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.

What makes a good running back? How do you evaluate how good a team's run game is?

The pro-football reference blog recently mentioned something I found fascinating:

What about rushing? . . . .In modern times, most RBs have a median carry length of three yards. I suspect that’s been the case for the majority of RBs for a long time. LenDale White and his 3.9 YPC last season? Median rush of 3 yards. Adrian Peterson and his 4.8 YPC? Median rush of 3 yards.

I think this has powerful implications. If most runningbacks tend to have the same median rush, then those who are more effective -- and hence have higher averages -- would be almost exclusively based on their big-play ability. (That big-play ability could still come in different forms, i.e. the guy who consistently can turn five yarders into 15 yarders, or the guy who can break every 10th or 15th rush into a 50 yarder.)

But this would imply that the powerback, or at least the powerback who is not considered so explosive, is overrated. (Earl Campbell could run you over and break off big gains.) The point is just that the premium would not be on the player's results on the average plays, but instead on the longer ones. Some of this too can be the surrounding cast. Indeed, as Homer Smith has said, a runningback who gets 130 yards on 20 carries plays in a better offense (either because of him or for whatever other reason) than a guy who gets 145 on 35 carries.

But this does all assume that average yards per carry is the most important stat. I'm not sure all would agree that it is. (In fact, I think the PFR Blog folks might not agree, as they ranked runningbacks and included their total carries and pure total yards as a key factor.) I'm not convinced that more carries means a better back or better running game, as that depends on the game situation (does the team get a lot of leads?) and also that the play-calling is optimal. I can also buy that on 3rd and 3, or third and goal, the point is to convert, not to help the average.

Yet then how else can we evaluate running backs, or even a running game more generally? A perusal of the best offenses and running games in college tends to show that the best all have high yards per carry; not too many BCS teams have averaged fewer than 4.5 yards per carry, and several have averaged well over five yards per rush attempt (including sacks, which count against the run game total in college).

So I'm opening the floor to better ideas. IF yards per attempt is the best metric (for either an individual back or a team's run game), and IF the median truly is right around 3 yards for great and average backs alike, then the difference between good and mediocre runningbacks and rushing teams would seem to be wholly in the explosiveness of the upper 50% of plays: a good team or player can rip off big gains, and turn big gains into touchdowns, while the average plays for both is about the same. (And maybe negative plays are overrated.)

But I'm interesting in everyone's thoughts on this question. How do you evaluate the running game?

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.

More on Gladwell and underdogs

Again, reiterating my point that likely underdogs benefit from a high variance (i.e. high-risk) strategy, but that it might be inappropriate for heavy favorites. From Dean Oliver, via Basketball Prospectus:

This is very important for a coach like Kentucky’s Rick Pitino. His game plan of three pointers and pressing defense is a high variance strategy, one that an underdog should take, not a favorite. This high variance strategy is how he got his unknown Providence team to the final 4 in 1986. This is how his Kentucky team came back from a record 33 point deficit a year ago. But continuously applying this high variance strategy on a team with great talent like Kentucky is asking for an upset. Kentucky has been among the favorites to win the NCAA title two out of the past three years, only to fall earlier than expected. Again this year, they were favorites, being preseason #1. But their high variance game plan cost them last night against Massachusetts. And it will likely cost them later on this season. Despite Kentucky’s immense talent, coach Rick Pitino’s risky game plan makes the team more susceptible to upsets.

Ravens' Ozzie Newsome and talent spotting (of all kinds)

Lots of interesting stuff from Sunday's NY Times article on the Ravens and Ozzie Newsome's approach to the draft. But maybe most interesting is this approach to identifying organizational talent -- guys within the organization who are smart, hardworking, and are willing to eat, breathe, and sleep football. All organizations and businesses look for this kind of person, but Ozzie Newsome has an interesting technique, though unsurprisingly he learned it from Bill Belichick.

In a program Newsome borrowed from Belichick, the Ravens rarely hire a scout from outside the organization. Rather, Newsome has his 20-20 club. He pays 20-somethings who hope to rise through the personnel department $20,000 a year. They work 20 hours a day filing tapes, picking up free agents at the airport and cleaning out the refrigerators of released players who have abandoned their apartments. In 1996, Coach Ted Marchibroda used to give DeCosta $100 and ask him to get an oil change for his car and keep the change. DeCosta dutifully scouted out the places that would do an oil change for $9.

In the meantime, Newsome and his staff get a read on an up-and-comer’s work ethic and intelligence. The older scouts tutor the younger ones in what to look for, so everybody’s eye is trained the same way.

“We even grade our lunches,” DeCosta said. “If I say it’s a 6.2 lunch — all the guys know what that means, pretty good, but not great. A 7.5 is like the Pro Bowl is, if I say the soup is a 7.5 today, everybody runs to get the soup.”

I will have more to say about the NFL draft in this next week, but it's worth pointing out that this is yet another area in football where you can only deal in probabilities, can only do your best and hope the dice roll works in your favor.

Newsome’s first draft as the director of player personnel in 1996 may define his career. Convinced the Ravens could support a troubled player, Newsome was prepared to take running back Lawrence Phillips because the Ravens needed a rusher. But offensive tackle Jonathan Ogden fell into the Ravens’ lap at No. 4. Ogden was rated higher on the Ravens’ draft board, so they took him. Phillips, eventually taken sixth, washed out of the league after playing only 35 games. Ogden is a near lock to join Newsome in the Hall of Fame. The Ravens got Ray Lewis later in the first round, too.

