Grinding it out: Good or bad?

I watch a lot of football with a Steelers fan. Invariably, it comes up while watching the Steelers -- either from him or by the announcers -- that, with a good running game and sturdy defense, the Steelers often attempt to "shorten the game" by "keeping the other team's offense off the field." The Steelers aren't the only team that does this, but it seems to come up a lot with them or when watching any team that's playing against Peyton Manning or Drew Brees or another elite quarterback (or, less frequently, against an elite running back or wide receiver).

This had always struck me as odd, and I think the feeling goes back to the first Super Bowl I really watched, Super Bowl XXV between the Giants and Bills. You might recall that the Giants controlled the ball for 40 of the 60 minutes of that game, including two long drives at the end of the first half and beginning of the second that, the analysts noted, kept the Bills' offense on the sideline for over an hour of real time. With Jim Kelly and Andre Reed and Thurman Thomas lined up on the other sideline, it seemed like a good strategy, right?

But then I got to thinking...don't football teams have, roughly, the same number of possessions each? Barring some shenanigans around the end of the first half or at the start of overtime, when you're done with your drive, the other team gets the ball. So what's the point of having a drive that's three minutes long versus one that's 10 minutes long? If, over a 60-minute game, each drive takes three minutes, that's 20 drives -- 10 for each team. If each drive takes five minutes, that's 12 drives -- 6 for each team. How does that actually help anyone? Yes, the Giants kept the Bills offense on the sideline in Super Bowl XXV, but, by the same token, they reduced the number of opportunities their offense had to score. What's the strategy there?

(I'll note here that I've never bought too heavily into the notion of "tiring out the defense" on long drives. Unless I'm mistaken, offensive players are pushing, shoving, and sweating on a drive, too. A 10-minute drive should have about the same effect on offensive players that it does on defensive players, shouldn't it? This article focuses solely on the strategy aspect of long drives.)

Then it hit me. To win, a team must score more on its possessions than the other team does on its (discounting things like return TDs). The "ground it out" (GIO) team generally has a worse offense than its opponent, usually because the opponent has a superstar QB and the other team doesn't. Take an individual drive by each offense, and you'd expect the QB-driven (QBD) team to do "better" (higher chance of TD or FG). Over a season's worth of drives, the QBD team will likely score more points than the GIO team, and the GIO's coach knows it.

But the GIT's coach realizes that, in a smaller sample size, his team can outperform the QBD team!

Here's a simple example. For those who've never played Dungeons & Dragons (yes, I am a complete geek), it uses dice of all kinds of shapes and potential values, including eight-sided dice (d8), which has values of, surprisingly, one through eight on its sides. Suppose I take a regular six-sided die (d6) and you take a d8. In any "who can roll higher" competition between us you clearly have the advantage. Even if you graciously allow me to win all ties, my chances of "winning" any individual roll is 43.75%.

Now, suppose we're going to put money on this. Clearly, this means I'm not too bright, but then suppose a third party gives us two odd numbers. These are the number of rolls we are to each make, and the person with the most "wins" gets $1,000. The catch is: I get to choose how many rolls we'll make, based on the numbers that third person gave us.

And I should always choose the lower number of rolls, because with fewer rolls, I have a better chance of getting lucky and beating you out. With just one roll, as mentioned, I win 43.75% of the time. With a best 2-out-of-3 contest, I win 32.30% of the time. 3-of-5 is 26.50%. 4-of-7 is 22.82%. And so on.

Now, back to football. If GIO's coach believes his offense is like a d6 and his opponent's is like a d8, the best strategy for him is to try and minimize the number of drives each team gets. If he could cut the game to one drive per team, he should. That's clearly impossible (and I'll admit I'm not taking defenses into account at all), but, failing that, he should try to limit the total number of drives in the game, by grinding out clock time with running plays and short passes.

Maybe.

I read somewhere that the typical NFL game has about 10 drives per team. I'm too lazy to do any real research on that, but it seems about right. Going back to my dice contest:

In a best 6-of-11 contest, the d6 beats the d8 18.24% of the time.
In a best 5-of-9 contest, the d6 beats the d8 20.22% of the time
In a best 4-of-7 contest, the d6 beats the d8 22.82% of the time.

If we assume that a typical game has around 9-11 drives and that a GIO coach can eliminate two drives with his clock-eating strategy, then he would appear to increase his winning percentage by only about 2%. This makes sense; as the number of trials increases, the difference in winning percentage by adding or subtracting a couple trials goes down. There's not much difference between a best 50-of-99 contest and a best 51-of-101 contest.

Now, a d8's average roll is 4.5; a d6 averages 3.5. 4.5/3.5 = 1.29, so the d8 is about 29% "better" than the d6. Thus, if QBD's offense is 29% better than GIO's, we might expect the percentages quoted above to be true. Considering that GIO typically has a better defense than QBD, thus reducing QBD's overall effectiveness on offense (sorry, they don't make seven-sided dice), you might even say that the differences are even smaller. For one example, Pittsburgh, the quintessential GIO team, scored 347 points in 2008. San Diego, which led the AFC in scoring, had 439. 439/347 = 1.27, which is close to the 29% difference between a d8 and a d6.

So, assuming that my relatively simplistic assumptions are true, the GIO team does increase its chances of winning using its GIO strategy, but only by a small amount. It would seem to me, then, that teams should cater more to their strengths than to a formula. In the case of the Steelers, with a questionable running game heading into next year, a strong-armed QB (Ben Roethlisberger), and three legitimate receiving threats (Hines Ward, Santonio Holmes, and Heath Miller), maybe they should air it out a bit more. That is, unless Jerome Bettis (or maybe Franco Harris) can come back from retirement.