Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Tuesday, June 24, 2008

Big Car Small Car

There are still a lot of big cars in America. A colleague in charge of certain North American automotive metrics today pointed me to a recent study from Duke University's Fuqua School of Business that proved the regularly quoted mpg figures are often misleading.

Simple numerical facts. As usual here, considering my own example instead of copying that from the study:

First car is a typical one, one that does 30 mpg. Could increase by 10 mpg to give 40 mpg.
Second vehicle is a large SUV. It does 15 mpg. Could increase by 10 mpg to give 25 mpg.

Where is the bigger benefit? Both increase by 10 mpg so benefit is the same, right? Wrong.

First increases mpg by 33%, second increases by 67%, so the second gives twice as much benefit, right? Wrong.

Say the SUV increases only by 33% like the first case, 15 up to 20 (corresponding to 30 up to 40). The benefit is the same, right? Wrong.

If the SUV increases only from 15 to 18 mpg, it still saves more fuel than increasing the car's mpg from 30 to 40. I've said it before: However far the journey.

The Europeans have been using litres per 100 km for years. It just makes more sense.

Wednesday, April 30, 2008

Counting up to two

The one place that is the birthplace of cricket is England and Wales. The one place. But that is not the issue. According to the BBC article today:

Glamorgan chairman Paul Russell has backed proposals to create a new Twenty20 competition in Britain.

"We have two things going for us: one is that in June the only place that cricket is played is England and Wales," Russell told BBC Sport Wales. "Secondly, all the players around the world are available."

Now surely that is only one thing and not explicitly two? Because cricket is played nowhere else at that time, that is the reason why all the players are available. All the players around the world are available, so it's pretty clear that cricket is being played nowhere else. Tautology. I'm pleased that he is chairman and not scorer.


Disclaimer: I first met Paul Russell on the very first day of my very first job after college. I was a fresh-faced new graduate, and he was the Partner in charge of Human Resources who said "welcome to the firm". We've both changed a lot since then.

Monday, February 25, 2008

Marketing Maths Money


I quoted about organ donors from the Data Strategy editorial only a few days ago, but the cover story from this month's issue has an equally relevant message: Clients, suppliers and agencies are crying out for data analysts and database managers, but the small number of recruits available is a growing problem for employers.

There is a very obvious first cause for this. Again quoting directly from the printed article: the number of students taking A Level Maths fell by nearly 40 per cent between 1989 and 2002. This was against a backdrop of a 15 per cent overall rise in the number of A Levels being taken.

As a fairly new and emerging industry, the employment market for these people should be fairly flexible. There is an obvious requirement for these skills, in fact the writing here always seems to return to the same theme of the need for better targeting, better measurement, and also the the growing requirement for increased statistical analysis as a compensating factor for increased data protection.

But these same skills are also in demand in the slightly stratospheric world of financial risk analysis and hedge fund management. Understandably, many maths graduates are drawn to the City to manipulate and model with numbers that are even further removed from the real world of people and commodities. It could be argued that there is a case for outsourcing of this analysis, but that is easier said than done, and at least in the marketing arena there is huge added value in knowing the local market as well as the local model. This again suggests that more skilled graduates are needed here.

So there should be a natural tendency for prices (salaries and contract rates) to rise to match the increased demand. If this does not happen, then it is hard to see how employers can complain about insufficient supply. And over time we should even see a regression of graduates back to the more "difficult" subjects.

There are alternatives. Perhaps the government will submit to industry demands for more professional immigration. Perhaps more jobs will be outsourced despite their practical difficulties. Or perhaps we will learn to value scientific skills before we become a nation of hairdressers, TV producers, insurance salesmen, personnel officers, security guards, management consultants, telephone sanitizers and tired bloggers.


Sunday, February 10, 2008

Estimating Project Delivery Time

I have spent a lot of my working life doing IT Project Estimation and IT Project Proposals, it is not the most interesting subject in the world, but it is important, and I touched upon it in an earlier post.

I could throw in a few key words used to manage the estimation, words like originality, uncertainty, statistics, experience, reductionism, but it would need thick volumes to explain them properly. What is interesting is why people keep getting their estimates wrong.

It is obvious that people tend to over-estimate their own abilities. That is such basic human nature and so well-documented that we may as well just call it fact.

