Here’s a problem for you. You’re an executive member of a medium-sized company. You have quite a few employees whose livelihoods are dependent on the ongoing success of the company. The company is performing reasonably well, but someone high up in the company – let’s, for argument’s sake, say the company’s owner – is a bit of a loose cannon. Maybe he’s prone to say the wrong thing in the wrong place sometimes. Maybe he’s got a skeleton or two in his cupboard that are best kept well-hidden. And bad publicity could badly damage the reputation and value of the company, potentially costing money and jobs. What are you going to do?

Well, it turns out you need the help of statisticians.

You’ll know all about car insurance. You pay a premium, whose cost is calculated on the basis of a number of factors including your likelihood of having an accident, the value of the car, the rate of claims in the area you live, and so on. And if you have an accident or your car is stolen, then you can claim against the insurance policy. It’s a negative value bet – on average you will pay out more money in premiums than you will regain in claims – but to protect yourself against the huge losses that might be incurred by writing-off your car, or in the damages you might cause to a third party, it’s a bet you would probably take. Actually, it’s a bet you’re legally obliged to make if you want to drive a car.

But how are the risks evaluated and the prices set? Essentially on the basis of  statistical models. An insurance company will have a record of previous claims and the individual and demographic characteristics of the customers making those claims. It’s then a fairly standard statistical modelling procedure to relate the chance of a customer making a claim, and the average cost when they do, to the available characteristics.

We met something like this before in the context of expected goals (xG). In that setting we had a number of characteristics on a game play and wanted to calculate the probability a goal would be scored. Swap game state for customer characteristics and goal-scored for claim-made and you can see the problem is structurally the same. Well, almost. A game play can only lead to a single goal, whereas an insurance customer might make several claims in given period. But essentially the principle is the same: use the characteristic information – game play or customer type – to get the best predictor of some outcome – goal scored or claim made.

But, I digress. It turns out that just like protecting yourself through insurance against the potential costs of a car accident, you can protect your company against the potential embarrassment of bad behaviour by any of its employees. Or owners.

Welcome to the world of: disgrace insurance.

Yes, it turns out that you can insure your company against the fallout of bad headlines caused by any disgraceful behaviour by the members of your company. This type of insurance has apparently been around for quite a while, but the avalanche of recent celebrity scandals and a shift in funding mechanisms has altered the dynamics. Leading the way now is the start-up company SpottedRisk. They say of themselves:

SpottedRisk™ has completely reinvented the decades-old disgrace insurance product in order to meet the needs of today’s market.

What’s especially interesting here from a statistical point of view is the risk evaluation aspect. SpottedRisk have amassed a database of some 27,000 celebrities and used various metrics of their behaviour as predictors for subsequent scandals. Then, like customer characteristics and insurance claims, or game position and goal scored, they can build a model to use one to predict the other. And once they’ve evaluated the risk of a scandal and it’s likely cost, they can set the premium accordingly.

The amount paid is after a scandal depends on its severity. Or what SpottedRisk call the ‘Tier of Outcry‘. And they give some theoretical examples:

  • Roseanne Barr. Sent a number of racist and conspiracy-theory tweets and was dropped from her own show. Tier of outcry level 2. Payout $6 million.
  • Kevin Spacey. Accused by several men, some underage, of sexual harassment. Dropped from various film productions and other work activities. Tier of outcry level 4. Payout $8 million.
  • Harvey Weinstein. Industrial amounts of sexual misconduct. Persona non grata pretty much everywhere. Tier of outcry level 5. Payout $10 million.

But there’s just something I don’t quite get with this business model. A celebrity will be publicly disgraced on the occurrence of two events:

  1. He/she will have done something disgraceful;
  2. That disgraceful thing will come to light and be publicised.

Now, the celebrity and the insurance company can each make an assessment about how likely the second of these, but the celebrity is likely to have much better knowledge than the insurance company about whether they really have something to hide – that’s to say whether the first of these points is triggered. So the value of an insurance premium is much better known to the customer than to the company, who can only have a vague idea of 1, even if they can calculate 2 better than the celebrity. This is unlike car insurance, where the company is probably better able to evaluate a customer’s total risk than the customer themselves. As such a client here is in the unusual position of knowing whether the premium offered is of good value or not. This doesn’t really make much sense to me.

