# Monthly Archives: June 2012

## what is the conditional probability of being struck by lightning? Part 3

This is my third post on the conditional probability of being struck by lightning in response so an NPR article (HT to Tim Hopper). The National Weather Service tweeted:

More than 80% of lightning victims are male. Be a force of nature by knowing your risk, taking action and being an example #ImAForce

This suggests that the conditional probability of being struck by lightning depends on your gender. You might think that the conditional probability of being struck by lightning for a man is four times higher than four a woman. Not so fast.

In the NPR article, Susan Buchanan, a spokeswoman from the National Oceanic and Atmospheric Administration offered four explanations for why. They are quoted below with some minor changes from me. The first two explanations would affect the prior probability of being exposed to a thunderstorm:

1.  Men are more likely to be outside.

2.  More are more likely to have jobs that require them to work outside.

The second two would affect the conditional probability of being struck by lightning given one’s gender and that he/she is in a thunderstorm.

3. Men take more risks than women. “If you look at the percentage of men who take part in high risk sports that might give you an idea,” said Buchanan. Therefore, a man would be less likely to go inside during a thunderstorm.

4.  Men don’t want to be seen as “wimps.” This theory, she said, was backed up by talking to the Boy Scouts who said no one wants to be the one to say it’s time to go inside.

Putting this together:

1 < [Conditional probability of being struck by lightning given that one is a man and is in a thunderstorm] / [Conditional probability of being struck by lightning given that one is a women and is in a thunderstorm] < 4.

## Is analysis necessarily data-driven? Does analytics include optimization?

A recent blog post by Jean Francois Puget and tweet by INFORMS President-Elect Anne Robinson asked about how to define analytics.

INFORMS defines analytics as:

“Analytics — the scientific process of transforming data into insight for making better decisions.”

I believe that optimization is a critical part of analytics. As Jean Francios Puget states, “Optimization seems covered by the ‘making better decisions’ part.” As an optimizer, I am completely biased in favor of this answer. The real question Jean Francios asks is not about optimization, but how analytics ultimately seems to start with data, even optimization. Is a data-centric view essential to analytics?

For the past few years, I thought “yes.”I did not have the foresight to take data-centric courses in graduate school. I have been trying to make up for that ever since. We live in a world that collects increasing massive and complex data sets. Being able to analyze data is generally a critical starting point from which to start doing analytics.

Some of my research is in the area of emergency medical services. Locating ambulances, for example, is a classic application of facility location, p-center, and p-median problems. Ambulance location models existed before ambulance data was routinely collected. Being able to build models without data necessitated assumptions regarding what the data would look (e.g., assuming that calls arrive according to a Poisson process, although I often find that assumption to be realistic!) Other models were built with limited data that was painstakingly collected: I like this model of fire engine travel times that led to the so-called square root law. Having a simple model for fire engine travel times made it easier to build models that were not data-driven. Having access to oodles of data today is a huge help in building good models and understanding which assumptions are okay to make. The more data the merrier.

Now, I think differently.  Building new models imposes a new and potentially useful way of looking at a problem. Data isn’t necessary to build a model (although it is surely helpful) nor should a data set be the ultimate starting point of every model. My students found it useful when I argued that bus accidents are a Poisson process. Without any real data, we could gain useful insights for how to view a cluster of bus accidents that occurred in the Richmond area one week.

Most data that is collected is not analyzed. Much of the analyzed data is “analyzed” using summary statistics. In my experience, statistical models often provide useful explanations of what happened in the past. Analytics is not backward-looking; it is forward-looking. “How would you improve what you do as a result of this data analysis” is a question that is not asked enough. Today, it’s hard to imagine data not being part of the answer, but it certainly could be excluded as part of an “analytics” solution. It is certainly possible/desirable to use a non-data driven approach to look to the future.

I realize that arguing for data not being included as part of analytics is going to be a tough sell. The “analytics” culture is aimed at those who are knee deep in data on any given day. Maybe people like me who have been trained more on the models/optimization side than on the data side just don’t want to be left behind. I hope there is some legitimate truth to this blog post.

A case study

A local fire and rescue station recently contacted me for feedback on their staffing levels. Yes, data was necessary for me to use analytical techniques in pursuit of some useful feedback, but it wasn’t the starting point. I started by interviewing the chief and other experts about the operations, constraints, and culture. At the end, I was able to look at the data, which was incredibly messy (lots of data was clearly not recorded). I was able to devise a clever way of at least bounding the amount of work that was performed to come up with bounds for staffing levels. Here, data was essential but was essentially not the starting point.

## pirates and operations research, part II

I thoroughly enjoyed the feedback I received for my podcast about pirates and operations research. I feel obligated to write a post about an actual paper in the latest Decision Analysis issue about pirates and operations research written by Juan Carlos Sevillano, David Rios Insua, and Jesus Rios. Here is the abstract:

We show how adversarial risk analysis may cope with a current important security issue in relation with piracy off the Somali coasts. Specifically, we describe how to support the owner of a ship in managing risks from piracy in that area. We illustrate how a sequential defend–attack–defend model can be used to formulate this decision problem and solve it for the ship owner. Our formulation models the pirates’ behavior through the analysis of how they could solve their decision problem.

