Friday
Mar292013

So you're saying there's a chance...

Opening day is just a weekend away, and baseball fever has reached its peak. I thought this would be the perfect opportunity to dig into a unique ticket-pricing promotion by my hometown Milwaukee Brewers. The package is called Chance 2 Advance and lets fans upgrade their tickets to better seating areas for minimal cost when the Brewers win select home games. Here’s an explanation of the package from the Crew’s website:

 

For just $99, we'll give you a Bernie's Terrace ticket to nine select Tuesday games at Miller Park. And, on Tuesday, April 30, you'll sit in Bernie's Terrace for the first game of the plan. When the Brewers win, you advance!

Every time the Brewers win, you exchange your Bernie's Terrace ticket for the next game in the plan for just $2 to the next best seating area (see list below). You remain in that seat location until the Brewers win the next game in the plan. If the Brewers don't win, you simply exchange your Bernie's Terrace ticket at no cost for a seat in the same section where you last advanced — no backsliding.

If the Brewers win the first eight games in the plan, the ninth game would enable you the opportunity to sit in the Field Diamond Box!

1. Bernie's Terrace

2. Terrace Reserved

3. Terrace Box

4. Loge Outfield Box

5. Loge Infield Box

6. Club Outfield Box

7. Field Outfield Box

8. Field Infield Box

9. Field Diamond Box

 

This sounds like an entertaining promotion and a great way to be even more interested (if that is even possible) in seeing the Crew win. But I couldn’t help wondering: Is this package a good value?

The short answer is yes. If you bought nine individual tickets for Bernie’s Terrace (the starting point of Chance 2 Advance) at $11 a ticket, you would pay $99, the exact same amount you would pay for the Chance 2 Advance package. So unless the Brewers lose all of their first eight games (keep in mind, we are talking about the Crew, not that poor excuse for a baseball team 90 miles south), you would end up with a better deal by purchasing the package because you will watch at least some of the games from a better seat.

But how much better? That depends on how many games the Brewers win and requires some probabilistic thinking.

Let’s start with the basics: They play eight games that give you an opportunity to advance to the next best seating area. That means there are 256 (or 28) different combinations of winning/losing during this eight-game stretch. And let’s suppose for the sake of this analysis (and to make the math easy) that the Brewers have a 50% chance of winning each of these games. This means each of these 256 possible outcomes is equally likely to occur. For example, one possible combination could look like this:

Win, Win, Loss, Win, Loss, Loss, Win, Win

In this scenario you would watch the nine games in these seating locations:

If you bought the Chance 2 Advance package, you would have paid $109 for these tickets ($99 initial payment, plus $2 for each of the five times you advanced). If you decided not to buy the package, however, and bought these exact same tickets individually, you would have paid a whopping $261 (see table for assumed face value individual game ticket prices). That means for this possible outcome, you would have saved $152 for the exact same seats by purchasing the Chance 2 Advance package. Not bad!

But that’s just one scenario. What if we did this for all 256 possible scenarios? You would find that you could expect to pay $107 for tickets with the Chance 2 Advance package and $223 for the exact same tickets if you purchased them individually. That means you could expect to save, on average, $116 by going with the package instead of buying the tickets individually.

So we know the Chance 2 Advance is a great deal, but let’s add one caveat: If you are buying the tickets with an expectation of watching the ninth game in the luxurious Field Diamond Box, prepare to be disappointed. Once again assuming the Crew has a 50% chance of winning each of these games, there is only a 0.4% chance you will be watching the last game in the Field Diamond Box.

But on the flip side, it’s just as unlikely you will be stuck in Bernie’s Terrace all nine games, so you have a great Chance 2 Advance, if you will. In fact, you have a better than one-in-three shot of watching the final game in Club Outfield Box or better. So no matter what, it’s a great value and another reason to visit Miller Park this season—just in case the Sausage Race wasn’t reason enough.

 

Friday
Mar082013

I'm going to steal

I can’t believe it’s March already. It seems like 2013 just started yesterday and I was resolving to work out more. But, like my fellow fools who decided to stop smoking, lose weight or read more books, I already quit. I couldn’t even make it two months. It shouldn’t really surprise me that I didn’t stick to my resolution; about 88% of people fail. Lucky for the weak-minded, economics provides a helpful tool for following through with achieving our goals: strategic precommitment.

If the dismal science teaches us only one thing, it’s that people respond to incentives when they make decisions. When I make the decision whether to work out today, I need to balance the long-term incentive of being healthier and looking buff with the short-term incentive of watching TV and avoiding sore muscles. My short-term incentives are well-defined: I don’t need to spend time punishing my biceps, and instead I get to watch the Situation punish his. My long-term incentives, however, are more abstract. If I workout today, it will only contribute sparingly to my future health. And how much does better health translate into better quality of life or increased life expectancy? I don’t really know; there’s no good way to compare it to the enjoyment of watching TV right now. So you can see the incentives are heavily stacked against working out. The same applies to saving for retirement: I know buying a 60-inch flat-screen television will make me happy now. Who knows if I will even be alive when I’m 65?