Additionally, the theoretical payout on Harvey Weinstein is $10 million. This is probably a fraction of the amount spent on any of the films whose production he was involved in, and it seems fanciful to think that a film studio would have bothered to insure itself against that amount of loss.

So, to my mind, something doesn’t quite add up.

Finally: is everyone insurable against disgrace? Apparently yes, except for R. Kelly and Donald Trump, the latter of whom would “probably trigger a claim every week”, according to SpottedRisk’s behavioural scientist Pete Dearborn.

The opening paragraph of this blog post is a work of fiction. Names, characters, businesses, places, events, locales, and incidents are either the products of the author’s imagination or used in a fictitious manner. Any resemblance to actual persons, living or dead, or actual events is purely coincidental.




Do I feel lucky?

Ok, I’m going call it…

This is, by some distance:

The Best Application of Statistics in Cinematic History‘:

It has everything: the importance of good quality data; inference; hypothesis testing; prediction; decision-making; model-checking. And Clint Eastwood firing rounds off a 44 Magnum while eating a sandwich.

But, on this subject, do you feel lucky? (Punk)

Richard Wiseman is Professor in Public Understanding of Psychology at the University of Hertfordshire. His work touches on many areas of human psychology, and one aspect he has studied in detail is the role of luck. A summary of his work in this area is contained in his book The Luck Factor.

This is from the book’s Amazon description:

Why do some people lead happy successful lives whilst other face repeated failure and sadness? Why do some find their perfect partner whilst others stagger from one broken relationship to the next? What enables some people to have successful careers whilst others find themselves trapped in jobs they detest? And can unlucky people do anything to improve their luck – and lives?

Richard’s work in this field is based over many years of research involving a study group of 400 people. In summary, what he finds, perhaps unsurprisingly, is that people aren’t born lucky or unlucky, even if their perception is that they are. Rather, our attitude to life generally determines how the lucky and unlucky events we experience determine the way our lives pan out. In other words, we really do make our own luck.

He goes on to identify four principles we can adopt in order to make the best out of the opportunities (and difficulties) life bestows upon us:

  1. Create and notice chance opportunities;
  2. Listen to your intuition;
  3. Create self-fulfilling prophesies via positive expectations;
  4. Adopt a resilient attitude that transforms bad luck into good.

In summary: if you have a positive outlook on life, you’re likely to make the best of the good luck that you have, while mitigating as well as is possible  against the bad luck.

But would those same four principles work well for a sports modelling company? They could probably adopt 1, 3 and 4 as they are, perhaps reinterpreted as:

1. Seek out positive value trading opportunities wherever possible.

3. Build on success. Keep a record of what works well, both in trading and in the company generally, and do more of it.

4. Don’t confuse poor results with bad luck. Trust your research.

Principle 2 is a bit more problematic: much better to stress the need to avoid the trap of following instinct, when models and data suggest a different course of action. However, I think the difficulty is more to do with the way this Principle has been written, rather than what’s intended. For example, I found this description in a review of the book:

Lucky people actively boost their intuitive abilities by, for example… learning to dowse.

Learning to dowse!

But this isn’t what Wiseman meant at all. Indeed, he writes:

Superstition doesn’t work because it is based on outdated and incorrect thinking. It comes from a time when people thought that luck was a strange force that could only be controlled by magical rituals and bizarre behaviors.

So, I don’t think he’s suggesting you start wandering around with bits of wood in a search for underground sources of water. Rather, I think he’s suggesting that you be aware of the luck in the events around you, and be prepared to act on them. But in the context of a sports modelling company, it would make sense to completely replace reference to intuition with data and research. So…

2. Invest in data and research and develop your trading strategy accordingly.

And putting everything together:

  1. Seek out positive value trading opportunities wherever possible.
  2. Invest in data and research and develop your trading strategy accordingly.
  3. Build on success. Keep a record of what works well, both in trading and in the company generally, and do more of it.
  4. Don’t confuse poor results with bad luck. Trust your research.

And finally, what’s that you say?  “Go ahead, make my day.” Ok then…