guys keep from getting beat? Gladwell of course can't resist bringing up that greatest of underdog stories, the American Revolution, where a definite David strategy birthed a nation. And now we're the hegemony, the Goliath. I don't necessarily think any of this is relevant to our country's place in the world, but there's a reason why it all fascinates us so.