As he prepares for next weekend’s draft with his reputation burnished, Newsome can afford to laugh at his early good fortune. “I might not be here if it had gone the other way,” he said.

Speculations on play-calling on first, second, and third and ten

From Advanced NFL Stats:

All the numbers that follow are from all 10-yards-to-go scrimmage plays in the first 3 quarters of regular season games from 2000-2007. The only other limitation was that the game score was within 10 points. I wanted to exclude situations when teams exercised an abundance of either risk or caution.

Note the percentage of play types called on 1st, 2nd, and 3rd downs (with 10 yards to go). There is a fairly even split between run and pass calls on 1st and 2nd downs. On 3rd and 10, the a pass is far more expected.

% of Play Types by Down, 10 Yds To Go

Type - 1st - 2nd - 3rd - Total
Pass - 47.2 - 52.7 - 91.1 - 49.6
Run - 52.8 - 47.3 - 8.9 - 50.4

Although 91.1% isn't 100%, it's close to where the anchor point on the lower right side of the game theory graph--almost the pure pass vs. pass defense strategy combination. Now let's look at the average outcomes for these situations.

Yds Per Attempt by Down, 10 Yds To Go

Type - 1st - 2nd - 3rd - Total
Pass - 7.0 - 6.3 - 6.5 - 6.9
Run - 4.2 - 4.4 - 6.9 - 4.3
Total - 5.5 - 5.4 - 6.5 - 5.6


When passing is most predictable, it yields half a yard less than on first down, when it is less expected. Conversely, running is most successful when it is least expected.

At this point, I should point out that passing on 3rd and 10 yields slightly more yards than on 2nd and 10, which isn't completely what we'd expect. This is almost certainly because defenses will allow short complete passes on 3rd down in exchange for being relatively assured to be able to stop the gain short of 10 yards. This is part of the problem posed by the fact that yards does not equal utility. We'll have to dig a little deeper. The next table lists interception rate by down.

Interception % by Down, 10 Yds To Go

Int Rate
1st - 2nd - 3rd - Total
2.6 - 2.9 - 3.5 - 2.7

Now we see more what we'd expect--a slight increase from 1st to 2nd down, then a large jump on 3rd down, in accordance with the associated increases in passing predictability. The next table lists adjusted yards per attempt, which is YPA with a -45 yd adjustment for every interception thrown. Adj YPA, however, still exhibits the same problem as plain YPA. It underestimates the drop off from 1st to 3rd down in passing effectiveness because defenses will allow gains, as long as they're not more than 9 yards.

Adj Yds Per Attempt by Down, 10 Yds To Go

Type - 1st - 2nd - 3rd - Total
Pass - 5.9 - 5.0 - 4.9 - 5.6
Run - 4.2 - 4.4 - 6.9 - 4.3


So what we can say is, the reduction in passing effectiveness due to predictability is likely at least 1 full adjusted yard per attempt. The drop from 1st down to 2nd was 0.9 yards, so the true reduction in effectiveness from 1st to 3rd down may be far larger.

Except that there's a problem with this analysis. There's a bias in the data. Which teams are more likely to face a lot of 2nd and 10s and 3rd and 10s? The ones that stink at passing. So the 2nd and 3rd down numbers are lower than would be representative of the league as a whole. In other words, poor passing teams 'get more votes' in the analysis.

All this is intended to tee up a game-theory analysis for finding some kind of ballpark run/pass equilibrium. Do read the whole thing.

But a few brief thoughts:

• The adjusted final numbers intrigue me, particularly second down as compared to first. (As Brian notes, third down is tougher to break down since it's really a binary question of conversion versus failure.) But I'm struck that on second down the yards per pass attempt drops by nearly a full yard while the yards per run goes up only .2: why does the defense get so much better on second down? Is the data skewed to losers? Is play-calling worse on second down?
  
  
• In that vein, I wonder if the old conventional wisdom about "getting back half on second and ten" works against the offense. On first down the passing plays are likely to involve play-action as well as quick or intermediate passes -- coaches can use their full asrsenal; maybe on second coaches are too concerned with screens and quicks -- trying to just get half -- that they give up too much in the way of expected points?
  
  
• But on the other hand, what if they get this 5.0 yards per pass attempt on second and ten with more certainty and less variance than the 5.9 on first down. If so, then possibly the offense is in better position to convert third down than they would be even with a greater expected play value that carried more variance. Could cut either way; football is complicated.

Hopefully Brian can shed some light as his series develops. I look forward to it.

Texas Tech - First-Year QB Comparisons

From Double-T Nation:

For the first time in two seasons, Texas Tech has a brand quarterback and although we're accustomed and grateful for what Graham Harrell did, it's time to look a bit forward and wonder what Taylor Potts might bring to the Red Raiders as a first year starter under Mike Leach's system.

Going into Graham's second year, I asked how much he could improve from one year to the other, but this time I thought that it might be a good idea to take a look at Symons, Cumbie, Hodges and Harrell's first (and sometimes only) year. The nice part about this is that it's a nice mix of players. It's not just one type of quarterback, which means that perhaps there's actually something to gain from looking at what we can expect.

. . .

Playing It Safe

What's the one thing that jumps out at Harrell's 2006 season? For me it's the fact that he had over 50 attempts for every interception. Contrast that with the touchdowns per attempt? Now, contrast that with Symons and what does that tell you? For me, it tells me that Symons was a guy that was going to take chances, while in Harrell's first year, he was dead set on playing it safe, evidenced by the lowest yards per attempt of any of the four, although he only beat out Cumbie in that category by one-one-hundredth of a point. There's got to be some middle ground here, and taking a look at Cumbie's 2004 season, his touchdown to attempt ration is far and away better than his partners in crime. Statistically, he's really not much better than his fellow quarterbacks and lost in all of this, sometimes is that Cumbie was just damned good at putting the ball in the endzone.

