Thursday
Oct032013

Hooray for Hollyworld

Every Monday, cinephiles pore over the weekend box office results, categorizing the newcomers even before theaters can empty their Dumpster-loads of popcorn. People tend to view that first week as the harbinger of a film’s fate. Some even combine those dollar amounts with ratings aggregated from multiple sources to construct elaborate indexes that tell moviegoers how foolish they were to give their money to Adam Sandler.

But, like every other industry on the planet, it’s hardly that simple anymore. The U.S. market is a shrinking piece of the puzzle as studios globalize their offerings, which means a movie’s true impact can’t be determined until the shockwaves die down in the United Kingdom, Russia, China and other locations with a growing appetite for American-made fare.

In short, the big screen keeps getting bigger.

Decade to decade

Let’s start by going back to 1993. Bill Clinton was in the White House, Snoop Lion was still Snoop Doggy Dogg, and Jurassic Park was the highest grossing movie in the world with a total of $978.2 million. One other topped $400 million (Mrs. Doubtfire), and three of the top 10 earners bested $200 million overseas, with only T-Rex and friends higher than $300 million.

Fast-forward 10 years to 2003. The Lord of the Rings: Return of the King grossed $1.12 billion, nine others finished north of $400 million, and eight of the top 10 grabbed at least $200 million overseas, with five besting the $300 million mark.

Then we have this year. Iron Man 3 is tops with $1.21 billion, 10 others have collected at least $400 million, and all of the top 13 have earned $200 million or more overseas, with eight above $300 million. And those are just year-to-date numbers, some of which will grow in the three months remaining in 2013—unless you’re After Earth, The Lone Ranger or R.I.P.D.

Fudging the numbers

It’s easy to ridicule flops like those three. And fun. But if you clicked over to the 2013 worldwide grosses in the previous paragraph (here’s another chance), you would see they were well into the $200 million range. Except R.I.P.D., which earned precisely what you would expect a trash fire like that to earn. Those other two, however, grossed more than their reported budgets—in the case of After Earth, more than $110 million more. So how can they be labeled flops and terribly written and really bad ideas that never should have escaped the binge-drinking session from whence they came?

It turns out the only thing movie studios spin better than their latest nine-figure M. Night Shyamalan mistake is numbers. For starters, reported budgets are reported production budgets and don’t include marketing. The Lone Ranger, for example, sported a $215 million production budget, but Disney forked over another $175 million in marketing and advertising, most of which went toward convincing people Johnny Depp is Native American.

Then there’s the matter of dividing the spoils. Obviously, movies don’t show themselves, so studios only receive a percentage of ticket sales. Domestically, it’s in the neighborhood of 50-55% by the time a movie wraps up its cinematic run. For the foreign box office, it’s even less.

Secret to Success

When you get done wading through the creative accounting and variable revenue streams, the general rule is that a movie needs to make about twice its reported production budget to break even. After Earth fell just short, The Lone Ranger didn’t come close, and R.I.P.D. didn’t earn enough to cover Jeff Bridges’ facial-hair stylist:

Then we have the big winners, many of which not-so-coincidentally share the trait of being highly global. Pacific Rim (overseas earnings: $305.8 million) took place in various locations around the world and staged its climactic scene in Hong Kong. Fast & Furious 6 ($550 million) also did a fair amount of globe-trotting, with scenes in Hong Kong, Russia, London and Spain. Iron Man 3 ($805.7 million) even went so far as to add a handful of China-centric scenes specifically for that market’s version.

For all three of those movies, at least 66% of their overall take came from the foreign box office. Compare that with Man of Steel, which featured a U.S. icon as its central character and logged a relatively paltry overseas share of 56.1%. With results like that, Superman may stand for truth, justice and the American way, but don’t count on him bragging about that last one too much in the sequel.

