Exploring Randomness: Delusions and Opportunities 1

Recent Criticisms of Statistics? Taleb, Nassim Nicholas (2007) Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, Second Edition, Random House, New York. Taleb, Nassim Nicholas (2007). The Black Swan: The Impact of the Highly Improbable Random House, New York. 2

Problems with Statistics Education Textbook-based and Technique-based Textbook content is circa 1960 Inference Logic was always controversial Computers & Software Change Everything Inertia to Curriculum Change 3

Examples of Modern Statistics Featuring Use of graphics, smoothing and simulation for exploration and summary Exploratory use of parametric models Claim Surprising Results (even though simple methods) Useful for real life 4

Example 1 - When is Success just Good Luck? An example from the world of Professional Sport 5

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His team: Geelong 7

Geelong 8

Recent News Report “A crowd of 97,302 has witnessed Geelong break its 44-year premiership drought by crushing a hapless Port Adelaide by a record 119 points in Saturday's grand final at the MCG.” (2007 Season) 9

Sports League - Football Success = Quality or Luck? 10

Are there better teams? How much variation in the league points table would you expect IF every team had the same chance of winning every game? i.e. every game is Try the experiment with 5 teams. H=Win T=Loss (ignore Ties for now) 11

5 Team Coin Toss Experiment Win=4, Tie=2, Loss=0 but we ignore ties. P(W)=1/2 H is Win, T is L 5 teams (1,2,3,4,5) so 10 games T T H T T H H H H T *TTHT *THH *HH *T * TeamPoints *LLWL W*LWW WW*WW LLL*L WLLW*  Typical Expt lg.points 12

Implications? “Equal” teams can produce unequal points Some point-spread due to chance How much? 13

Sports League - Football Success = Quality or Luck? 14

Simulation of 25 league outcomes with “equal teams” 16 teams, 22 games, like AFL lg.points.hilo 15

Sports League - Football Success = Quality or Luck? 16

Does it Matter? Avoiding foolish predictions Managing competitors (of any kind) Understanding the business of sport Appreciating the impact of uncontrolled variation in everyday life (Intuition often inadequate) 17

Postscript! 2008 Results 18

Example 2 - Order from Apparent Chaos An example from some personal data collection 19

Gasoline Consumption Each Fill - record kms and litres of fuel used Smooth ---> Seasonal Pattern …. Why? 20

Pattern Explainable? Air temperature? Rain on roads? Seasonal Traffic Pattern? Tire Pressure? Info Extraction Useful for Exploration of Cause Smoothing was key technology in info extraction 21

Aside: Is Smoothing Objective? Data plotted ->> 22

Optimal Smoothing Parameter? Depends on Purpose of Display Choice Ultimately Subjective Subjectivity is a necessary part of good data analysis Note the difference: objectivity vs honesty! 23

Summary of this Example Surprising? Order from Chaos … Principle - Smoothing and Averaging reveal patterns encouraging investigation of cause 24

Example 3 - Utility of Averages Arithmetic Mean – Related to Investment? AVG = 5.5/4=

Stock Market Investment Risky Company - example in a known context Return in 1 year for 1 share costing $ % of the time % of the time % of the time % of the time i.e. Lose Money 50% of the time Only Profit 25% of the time “Risky” because high chance of loss Good Investment? 26

Independent Outcomes What if you have the chance to put $1 into each of 100 such companies, where the companies are all in very different markets? What sort of outcomes then? Use coin- tossing (by computer) to explore …. HH,HT,TH,TT each with probability.25 27

Stock Market Investment Risky Company - example in a known context Return in 1 year for 1 share costing $ % of the time % of the time % of the time % of the time HH HT TH TT 28

Diversification: Unrelated Companies Choose 100 unrelated companies, each one risky like the proposed one. Outcome is still uncertain but look at typical outcomes …. One-Year Returns to a $100 investment Break Even Average profit is 38% - Actual profit usually +ve risky 29