So the key to forcing yourself to work out (or save for retirement) is to change your incentives. Either make it more rewarding to work out now or make it more painful to not work out right now. That’s where strategic precommitment comes in. Before you attempt to change your workout habit, add a disincentive for failing to reach a workout goal. For example, you could commit to giving away $100 if you fail to lose 10 pounds in two months. Now your incentives have changed. Instead of weighing the pleasure of watching TV against the abstract benefit of better health, you’re weighing it against the possibility of losing $100, which is much more tangible. And to prevent you from reneging on your deal with yourself, it’s best to make the deal with a friend. Tell your friend you will pay them $100 if you don’t make your goal. Now you can’t back out when you don’t reach your goal and you added the social pressure of avoiding public failure—that’s an incentive double-whammy.

Keep in mind that strategic precommitment is not a fail-safe method for reaching your goals. Let’s not forget Congress tested the same tactic when trying to reach a deficit-reduction deal in August 2011. In an attempt to force itself to agree on plan, it decided to impose drastic cuts of $1.1 trillion to defense and civilian spending—known as the “sequester”—beginning March 1 if a plan wasn’t reached. You already know how this story ends. Like the resolver who doesn’t put a dear enough price on failing to meet his resolution, Congress was unsuccessful in reaching a deficit-reduction deal, instead allowing the sequester to take effect. As this post by The Economist argues, the reason the two parties didn’t reach an agreement was because the sequester wasn’t a legitimate disincentive for politicians who weren’t up for reelection for at least two years.

A more entertaining example of a precommitment strategy comes from an obscure U.K. game show called Golden Balls. The rules of the game are simple: Two players are awarded a sum of money based on their simultaneous decision of whether to split that money with the other player or steal it all for themselves. If both players choose to split the money, they do. If one chooses to steal and the other chooses to split, the stealer takes it all. If both choose steal, neither gets anything.

It’s a classic example of game theory (prisoner’s dilemma) in which the player has a dominant strategy to choose to steal from their opponent because:

  • If their opponent chooses to split, the player will get all the money.
  • If their opponent chooses to steal, the player will get nothing regardless of whether they choose steal or split.

Watch this clip to see how one player uses a strategic precommitment to his advantage in the game:

 

 

So keep this blog post in mind the next time you’re debating whether to work out. Because strategic precommitment might just be the thing you need to get back on the treadmill. Or ensure your friend doesn’t rob you blind on U.K. television.

 

Wednesday
Feb272013

When Is a Free Throw Not Just a Free Throw?

In interviews during the 2012-2013 college basketball season, Marquette Head Coach Coach Buzz Williams has mentioned repeatedly that he’s not sure what his team does well. Maybe nothing. Maybe his team just wins well. Surely, that can’t be it. After all, the Golden Eagles were 20-7 and 11-4 in the Big East as of Feb. 27, keeping it in the race for the conference’s regular season title.

A team in this position must be doing something much better than its opponents. At first glance, Williams is right: It’s not clear what Marquette does well:

Marquette’s highest conference rank in any efficiency stat is sixth, and its overall average efficiency rank is eighth. How could a team with middling stats such as these be fighting for the top spot in one of the nation’s toughest conferences?

It’s simple: free throws. The key is not just getting to the line, but rather how many a team makes relative to the possessions available in a game. This is where we can start to see how Marquette wins.

The table below shows the number of free throws each team in the Big East makes relative to a particular number of possessions. Marquette makes a little more than 25 free throws per 100 possessions, which is second only to Villanova’s 27.5 made per 100 possessions.

But this isn’t the full story. We need to consider how many more free throws a team makes per 100 possessions relative to its opponent. On average, Marquette makes 6.7 more than its opponents, which is tops in the Big East and good enough for 17th best in the nation (FYI: Green Bay, which defeated the Golden Eagles on Dec. 19, is currently 24th in the nation in this statistic).

That’s all well and good, but how does it translate to winning? If Marquette were to make the same number of free throws per 100 possessions as its opponents while keeping its other efficiencies the same, its winning percentage would decline 5.72%.[1] Through 27 games, that amounts to 1.54 games. That would put Marquette at roughly 18–9 overall and 9–6 in conference, or in seventh place—right in the middle.

Let’s look at it a different way. Marquette averages a turnover on 20.5% of its possessions thus far this season and averages 25.6 FTM/100. There have been 14 games in which it had a turnover rate higher than 20.5%. In nine of those 14 games, the Golden Eagles had a FTM/100 below 25.6. They lost six of those nine games (Green Bay was one of them). In the other five games, Marquette had a FTM/100 above 25.6 and won four of those games.

Williams says he’s not sure how this Marquette team wins, as he’s not sure what it’s good at—but don’t let him fool you. He emphasizes getting touches in the paint for a reason: They provide open shots on a collapsed defense and, maybe more importantly, a decided free-throw advantage.

 


[1] This calculation is derived from results of a previously run regression that looks at how each efficiency determines winning percentage. These results can be provided to the reader if desired.