But many people, even educated ones, seem to have trouble with simple extrapolation, even for things as commonplace as car journeys. The British Psychology Society just published a simple study that asked:

for both pairs, just make an intuitive judgement about which jump in speed will make the largest difference to your time of arrival (i.e. save the most time):
a)Travelling at 50km/h instead of 40km/h.
b)Travelling at 130km/h instead of 80km/h.

a)Travelling at 50km/h instead of 30km/h.
b)Travelling at 130km/h instead of 60km/h.
If you're like most of the participants in Svenson's study, you will have assumed that option (b) in both pairs is the most time saving.

That guess is simply wrong. In each case, option (a) saves more time. However far the journey.

Wednesday, January 09, 2008

Random numbers and letters

Measurable marketing requires the use of control groups. Control groups require the selection of random samples. Ensuring statistical validity across overlapping groups, even with normal distributions, can be difficult. But randomization is easy.

The New Hampshire Democratic primary has just given Hillary Clinton a shock victory, whereas Barack Obama was predicted to win by the pollsters. I am not going to comment on policies, just on the most pathetic randomization that I have ever heard seen. Not in the poll sample selection, which can be difficult. But in the ballot itself, which is ridiculous.

It has been suggested, and tests have proved, that a name listed at the top of the ballot is more likely to be picked than when placed at the bottom. The effect could be up to 3%, but I think we still do not have enough data yet to quantify exactly.

As ABC News reported: This year, the secretary of state changed the procedure so the names were alphabetical starting with a randomly selected letter, in all precincts. The randomly selected letter this year was Z.

Now that is just ridiculous. So given the lack of surnames ending in Z, the order was simply alphabetical. The fact that "this year" it was Z implies they are going to maintain this crazy idea. So a name like Miller is nearly always going to be above a name like Nader, in fact about 96% of the time. How is that random? And a name like Cleasby is always going to be above a name like Courtney.

Life is unfair, but ballots should not be.

Sunday, December 09, 2007

666 is a good score

Some numerology. According to the legendary QI, Revelation 13:18 may refer to a slightly different number.

Various estimates quoted ranged from 216 to 616 to 665, the neighbour of the beast.

Having won the 20-20 World Cup, in which Yuvraj Singh scored 6 6's in an over, India are currently playing a test series against Pakistan. They are playing splendidly. Just look at the first innings scores. In the first test match, which they won comfortably, the score was 276. That looks a bit like 216. In the next , they scored 616. And today they scored 626.

Going up at 10 per match, by the time of the deciding match against Australia, I predict a first innings score of 666. That'll show 'em.

Although what's more likely is that, like England, we'll get soundly thrashed there.

Sunday, November 25, 2007

Maradona and Statto


I usually play football twice per week. One of those games involves a group of us who have been playing at the same time each week for nearly a decade. The sides vary, but we have records of the match results, and also on how often each player wins. But in today's lesson on how stats can mislead, a reminder that win ratio does not correlate to talent or ability.

It should be obvious, but to help understand why, assume that one player (for the sake of argument let's call him X) is much better than everyone else. Fair enough, X would be expected to have a decent win ratio. But look at the effect on everyone else.

When we are choosing sides before the games, we make a conscious decision to balance them. And if we have said that X should expect a high win ratio, then those players who are almost as good will naturally have a correspondingly low win ratio. Yet we have just implied that they are amongst the best players that we have!

Common sense? Or just an excuse for poor results?



Friday, November 02, 2007

Paramedics

This is a blog for common sense (and for unnecessary puns) - not for discussion of metaphysics or formal philosophy.

In a detective story, the initial diagnosis may look like it is causing a paradox. But once you have watched or read through to the end, it is always the case that there was no paradox, just an incorrect deduction.

In my example yesterday, we had two conclusions, one drawn from each line of data. Those two were fair enough. But it was then just lazy or presumptuous to draw another conclusion from those two conclusions, instead of from the data.

So once we understand the data then there is no paradox.

That only leaves quantum theory ...

Wednesday, October 31, 2007

Touching the Data

This note is not really new material for those who work with me, it is one of those examples that I have been dredging out for year after year. But as I've just mentioned the reverend Simpson, and as this blog is holistic, it seems appropriate to head back to the analysis and evaluation of marketing activity.