Thursday
Sep262013

Standard Deviation and Aggressive Strategies: Why Bad Teams Should Play Risky (But Don’t)

It was arguably the biggest upset in the history of college football. The fifth-ranked Michigan Wolverines hosted the relatively unknown Appalachian State Mountaineers in both teams’ first game of the 2007 season. The Wolverines were heavily favored, so much so that Vegas didn’t even offer a betting line on the game. Of the 100,000+ people in attendance, nobody expected the Mountaineers to win except their parents—and they would have been forgiven for having their doubts. Then, a couple failed two-point conversions and a blocked kick later, the Mountaineers stunned Michigan, 34-32.

Underdogs need to have a lot of breaks go their way to beat a favorite: lucky bounces, opponent’s mistakes, unlikely plays and questionable officiating, to name a few. Appalachian State got plenty of these breaks en route to their victory. Almost every game has some of these occurrences, though they are few and far between. But, with the strategies they emply, teams can also create situations that lead to more of these occurrences. In particular, playing more aggressively and taking more chances makes the game much less predictable, giving rise to opportunities for lucky breaks to change the game.

Think about a great team (Team A) and a not-so-great team (Team B) that are set to play one another. Team A scores an average of 35 points per game and Team B an average of only 20 points. Though we know Team A is better, this information alone won’t tell us how likely it is each will win.

Consider two different scenarios:

1. Team A scores exactly 35 points in every single one of its games, and Team B scores exactly 20 points in every single one of its games. Team A will beat Team B every time they play (the probability of victory for Team A is 100%).

2. Team A scores exactly 35 points in every single one of its games, and Team B scores three points in half of its games and 37 points in the other half of its games. Team A will blow out Team B in half of the games they play but lose by two points in the other half (the probability of victory for Team A is 50%).

It is clearly in Team B’s best interest to play a game that reflects the second scenario, giving it a 50% chance of winning instead of no chance. Obviously, this is an oversimplified example with only two scenarios. But if you extend it to many scenarios, you can see how the distribution of possible points scored for each team can affect their probabilities of winning.

Figure 1 shows the first scenario, with the assumptions regarding the number of points scored relaxed a bit. This is the scenario in which both teams play conservatively—neither is trying to increase the variability in the number of points they score. You see Team A is still more likely to score 35 points than some other total, but there is also a chance it scores slightly more or less than 35 points. The same goes for Team B; it is more likely to score 20 points than any other total, but it also could score slightly more or less. In this scenario, Team B has an outside chance of winning if it hits the far right end of its curve on the same day Team A hits the far left end of its curve. But Team A wins the vast majority of the games—typically by 10 to 20 points.

 

Figure 1

Figure 2 shows a scenario in which Team B plays aggressively—for example, going for it on fourth down instead of kicking the field goal, trying onside kicks or lunging for the interception instead of making a sure tackle. The variability in the number of points it scores is now much higher. It is still most likely to score 20 points, but it has a higher chance of scoring much more. On the flip side, it also has a much higher chance of scoring very few or no points. In other words, it has a better chance of beating Team A than if it employed a conservative strategy, but it also has a better chance of getting blown out.

 

Figure 2

So why don’t bad teams play more aggressively when competing with clearly superior teams? Why don’t the Appalachian States of the football world choose to onside kick and go for it on fourth down every time they play the Michigans? It would seem to give them a better chance of winning than playing it by the book—within reason, of course. I’m not advocating going for it on fourth and 40.

It may be because teams hate getting blown out, which increases in likelihood if you play risky. Players get demoralized losing 85-0, and coaches start to feel their seats getting warm. The safest way for a coach to keep his job is to follow the typical conventions: punt on fourth down, settle for the field goal and don’t onside kick. The same goes for players: Throwing interceptions trying to get lucky on the big play is more likely to get you benched than throwing the safer check-down passes.

For now, what could increase the team’s chance of winning isn’t always in the best interest of the coach or player. Until that changes, we’ll just need to settle for enjoying these monumental upsets for the rare events they are. 

Monday
Sep092013

Drive for Dough, Putt for Dough

If you find yourself wondering if you read that correctly, you did. The old golf adage really goes, “Drive for show, putt for dough,” which implies a golfer who hits the ball far may look flashy and impressive, but what really matters is how well a golfer putts. With the PGA Tour’s FedEx Cup Playoffs under way, we figured it would be a topic worth addressing.