My Favorite QB Stat

I've probably beaten everyone over the head about yards per attempt and it's a really bad habit, but if you'll indulge me here, I'll try to make this quick. In the Air Raid offense, there may not be a more telling statistic about the success of a quarterback than yards per attempt. Every offense is better when the team is moving the ball vertically, rather than horizontally. That's probably one of the real misconceptions about Leach's offense, is that the intent may be to make it a dink-and-dump offense, but I think this is more than likely a product of the quarterback rather than the offense itself. Exhibits "A" and "B" are Symons and Hodges. Granted, the Air Raid is not as vertical as many other offenses, but taking last year as an example, Texas Tech ranked 20th in the nation at 8.11 yards per attempt. The offense bogs and becomes not as effective if the pass is going sideline to sideline.

While I completely agree that yards per pass attempt is the most valuable passing statistic, I also think it can be adjusted slightly to better capture the issue Seth is looking at here. Specifically, you can factor in interceptions using a simple rule of thumb. This is relevant here particularly for the raw numbers between Graham Harrell's first season, in 2006, and B.J. Symons's first and only season, in 2003.

- With raw numbers, Symons threw for 5336 yards on 666 attempts, for a yards per attempt of 8.01. He also threw 21 interceptions.

- For Harrell in 2006, he threw for 4555 yards on 617 attempts, along with only 11 interceptions.

What the stat guys are doing now is subtracting 45 yards for every INT thrown: they've crunched the numbers, and this is about what it takes away from you in terms of field position, scoring probability, etc.

If you did that for Harrell in 2006 (multiplying 11 times 45 yards and subtracting that from his raw passing yards) you get him 4060 adjusted total yards. Compare that with Symons' 21 INTs, which brings his total down to 4391. This makes their adjusted yards per attempt stats now 6.58 (Harrell) and 6.59 (Symons) -- nearly the same, though by different roads. Interesting, no?

The other X factor is QB sacks/runs. College stats make this hard of course: in the NFL, sacks are counted against passing yards and thus factored into yards per attempt. For Texas Tech QBs I think the safest thing is to just count the rushing attempts and yards all as part of the adjusted yards per attempt. (If this was Oregon or Tebow at Florida it'd be very difficult to do this without completely going back to the raw data and recreating the "sacks" and "yards lost by sack" statistics.)

Harrell's rushing stats in 2006 were 32 rushing attempts for -66 yards. Throwing that with the above adjusted numbers makes his new adjusted-adjusted total yards 3994, his total adjusted-adjusted attempts 649, and his adjusted-adjusted yards per pass attempt 6.15.

For Symons, in 2003 he rushed 74 times for 140 yards. Adding this to his passing attempts/yards we get 740 attempts and 4531 adjusted-adjusted yards. (I know that this number, unlike Harrell's, is actually positive, but I think it defensible to add it all back in because few Tech QB runs -- other than sneaks -- are called run plays.) So the adjusted yards per attempt is 6.12.

So Harrell actually beats out Symons in adjusted-adjusted yards per attempt, 6.15 to 6.12, though that's basically too close to make a call. I think it reinforces Seth's point that Leach has gotten it done with QBs of vastly different styles, especially considering these two guys were (probably) the best of that run by Leach where each first-year QB excelled that Harrell broke by starting more than one season.

In any event, the real point of this is to show how you might compare apples to oranges for any system or QB, with a guy like Symons who was acting as more of a gunslinger and Harrell who -- within the confines of Leach's wide-open offense -- was operating slightly more conservatively.

(I don't have exact cites but credit must be due to Advanced NFL Stats and the Pro Football Reference Blog, both of whom have undertaken similar analyses.)

Conservative and risky football strategies (and kurtosis)

Brian from Advanced NFL stats recently posited that some NFL teams (namely, the Washington Redskins under Jim Zorn) might have been throwing too few interceptions. This was because the lack of interceptions was a symptom of playing too conservatively, and therefore costing the Redskins games.

Implicit in Brian's thoughtful article are a couple of assumptions that I want to unpack, because radically different strategies might be appropriate depending on the level of football.

• The first assumption is that a lack of passing (or passing aggressively) costs the offense points. This is undoubtedly correct: on average, passes garner more yards per play than runs, and an equilibrium playcalling strategy will seek to maximize the returns for each play (whether in terms of yards, first downs, or points).
  
• The second assumption appears to be that maximizing yards and points is the optimal strategy for an offense. Hence, the lack of interceptions means that the team is leaving points on the board, thus costing it games. This is the assumption I want to address in slightly more detail.

Is it always "optimal" to set your strategy to maximize points scored?

In the NFL -- which is what Brian focuses on -- this is likely true and the assumption holds. NFL teams are almost all competitive with each other, and even the worst teams can beat the best in a given game. So any reduction in expected points is likely to hurt a team's chances of winning because they need to maximize that out to get wins.

But is that true in college? Or in high school? 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. (I leave aside BCS calculation questions, which very well might make it worth it to increase the risk of loss to get a bigger chance of a blowout victory.)

The upshot then is that, for the storied programs with large talent advantages, there is seemingly more downside than upside to being very aggressive, either on offense or defense. While it might increase the risk of blowing the opponent out, it also increases the risk of stumbling.