Gamblers like Averages and Sums! The sum of 100 independent investments in risky companies can be low risk (>0)! Average > 0 implies Sum > 0 Averages are more stable than the things averaged. Square root law for variability of averages Variability reduced by factor  n 30

Summary of Example 3 Diversification of investments allows tolerance of risky investments Simulation and graphics allow study of this phenomenon 31

Example 7 - Survival Assessment Personal Data is always hard to get. Need to make careful use of minimal data Here is an example …. 32

Traffic Accidents Accident-Free Survival Time - can you get it from …. Have you been involved in an accident? How many months have you had your drivers license? 33

Accident Free Survival Time Probability that 34

Accident Next Month Can show that, for my 2002 class of 100 students, chance of accident next month was about 1%. 35

Summary of Example 7 Very Simple Survey produced useful information about driving risk Survival Analysis, based on empirical risk rates and smoothing, is a general way to summarize duration information 36

Example 8 - Lotteries: Expectation and Hope Cash flow –Ticket proceeds in (100%) –Prize money out (50%) –Good causes (35%) –Administration and Sales (15%) 50 % $1.00 ticket worth 50 cents, on average Typical lottery P(jackpot) =

How small is ? Buy 10 $1 tickets every week for 60 years Cost is $31,200. Lifetime chance of winning jackpot is = …. 1/5 of 1 percent! lotto 38

Summary Surprising that lottery tickets provide so little hope! Key technology is exploratory use of a probability model 39

Example 9 - Peer Review: Is it fair? Average referees accept 20% of average quality papers Referees vary in accepting 10%-50% of average papers Two referees accepting a paper -> publish. Two referees disagreeing -> third ref Two referees rejecting -> do not publish Analysis via simulation - assumptions are: 40

Ultimately published: *13 (approx) =9 papers out of others just as good! peerpeer 41

Peer Review Fair? Does select some of the best papers but Does not select most of the best papers Similar property of school admission systems, competition review boards, etc. 42

Summary of Example 9 Surprising that peer review is so dependent on chance Key procedure is to use simulation to explore effect of randomness in this context 43

Example 10 - Investment: Back-the-winner fallacy Mutual Funds - a way of diversifying a small investment Which mutual fund? Look at past performance? Experience from symmetric random walk … 44

Trends that do not persist rwalk 45

Implication from Random Walk …? Stock market trends may not persist Past might not be a good guide to future Some fund managers better than others? A small difference can result in a big difference over a long time … 46

A simulation experiment to determine the value of past performance data Simulate good and bad managers Pick the best ones based on 5 years data Simulate a future 5-yrs for these select managers 47

How to describe good and bad fund managers? Use TSX Index over past 50 years as a guide ---> annualized return is 10% Use a random walk with a slight upward trend to model each manager. Daily change positive with probability p Good managerROR = 13%pa p=.5 6 Medium manager ROR = 10%pa p=.5 5 Poor managerROR = 8% pa p=

fund.walk.test 49

Simulation to test “Back the Winner” 100 managers assigned various p parameters in.54 to.56 range Simulate for 5 years Pick the top-performing mangers (top 15%) Use the same 100 p-parameters to simulate a new 5 year experience Compare new outcome for “top” and “bottom” managers 50

Top 18% Start=100 fund.walk.run Futility of Past Performance Indicators 51

Mutual Fund Advice? Don’t expect past relative performance to be a good indicator of future relative performance. Again - need to give due allowance for randomness (i.e. LUCK) 52

Summary of Example 10 Surprising that Past Performance is such a poor indicator of Future Performance (not enough for “due diligence”) Simulation is the key to exploring this issue 53