If programme 1 performs better than programme 2 in a first phase, with a significantly higher response rate, and if programme 1 also performs better than programme 2 in a second phase, - then that does NOT necessarily mean that programme 1 has performed better than programme 2 overall. Even if programme 1 "wins" subsequent phases.

Nothing to do with creative or external factors, just really simple maths. Hence common sense.

But most people seem to understand this better when related to football than to marketing. With my invented numbers:





Easy.

I just need to recognise, manage and control this effect in real campaigns every single day.

Wednesday, October 24, 2007

Disinterested

The word is often misused, but this blog has broader ambitions than pointing out minor semantic errors.

Before my diversion into the future of customer relationship marketing, I almost did a typical diary post … I went to x show, it got x stars from me etc. But this blog is broader than that too.

I said that most of the reviews that you see elsewhere are only the the gushing sycophantic praise of professional critics who long to get quoted on billboards and invited for celebrity interviews.

If any magazine really gave honest reviews to the 50% of releases that are below average, then it would be highly unlikely to get the next exclusive interview with the famous cover star. That applies as much to the criticism of strikers' performance on Football Focus as to product reviews or film reviews in any glossy publication.

And the same thing goes for any articles that do not criticise those who advertise around there. Be careful whose opinions you trust.

Thursday, September 20, 2007

Being rude to your hosts


The Indian cricket team had to win today's match against the host nation South Africa to qualify for the semi-finals of the 20:20 World Cup. They scored 153 batting first.


The math was then very simple. Even if South Africa scored between 126 and 152, they would still go through with India because they both had a higher run rate than New Zealand.


It was very clear from early in the SA innings that they would never get the 154 to win the match. However, they could still have made 126 if India slacked off once victory was secure.


India did not slack off. Not a very nice way to treat your hosts. Without any hurt to themselves, they could have given the host nation, the tournament, and possibly the future of cricket a huge lift by allowing them a few more runs.

But they were right to keep up the pressure. Enormous credit to the players and to the very principle of sport. Integrity won here today.


Wednesday, September 05, 2007

Two per cent


I should add another note to yesterday's question instead of hiding clarification in the comments - damn this artificial hundred word limit :)

But I was not trying to trick anybody. There was no lateral thinking required. I was not hiding anything. The weight of the basket is completely irrelevant. It was really just very simple maths. Nothing else.

I was only doing the same thing that I often do in my job as a marketing consultant, showing that a very simple mathematical result does not always correspond with what your "intuition" tells you when you first see the question.

What is correct, the maths or your intuition?


Tuesday, September 04, 2007

One per cent


Recent stuff was about words. I am a marketing consultant, but I mainly work with numbers, and I believe in things that can be measured. Sometimes those things may initially appear unpalatable. But with just a few seconds of thought, it should all be obvious.

I'll keep the numbers round and simple. Imagine that you got a large basket of 100 kilos of fresh organic fruit delivered to your door while you were out.

Obviously fruits left outside will slowly shrivel as water evaporates. By the time that you got home, let's assume that the proportion of water has dropped from 99 percent to 98 percent

So, very approximately, how much does the basket of fruit now weigh? About 98 kilos?

...

Does your common sense tell you that the answer is only 50 kilos?



Sunday, September 02, 2007

ESP

Following on from last week's incident on the roof, today I heard from another psychic. I don't even know his name, he is some sort of expert on living underground, but this guy's extra-sensory abilities seem comparable to any celebrity psychic.

I need to put in context and give specific facts to prove the point. Today I had lunch at my parents' house with some old friends from Zambia. It was more than just lunch really, I picked them up from their home in East London, drove them down South, spent the afternoon there, then drove them back in the evening.

The psychic was on the radio. I don't normally listen to Radio Four at weekends, but the conclusion to the cricket provided interest and entertainment on the long drive back. Then, on conclusion of the match, it switched back to rejoin with the normal Sunday programming. And then I heard this guy waffling about going down a mine. And then he said the mine was in the copperbelt of Zambia.

And I had just spent the afternoon listening to old stories about Zambia. The probability must be so astronomical as to rule out coincidence. There was no way the guy on the radio could have known that. Sally Morgan eat your heart out!