The flipside: the underdog

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?

Get technical

Let's take a quick step back and talk about what is happening from a probability standpoint. What does a more aggressive (and thus more risky) strategy do to our expected outcomes? Hopefully everyone is familiar with the bell-curve, which is a graphic way of depicting the range of possible outcomes based on the probability of their occurrence. The normal distribution is the most common, and it assumes that outcomes on the left and right are as likely as the average outcome. Here, let's assume this is the curve for an offense that can be expected to score around 28 points a game.

Now, let's say they decide to ramp it up. They want to score more points, but this is a riskier strategy, and therefore the range of outcomes will vary more wildly. Below is the new curve, which has moved to the right (to reflect the greater expected points) but is also flatter -- a measure of kurtosis -- which makes the "tails," or ends of the curve "fatter."

(Remember, the height of the curve is the probability of the event happening. Although with the moved curve the whole offense now is expected to score more points, it is now less bunched around the middle because the strategy employed is riskier and hence has more variance or variety.)

What does this tell us? It really just reaffirms what we'd already guess (and assumes that we know what strategies are both riskier and more rewarding, which is an assumption but generally involves passing more). Our offense now: (a) averages more points, (b) has an increased chance of scoring in the forties and blowing out the opponent than before (represented by the shaded green area), but (c) has an increased chance of blowing it and scoring fewer points than our more conservative -- and less variant -- strategy from before. Hence, you might maximize your points but you might actually increase your chance of losing in the process.

Now, remember I'm making assumptions about the nature of the curve. There's also a probability phenomenon known as skewness, which might mean that the improved strategy actually will rarely ever incur a bad game and all the variance will be good.

But the reason I took this mathematical approach to this is that this is really the lesson of the financial crisis as applied to these Wall Street gurus, imported to football: you can "improve" your strategy, you can increase your expected gain, you can increase your chance of blowout wins, but in the process you might be sowing the seeds of your own unlikely, but catastrophic demise. Sort of Black Swans for football.

Spurrier and keeping it close

So in the NFL, where teams are almost all competitive (save, maybe the Detroit Lions), it's likely the best strategy to simply maximize expected points and to go from there. But in other levels, with talent disparities of all sorts, it is trickier, as we have seen.

In the 1990s, Steve Spurrier's Florida Gators were undoubtedly some of the most talented teams of the decade. They were also some of the most aggressive. As a result, they absolutely destroyed some teams. Of course there were the seventy-point blowouts of Kentucky, but what about when they scored more than sixty against Phil Fulmer's Tennessee Volunteers? Yet, Spurrier never once went undefeated with the Gators: his teams always seemed to drop a game or two that maybe they shouldn't have. And those losses almost always had the same profile -- too many interceptions, couldn't run the ball at all, and too many big plays given up on defense. I can't believe I'm inclined to say this, but maybe Spurrier should have been more conservative? He might not have won as many games by sixty or seventy, but maybe they would have gone undefeated and won more than one title?

On the flipside, almost every week of the season I see teams go to Southern Cal, LSU, or Ohio State, and pretty much give up all hope of winning in the name of "keeping it close and winning it in the fourth quarter." As outlined above, this might be the worst strategy against such teams. They have little chance of winning on the merits, so what they need to do is flatten the tails and increase the chance for a shocker: take risks, and hope their coin flips go in their favor. Maybe they won't. Maybe they get blown out. But not taking those chances is a surefire way to set their low chance of winning in stone.

Yet, much like with David Romer's paper where he observed that NFL coaches probably don't go for it on fourth down enough, there are external and likely irrelevant reasons that deter coaches from employing a true "risky-underdog" strategy: the risk that the coach will get fired. I am advocating here that underdogs go for it and increase the calculated risk they take on. (Keep in mind that you can go overboard on this. Chucking the ball forty yards downfield every play, while risky, would not increase your scoring or even chance of winning because you'd become predictible and downright silly. It's about calculated risk.)

But there are real costs -- at least for the coach -- of getting blown out. And make no mistake, the bargain for a greater chance of winning includes the greater chance of getting thrashed. Maybe this should be irrelevant -- a win is a win and a loss is a loss. But a blowout loss has collateral effects, even if they are purely psychological and emotional. You can lose recruits, you can lose donations, and you can lose your job. Look at Mike Shanahan with the Broncos. He was on the hotseat, but he lost his job primarily because Denver got blown out in their final game. I don't necessarily think that was because his team took on increased risk, but people do not tolerate ugly defeats, rational or not.

Similarly, there might be real gains for an underdog to just "keep it close" with a big boy without ever having a real chance of winning. People discount moral victories, but if such and such team can "keep it close" with USC, then they get all kinds of accolades and possibly even confidence going into the following weeks. But if they employed the risky-underdog strategy, then they might gain a slight marginal increase for a victory, with a steeper increase in the chance of getting buzzsawed right off the field (remember skewness).

So, from the perspective of being purely focused on winning football games, I think the implications of the risky/conservative strategy dynamic in the context of teams with wide talent disparities has some pretty dramatic implications. But in the real world, there's lots of other factors, including the felt need by the coach to protect his own skin. Yet, he might be costing his team a chance at victory.

The Lions' new coach Jim Schwartz: football pragmatist?

The Detroit Lions hired former Tennessee Titans defensive coordinator Jim Schwartz to be their new head coach. A daunting gig, to be sure: achieving success in Detroit might be beyond any coach's realistic hopes. But, insofar as they might have a shot, this is an excellent hire.