Ten Surprising Findings 1.Sports Leagues - Lack of Quality Differentials 2.Gasoline Mileage - Seasonal Patterns 3.Stock Market - Risky Stocks a Good Investment 4.Industrial QC - Variability Reduction Pays 5.Civilization - City Growth can follow Zipf’s Law 6.Marijuana - Show of Hands shows 20% are regular users 7.Traffic Accidents - Simple class survey predicts 1% chance of accident in next month 8.Lotteries offer little hope 9.Peer Review is often unfair in judging submissions 10.Past Performance of Mutual Funds a poor indicator of future performance 54

Ten Useful Concepts & Techniques? 1.Sports Leagues – Simulate to Distinguish Quality from Luck 2.Gasoline Mileage – Averaging, and Smoothing, Amplifies Signals 3.Stock Market – Diversification Tames Risk 4.Industrial QC - Management by Exception 5.Population of Cities – Utility of Models 55

Useful? 6.Marijuana - Randomness can protect privacy 7.Traffic Accidents – A Simple Survey Can Predict Future Risk 8.Lotteries – Charity, not Investment 9.Peer Review – Fairness could be Improved 10.Mutual Funds – Past Performance Unhelpful 56

Questions Will SFU graduates be “fooled by randomness”? How can stats education be improved? 57

For More Background … Taleb, Nassim Nicholas (2007) Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, Second Edition, Random House, New York. Taleb, Nassim Nicholas (2007). The Black Swan: The Impact of the Highly Improbable Random House, New York. 58

The End Questions, Comments, Criticisms….. 59

ExampleSlide # No. of Slides Leagues514 Gas196 Risky256 Accidents325 Lotteries373 Peer Rev.404 Mutual Fd4410 Overview543 Qual. Ctl614 City Pops659 Marijuana764 60

Example 4 - Industrial Quality Control Filling Cereal Boxes, Oil Containers, Jam Jars Labeled amount should be minimum Save money if also maximum variability reduction contributes to profit Method: Management by exception …> 61

Management by exception QC = Quality Control <-- Nominal Amount 62

Japan a QC Innovator from 1950 Consumer Reports (2007) –Best Maintenance History Almost all Japanese Makes –Worst Maintenance History American and European Makes Key Technology was Variability Reduction Usually via Control Charts 63

Summary Example 4 Surprising that Simple Control Chart could have such influence Control Chart is just an implementation of the idea of Management by Exception 64

Example 5 - A Simple Law of Life Sometimes we see the same pattern in data from many different sources. Recognition of patterns aids description, and also helps to identify anomalies 65

Example: Zipf’s Law An empirical finding Frequency * rank = constant Example: Frequency = Population of cities Largest city is rank 1 Second largest city is rank 2 …. Constant =

Canadian City Populations 67

Population*Rank = Constant? (Frequency * rank = constant) CANADA 68

USA 69

NZ 70

NZ 71

AUSTRALIA 72

EUROPE 73

Other Applications of Zipf Word Frequency in Natural or Programming Language Volume of messages at Internet Sites Number of Employees of Companies Academic Publishing Productivity Enrolment of Universities …… Google “Zipf’s Law” for more in-depth discussion 74

Summary for Zipf’s Law Surprising that processes involving many accidents of history and social chaos, should result in a predictable relationship Models help to describe complex systems, and to focus attention when they fail. 75

Example 6 - Obtaining Confidential Information How can you ask an individual for data on Incomes Illegal Drug use Sex modes …..Etc in a way that will get an honest response? There is a need to protect confidentiality of answers. 76

Example: Marijuana Usage Randomized Response Technique Pose two Yes-No questions and have coin toss determine which is answered Head 1. Do you use Marijuana regularly? Tail 2. Is your coin toss outcome a tail? 77

Randomized Response Technique Suppose 60 of 100 answer Yes. Then about 50 are saying they have a tail. So 10 of the other 50 are users. 20%. It is a way of using randomization to protect Privacy. Public Data banks have used this. 78

Summary of Example 6 Surprising that people can be induced to provide sensitive information in public The key technique is to make use of the predictability of certain empirical probabilities. 79