The question at hand essentially breaks down into two parts:

  1. Which of the two skills, driving and putting, are statistically relevant to a golfer’s success?
  2. If both are relevant, which one is of greater value?

Naturally, this begs the question as to what other skills add value. To answer that, we examined seven different player skills:

  1. Driving distance.
  2. Driving accuracy.
  3. Iron play - skill used to hit approach shots toward the green.
  4. Recovery - ability to hit proficient shots from difficult situations and ball placements (e.g., from behind a tree).
  5. Chipping - skill used to hit short shots from around the green.
  6. Sand play - skill used to hit shots from sand bunkers.
  7. Putting.

Using data from 10 seasons of PGA Tour golf and regression analysis, we found evidence suggesting putting and driving distance both play a statistically significant role in determining a golfer’s success.[1] More specifically, it was implied putting had a greater marginal value than driving distance and the greatest marginal value overall.[2] In the hierarchy of marginal values, on average, driving distance was third, right behind iron play in second. As such, it would appear the old adage is neither entirely true nor entirely false. Both skills were significant, yet putting was of greater value, hence the title of this post: “Drive for Dough, Putt for Dough.”

Furthermore, the recovery skill came in fourth in terms of marginal value, which comes as no real surprise considering it isn’t used often by the world’s best golfers. One notable exception: Bubba Watson’s shot during sudden death in the 2012 Masters (Figure 1). For those not familiar, Bubba was caught far to the right of the fairway when he hit the shot of his life out of the trees and onto the green.

 

Figure 1

Needless to say, Bubba’s ability to hit that shot was essential to his victory.

As for the other skills examined, chipping followed the recovery skill at fifth in value, and sand play brought up the rear of statistically significant factors. The only skill found to be statistically insignificant was driving accuracy.

But wait, there’s more. In typical nerd fashion, we upped the ante by employing quantile regressions. Sparing you the economic mumbo jumbo, these types of regressions allow you to analyze the marginal values of skill at various overall levels of golf proficiency. In other words, it’s possible to see whether the values of these skills change as a golfer gets better overall.

The results of these regressions offer perhaps the most insight, as three notable trends arise along with one other tidbit. Unsurprisingly, the three trends concern the three most valuable skills—driving distance, iron play and putting—and the tidbit involves driving accuracy.

What we ultimately find is that as a golfer becomes more skilled overall (Tiger Woods v. you), the marginal values for iron play and putting tend to decrease, whereas the marginal value for driving distance tends to increase. In fact, it increases so much that at the highest levels of overall skill, driving distance adds the next most value behind only putting.

The results seem to be intuitive. As a golfer becomes more skilled overall, said golfer will relatively gain more benefit from longer drives. This is because longer drives result in closer approach shots. And because the golfer is more skilled in general, said golfer is better suited to take advantage of the better positioned shot. Then, since a closer approach shot increases the likelihood of a shot closer in proximity to the hole, the golfer will likely face a shorter putt, which is again advantageous. Thus, a more skilled golfer will benefit from longer drives more so than one of lesser skill.

As for the tidbit of information, we find driving accuracy to be statistically significant exclusively at the lowest levels of overall skill. Again, this is not surprising because a golfer who is of lesser skill overall will likely need to be in or around the fairway to have a legitimate chance at reaching the green.

To recap, the results suggest putting returns the greatest value for golfers. In general, the next skill in terms of value was iron play, which was followed closely by driving distance. The rest of the observed skills in order were recovery, chipping and sand play. Further, as a golfer becomes more skilled overall, they will benefit relatively more from increases in driving distance and less from increases in putting and iron play. Lastly, the ability to drive accurately was statistically significant exclusively at the lowest overall skill levels.

So the next time you’re practicing the world’s longest drive, you can rest a bit easier knowing you’re adding value to your game. Just consider heading to the putting green after you’re done.

 


[1] Variable definitions are available upon request.

[2] Marginal value represents the change in output brought about by an incremental change in inputs. For our purposes, this represents the change in golfer earnings corresponding to unit changes in the observed skills.