There are the obvious and ESPN-ready reasons to hire Schwartz: (a) that he has been defensive coordinator with the Titans under Jeff Fisher, running one of the league's best units there, and (b) that he has worked with Bill Belichick, which come NFL hiring time is like holding a golden ticket.

But there's a better reason, and it is one that should give Lions fans at least a glimmer of legitimate hope: the guy has a brain. Yes, he has a degree from Georgetown, which puts him ahead of most NFL coaches, but more importantly he has proven that he has an inquisitive, analytical mind, which is all-too-often in short-supply in the NFL.

This past fall, the New York Times ran an article on Schwartz saying he was like the NFL's version of Billy Beane, the empirically minded general manager of the Oakland A's made famous (and in some circles, infamous) in Michael Lewis' great book, Moneyball. Beane, as you may remember, helped revolutionize baseball by favoring detailed statistical analysis to aid him in determining his draft picks, batting order, and pitchers. It famously led him to pick up and use guys no one else had any interest in or had even heard of.

(A running theme in Moneyball was Beane's repeated failed attempts to trade for some then-unknown minor league player for the Red Sox that he nicknamed the "Greek God of Walks" for the player's ability to repeatedly get walked more than just about anybody, while also driving up the pitch-count and consistently getting on base. He even had trouble getting him because the then Red Sox's front-office couldn't even remember that he was on their roster. That player? 2008 All-Star Kevin Youkilis.)

The other thing Beane did was win against the odds. The A's repeatedly made the playoffs despite having a payroll a mere fraction not only of juggernauts like the Yankees, but most other teams in their division and around the league. Lewis' answer to the question "How was Beane doing it?" was that Beane was outsmarting his opponents. It was not necessarily that he was smarter, but his approach was: the A's were willing to do away with "common wisdom" and even the kind of impressions most scouts give regarding a prospect: "Wow, look at the guns on him. He just looks like a baseball player." As a result, the A's routinely beat teams with payrolls twice theirs. And, now, the so-called sabermetric revolution has almost entirely swept through baseball. Even teams that don't rely on it as heavily as the A's still have some guys with laptops and Ivy League degrees slipping around their front offices these days. (The Red Sox too are now somewhat considered a Moneyball based organization, though one with a rather large payroll.)

But football is a different animal. On the one hand, football coaches and aficionados were engaged with advanced statistics long before baseball. Virgil Carter, former quarterback under Bill Walsh, actually computed the "expected value" of field position back in the 1960s. (He actually did it while enrolled part time in Northwestern's MBA program while also a player with the Chicago Bears.) Yet, as I have previously written, football is the most complex sport of all. You cannot model the game as a series of one-on-one battles as you can with baseball; indeed, the goal for both offense and defense is often to get two on one or three on two. But that has led far too many coaches, fans, and commentators -- maybe it is the machismo, maybe it is just the complexity -- to denounce and deride statistics out of hand, without basis.

Enter Schwartz. As the New York Times reported:

Schwartz, now the defensive coordinator for the Tennessee Titans, had an economics degree from Georgetown University, an abiding fascination with statistics and a preference for watching game film over television. That made him a kindred spirit with his first N.F.L. boss, Bill Belichick. But when Schwartz told Belichick his findings from an early N.F.L. research project almost 15 years ago, Belichick said he did not believe him.

“Fumbles are a random occurrence,” Schwartz said he told Belichick. “Being able to get interceptions or not throw interceptions has a high correlation with good teams. But over the course of a year, good teams don’t fumble any more or less than bad teams. Bill didn’t agree. He said, ‘No, good teams don’t fumble the ball.’ But actually, they fumble just as often as bad teams.”

With the Titans, Schwartz once encouraged the former offensive coordinator Norm Chow to run more on third-and-short because his research indicated that it was more effective than passing.

Unorthodox thinking like that has earned Schwartz, 42, a reputation as one of the N.F.L.’s leading practitioners of statistical analysis — “Moneyball” for the shoulder-pad set — using them in coaching the defense for the league’s only unbeaten team . . . . Belichick regards Schwartz as one of the smartest coaches he has been around.

As the Times points out, however, in the NFL, being known for your analytical skills is, strangely enough, not always a plus:

But being known as a “stats guy” is not necessarily a compliment, because statistics do not hold the romantic place in football that they do in baseball. Although every coach uses plenty of data — the Titans’ Jeff Fisher tracks how long his team takes to break the huddle — football is unlikely to bestow statistics-driven celebrity on anyone the way the baseball book “Moneyball” did on Billy Beane, the general manager of the Oakland Athletics.

(Of course, as Salon's King Kaufman points out in his article "Ignorance is not a sportswriting skill," baseball isn't always that enlightened either.)

In a previous article I discussed the anti-stats view, which I said can be described as nothing but neanderthal in nature. But sometimes it is just inertia and an unwillingness to be beholden to anything that doesn't seem "up front" or real; to these people, they feel like they have the experience and perception to "just know" -- Hey, it's common sense. But as Lord Keynes warned, what many call "common sense" is often just some past blowhard's own shoddy analysis or comment preserved and repeated over time, without examination.

"Practical men, who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist. " - John Maynard Keynes

Think of the myriad examples, like "balance," play-calling, spiking the ball, or going for it on fourth-down. This is why Schwartz offers some hope. He may not succeed in Detroit, but, to me, he appears more likely to do so than anyone else. He will no doubt attempt to go in there and put together the best possible plan, not just a collection of truisms and cliches: Orwell's advice about writing can be applied to putting together a football team and organization; he discusses reading a writer who, in his opening paragraph, appears to have something important to say. But the rest of the writer's piece collapses because whatever fresh thought he began with was quickly replaced with a series of tired cliches and overused metaphors. The final product was thus imprecise, impersonal, and banal.