When Richard and I recorded the podcast a few months ago, we had no idea that there were actual research projects involving pirates and operations research. What a pleasant surprise!

## JC Penney, game theory, and price shrouding

JC Penney now has everyday low prices that replace having everything on sale all the time, with occasional special sales (usually on Saturdays) with rock bottom prices. Some items go on sale, and the sale lasts the entire month (instead of the week).

The motivation: three-quarters of everything sold at JC Penney occurs when the products are marked at a ~50% discount from list price.  Customers wait until the really good sales and then stock up: Items are marked down 30% of the time for 6.5 days a week and occasionally go on sale for ~50% off.  Most items are sold on the days with 50% markdowns. JC Penney’s new approach is to keep everything at almost-rock-bottom prices, thus encouraging shoppers to stop by every day of the week. The prices are quite low, but not quite as low as they used to be. Consumers have to weigh being able to wait to buy something at a time that is less convenient with saving a small value on price.

At first, I thought that this was a nice game that hasn’t played out yet. The idea is that if every other department store offers big weekend sales, then JC Penney might lose out on the customers who are at Kohl’s and Macy’s (there is only so much shopping you can do on Saturday mornings). Moreover, JC Penney is missing out on the customers who might have wanted to pop in on Thursday but didn’t because the prices weren’t low enough. JC Penney is finding its niche in the market that will eventually win over consumers, since they have no department store competitors. A similar game theory analysis has done been done on Starbucks’s approach to investing in training rather than advertising (see this blog or this blog for example). By distinguishing themselves from their competitors, Starbucks can corner a certain segment of the market.

I love the new JC Penney. But when I am there, the store is basically empty. JC Penney sales have slumped. Some speculate that JC Penney needs to educate the consumer so that customers figure out how to play the game. They have recently started to do this in the ads, showing that the new price is lower than the old price on sale. And by the way, the new ads are beautiful– even my kids like to pore over them.

A new article on the Red Tape blog on MSNBC suggests that JC Penney is doomed regardless. People don’t want cheap everyday prices, they want mysterious, shrouded prices in deceptive circulars that promise uber-low prices and that ultimately trick consumers. The article mentioned anchoring: Consumers love to buy a \$20 item that is 50% off. They do not like a regular priced \$10 item. We have been trained to look for discounts, anchoring on the high, undiscounted price.

If you think about it, shrouded price tags are everywhere. The hotel website might say “\$99 a night” but you know the bill will be more like \$120 or \$130…

Consumers complain about this constantly. That’s the basis of the Red Tape Chronicles in fact. At its best, the maddening mixture of coupons, rebates, sales and fine print fees can feel like a game. At worst, it’s being cheated. You’d think shoppers would love a chance to buy from a store that doesn’t play these games, the way car buyers (allegedly) like shopping at no-haggle auto dealerships.

They don’t, says Gabaix, and Penney should have known better. “I think it was an ill-advised move,” he said.

All this price manipulation is really an information war, he says. Shoppers hunt for the tricks that let them save money. Stores hide booby traps that let them take money. It’s a bad system, one I’ve labeled “Gotcha Capitalism.” But it is the system we have now.

And it’s simply impossible, Gabaix argues, to be the one company that attempts to bridge this information gap.  If a firm tries to educate consumers on tricks and traps, and tries to offer an honest product, a funny thing happens: Consumers say, “Thank you for the tips,” and go back to the tricky companies, where they exploit the new knowledge to get cheaper prices, leaving the “honest” firm in the dust.

“Once you educate consumers on the right way to shop, they will seek out the lowest cost store, and that will be the one with the shrouded prices,” he said. “Once they are savvier consumers, you make less money from them.”

Gabaix calls this the “curse of debiasing.” And it leads to this depressing conclusion: “Shrouding is the more profitable strategy.”

The above article seems accurate to me. I no longer buy the brands that are not exclusive to JC Penney, because I can wait for a sale at Kohls, for example, and get them for cheaper. JC Penney also didn’t do a good job at comparing the new prices to the old. The ads only contain the new everyday prices without a comparison to what they used to be. I have been conditioned to look for a % off, so the new, low prices don’t seem “low” to me, even when they are a great deal.

Despite this, I like the new store. My Saturdays are busy with the kids. JC Penney is near my house and on my route home from work. It is easy to shop at other times, and I prefer to shop when it is not so crowded. Yes, I could get something at epsilon cheaper, but I used to have to make multiple trips to the store to get the “best” prices. The prices are low enough that the extra epsilon on price is well worth the time savings.

Do you think JC Penney can overcome the odds and succeed?