The analogy works for coaches. You might be talented and have a vision, but if all you can say is that we're going to "outwork our opponents," "we're going to have balance," "we will establish the run," or "we will be more disciplined than our opponents," then you're in trouble. All those are worthy goals (mostly), but they aren't always particularly constructive. Indeed, although in high school, maybe you can do these things because you might know the game more and be better organized, the NFL is a different animal. In the NFL, if a guy doesn't work he's cut; if a coach doesn't win he's fired. Rod Marinelli's Lions rarely lacked effort. They simply lacked wins.

In gleaning other hints about Schwartz's mindset and approach, I saw his name arise in the context of another Michael Lewis piece, this one about Texas Tech's Mike Leach:

At least one N.F.L. defensive coordinator, Jim Schwartz of the Tennessee Titans, had stumbled upon Texas Tech accidentally and said, Oh, my. The surprise runner-up in the search earlier this year for a new San Francisco 49ers head coach, Schwartz had scrambled to answer a question: if he got the 49ers job, whom should he hire? He was just in his mid-30's, and his football career stopped at Georgetown (where he graduated with honors in economics), so he really hadn't thought about this before.

The 49ers had not bothered to interview college coaches for the head-coaching job in part because its front-office analysis found that most of the college coaches hired in the past 20 years to run N.F.L. teams had failed. But in Schwartz's view, college coaches tended to fail in the N.F.L. mainly because the pros hired the famous coaches from the old-money schools, on the premise that those who won the most games were the best coaches. But was this smart? Notre Dame might have a good football team, but how much of its success came from the desire of every Catholic in the country to play for Notre Dame?

Looking for fresh coaching talent, Schwartz analyzed the offensive and defensive statistics of what he called the "midlevel schools" in search of any that had enjoyed success out of proportion to their stature. On offense, Texas Tech's numbers leapt out as positively freakish: a midlevel school, playing against the toughest football schools in the country, with the nation's highest scoring offense. Mike Leach had become the Texas Tech head coach before the 2000 season, and from that moment its quarterbacks were transformed into superstars. In Leach's first three seasons, he played a quarterback, Kliff Kingsbury, who wound up passing for more yards than all but three quarterbacks in the history of major college football. When Kingsbury graduated (he is now with the New York Jets), he was replaced by a fifth-year senior named B.J. Symons, who threw 52 touchdown passes and set a single-season college record for passing yards (5,833). The next year, Symons graduated and was succeeded by another senior - like Symons, a fifth-year senior, meaning he had sat out a season. The new quarterback, who had seldom played at Tech before then, was Sonny Cumbie, and Cumbie's 4,742 passing yards in 2004 was the sixth-best year in N.C.A.A. history.

... Whoever played quarterback for the Texas Tech Red Raiders was sure to create so much offense that he couldn't be ignored.

Schwartz had an N.F.L. coach's perspective on talent, and from his point of view, the players Leach was using to rack up points and yards were no talent at all. None of them had been identified by N.F.L. scouts or even college recruiters as first-rate material. . . . Either the market for quarterbacks was screwy - that is, the schools with the recruiting edge, and N.F.L. scouts, were missing big talent - or (much more likely, in Schwartz's view) Leach was finding new and better ways to extract value from his players. "They weren't scoring all these touchdowns because they had the best players," Schwartz told me recently. "They were doing it because they were smarter. Leach had found a way to make it work."

. . . This offense was, in effect, an argument for changing the geometry of the game. Schwartz didn't know if Leach's system would work in the N.F.L., where they had bigger staffs, better players and a lot more time to prepare for whatever confusion the offense cooked up. On the other hand, he wasn't sure it wouldn't.

The takeaway is not that Schwartz will be hiring Mike Leach as offensive coordinator. (In fact, he has hired Scott Linehan, which -- despite some outcry -- is generally a good choice. Many coaches, including Urban Meyer, still think Linehan is a bright, bright guy, and as a coordinator his offenses always put up points.) But the fact that he'd even consider back then should be heartening: it means Schwartz is looking for results backed up by the numbers, appearances and cliches be damned. Leach's offense looks screwy: the linemen are linemen split out wide, four receivers line-up on nearly every play, yet it gets results, and results with inferior talent at that. Beane was derided and mocked when he'd pick up a pitcher with a funky sidearm delivery where the ball was released only a few inches from the ground -- a release no scout could ever condone. Yet the derision would fade when they realized that few hitters could hit that crazy delivery, at least for a time. Beane was shopping for discounts.

Schwartz, as head coach of a struggling team, no doubt will be looking at the bottom line, and he too will have to shop for discounts. Traditional or different, he wants results. He appears to be a pragmatist. In that job, he'll have to be.

Winning football games on Mondays through Saturdays

One part of the Times piece on Schwartz particularly struck me:



"Sometimes, [being statistics-driven is] an easy thing for people in the media to use against you,” Schwartz said. “ ‘Oh, yeah, he can’t adjust; he’s just a stats guy. They don’t really understand the game.’ That’s why sometimes, the whole stats thing is a dirty word.

“If you ask me, Would you rather have a great fly-by-the-seat-of-your-pants guy on Sunday, a guy who can dial up plays and he’d be the best in league, or a guy who is best in the league from Monday to Saturday preparing, I respect the guy who prepares. You’re not always going to be rolling 7, 7, 7 and be hot every week. But if you prepare well during the week, you’ll be consistent from week to week.”

This exact sentiment formed the gravamen of Walsh's west coast offense. Quotes from Walsh:

I have been afforded the experience that allowed us to conceive an offense, a defense, and a system of football that is basically a matter of rehearsing what we do prior to the game. . . .

What we have finally done is rehearse the opening part of the game, almost the entire first half, by planning the game before it even starts. . . .

Now why would you do such a thing? I know this, your ability to think concisely, your ability to make good judgments is much easier on Thursday night than during the heat of the game. So we prefer to make our decisions related to the game almost clinically, before the game is ever played. We've scouted our opponent, we have looked at films, we know our opponent well. . . . To be honest, [in the heat of the game] you are in a state of stress, sometimes you are in a state of desperation and you are asked to make very calculated decisions. It is rarely done in warfare and certainly not in football; so your decisions made during the week are the ones that make sense. In the final analysis, after a lot of time and thought and a lot of planning, and some practice, I will isolate myself prior to the game and put together the first 25 plays for the game. They are related to certain things.

...But whatever you have, if you have planned it and fail, you can't blame yourself for losing your poise. You can't blame yourself for panicking if you have planned these things and they fail. You may really search yourself for the kinds of decisions you made on Thursday night, but you certainly can't make the decision during the game. As a coach, one of the things you are always fighting during the game is the stress factor, breaking your will. The stress factor will affect your thinking. I have been in situations where I could not even begin to think what to do. From that point on, I knew that I had better rehearse everything.

And, too, you can add in analysis that there is no time to do during the game. You analyze the probabilities, you remove the irrational choices like going for certain field goals on certain fourth and shorts.

A few years ago I wrote about the idea that gameplanning and weekday work is advantageous both because you can be meticulous but also because you gain important self-restraint capabilities. I drew on a lecture given by Nobel Laureate in Economics, Thomas Schelling (yes I know, it is not exactly the same as a Nobel Prize as established by Alfred Nobel). To illustrate, Schelling used a story about Captain Ahab; you can read it here.

But a similar story with the self-constraints that gameplanning puts on the coach (as compared with the seat-of-the-pants approach favored by so many) is the story of Odysseus (or Ulysesses) and the Sirens: when Odysseus's boat approached the sirens -- whose sweet singing had lured many sailors to their deaths -- he first put wax in his sailors' ears to block out the music, then had his crew tie him to the mast, thus making him powerless. In the moment, when his boat went by the sirens, he was irrational, and wanted nothing more than to steer the boat to him. But his rational self had already judged this, decided against it, and denied his later, weaker self the same choice.

Although not nearly so dramatic, gameplanning and the script often works the same way (though with slightly more flexibility than one has tied to the mast). Hopefully, for Lions fans, it is this methodical, analytical approach that Jim Schwartz offers.

Moreover, this story highlights the interdependent role that head and assistant coaches must have: they must take turns as Odyssesus and the crew, tying each other up, making the plans in advance, and even, sometimes, in the heat of the moment, entirely ignored, as Odysseus was.

As noted above, gameplans should nevertheless be contingency based; they must be flexible enough to respond to what an opponent does. But of course gameplans are based on this: those who reject scripting because they are too wooden just really don't understand what scripting is. But, a well crafted gameplan can still handle these scenarios and be created in a detached setting.

Moreover, the other important factor is that some information simply cannot be processed merely in-game; answers will only be yielded by careful study through the week. You simply don't have time to crunch all the numbers, assemble data on all the fronts and schemes, nor run down the variety of contingent scenarios. But if you do that, and then combine it with what you learn during a game, you have a chance to win. And, through your study, you might see options -- like maybe what Mike Leach does, the wildcat, or some other forward thinker -- that traditional football intertia blinds you to. As I wrote a few weeks back:

[F]rom Peter Bernstein's book, Against the Gods: The Remarkable Story of Risk.

The story that I have to tell is marked all the way through by a persistent tension between those who assert that the best decisions are based on quantification and numbers, determined by the patterns of the past, and those who base their decisions on more subjective degrees of belief about the uncertain future. This is a controversy that has never been resolved.

And it will remain controversial . . . because the future will be paved by numbers and judgment, marching, somewhat awkwardly, hand in hand.

Good luck to Jim Schwartz.

Probability, Pragmatism, and Football

I recommend Joe Nocera's recent New York Times Magazine piece on the failures of Wall Street's risk models and overall risk management. It's a worthwhile read of its own right. But I see a football angle.

I've long been a proponent of more rigorous analysis of football, and in particular its associated probabilities. But -- and this is why I am posting this article here -- football is simply so complex that there are limits to our current understanding. With baseball and the "sabermetric" movement, there are attainable gains: the game can be modeled largely as batter versus pitcher, and, within this dynamic, there is only so much change and a finite number of extra variables to control.

With football, however, you have twenty-two players, a variety of formations, receivers, combination blocks, movements, and areas to defend. The game itself follows a dizzying path to completion, with score changes, possessions, downs, field positions, yards to first down, and so on. It's not impossible to model, and there is much we can and have learned, but with football -- as with Wall Street -- what appears certain in your models and statistics may not tell the full story.

"Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital." - Aaron Levenstein

And, I am sorry to say, that when I read this article I did not think of the excellent work being done that is very useful to coaches and real practitioners, but instead of one group in particular: Football Outsiders. Now, I don't want to be too harsh. They do some great, interesting work, they have illuminated a number of subjects, and, if nothing else, the sheer breadth of what they have addressed will pave the way for more sophisticated analysis. And maybe criticism is unfair, as much of their current stuff is not focused on real football or what might bring real knowledge to the game, but instead on aiding the fantasy football player.

This is understandable, since fantasy football provides ready benchmarks and fantasy footballers are a much broader and more accessible audience than are football coaches. But if we want to be honest about what we're doing, then, to me, we ought to be honest that many of these statistics are for fans and do not actually help anyone (coaches, players, GMs) make decisions.

Football Outsiders' big stat is called DVOA, or Defense-adjusted Value Over Average. It's a nice stat, and certainly it is an improvement over just trying to compare Jimmy and Joe based on their total yards or yards per carry or whatever else. But it's a bit of a fan's statistic, and, further, there's a tendency to adjust it and use it in a way that reinforces what we already know. If DVOA doesn't tell us that Tom Brady and Peyton Manning are the best quarterbacks, then it gets revised until it does, or is rejected until a different measure tells us this unassailable truth. Same with teams: DVOA helpfully tells us that the 2007 Patriots, 1999 Rams, and 1996 Packers were all very good. And, all too often, as Brian of Advanced NFL stats has observed, Football Outsiders far too often "use[s] statistics like a drunkard uses a light post, for support rather than illumination." (Quoting Mark Twain). (One exception: Mike Tanier, though at times his analysis is a bit shaky, is clearly coming into his own and the fact that he has access to NFL film and his practice and diligence is starting to show through.)

Don't get me wrong, I adore statistics and, even more than stats, I think probabilities are the key to understanding almost everything about the world around us. I don't like dealing in absolutes. (Though some seem to vigorously disagree with me when I say that.) If I have to choose between what can only be referred to as the neaderthal view:

"We don't worry about numbers here. Statistics are for losers. I'm not a stat guy. I'm not interested in them, because you can do anything you want with numbers, you can manipulate them, and work around with them. Look at all the financial [problems] we're having in Wall Street right now. That's all those guys lying and playing with numbers. And now all of us are suffering. So I don't believe in numbers, because any crook can play with numbers....It angers me. You know? That's the whole thing, people play with numbers."

- Washington Redskins defensive coordinator Greg Blache

And what I consider the modern view:

"They say statistics are for losers, but losers are usually the ones thinking that. Statistics are great. Our whole game plan is based off statistics. Our management of the game is based off statistics. Our recruiting is based off statistics. Everything we do is analyzed. Is that the bottom line? No. You can't analyze the heart of Tim Tebow."

- Urban Meyer

Then clearly put me in the modern camp. So I really don't mean to denigrate the work of Football Outsiders or anyone else doing progressive work -- we certainly need more of it. Coach Blanche brings up the financial crisis, but it's not like -- even there, where the problems have been widespread -- that numbers and stats can just be dismissed out of hand. They are still useful, but you embrace the limitations: even if your statistics are imperfect, they are often better than nothing, and you must simply recognize and be aware of where the pratfalls are in how they might aid or hinder your decisionmaking. This was lost on the finance world recently, but it applies equally to football decisionmaking.

And, because I also consider myself something of a pragmatist, I nevertheless ask of those doing this work is the same question I would ask of any other idea (because the value of football statistics is simply another permutation of an idea about the value of statistics):

Pragmatism asks its usual question. "Grant an idea or belief to be true," it says, "what concrete difference will its being true make in anyone's actual life? How will the truth be realized? What experiences will be different from those which would obtain if the belief were false? What, in short, is the truth's cash-value in experiential terms?"

- William James, Pragmatism (1907).

So to me, there's a grand opportunity for these statisticians to change the way decisions are made and overall just improve the game -- to make a "concrete difference." Some statisticians have done this, most notably David Romer. His work is so far thorough, practical, and challenging.

I'm not a true statistician or econometrician. And, as I said above, one of the difficulties with doing real, relevant football statistics is that the game is quite complex, and one needs to understand it to model it (and those who understand usually can't model, and those who can model usually don't understand). One of my goals with this site is to try to help bridge this gap.

Nocera's piece begins with this quote from Peter Bernstein's book, Against the Gods: The Remarkable Story of Risk.

The story that I have to tell is marked all the way through by a persistent tension between those who assert that the best decisions are based on quantification and numbers, determined by the patterns of the past, and those who base their decisions on more subjective degrees of belief about the uncertain future. This is a controversy that has never been resolved.

And it will remain controversial -- in finance as well as football -- because the future will be paved by numbers and judgment, marching, somewhat awkwardly, hand in hand.

Colts-Chargers

Football -- and particularly the NFL -- is a percentages game. The storylines coming out of this game will be manifold, but to me it was quite simple.

• On the Colts side of the equation, they had the advantage in turnovers -- zero to the Chargers' two. That was huge for the Colts, and they probably would not have been in the game without that advantage.
  
  
• On the Chargers side, the Colts spent the entire game trying to start drives from what seemed like their own half-yard line. And we know that, when you have the ball far on your own end of the field -- even on first down -- your expected point value from the drive is negative: namely, the other team is still more likely to score than you are. So that was quite bad for the Colts.
  
  
• But those two effects sort of canceled each other out in this game. The final tiebreaking probability push was the coin flip, which in the context of overtime is a fifty-fifty gamble where the winner gets a +10% increase in their chance of winning in an otherwise evenly matched game: the team that wins the coin flip wins the game roughly 60% of the time. (And the situation we had in this game, where one team wins the coin-flip and wins it without the other teams' offense taking the field, happens about 30% of the time.)
  

For the Chargers, two out of three ain't bad.