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10 Data Commandments to Overcome the Law of Small Numbers
1. 10 Data Commandments
for Overcoming
the Law of Small Numbers
Lessons learned during Seven Years of
Actuarial Work
By Stephen L. Kolk, ACAS
Vice President of Actuarial Services
& Chief Actuary of Grange Insurance Group
4. Always advance, or else
• He who moves not forward, goes
backward. – Johann Wolfgang von Goethe
• If everything's under control, you're
going too slow. –Mario Andretti
• Even if you're on the right track, you'll
get run over if you just sit there.
– Will Rodgers
5. TEAMWORK
• Coming together is a
beginning
• Keeping together is progress
• Working together is success
- Henry Ford
6. The LAW of LARGE NUMBERS
• The Law of Large Numbers states that
regardless of the shape of the original
distribution, the taking of averages results
in a normal distribution.
• Insurance is an uncertain business, so we have to use averages
• The bigger the number of items in our average, the smaller the
error.
• You need to average lots of items to be sure your average is
indicative.
• This is why we looked and will continue to look at industry results…
• This is also why we watch larger states more closely
7. GRANGE INSURANCE GROUP
by Company
0
20,000,000
40,000,000
60,000,000
80,000,000
100,000,000
120,000,000
140,000,000
160,000,000
1997 1998 1999 2000 2001 2002
GIA
RM
8. GRANGE INSURANCE GROUP
DWP by Major Product
0
20,000,000
40,000,000
60,000,000
80,000,000
100,000,000
120,000,000
140,000,000
160,000,000
1997 1998 1999 2000 2001 2002
PP Auto
Home
Farm
Comm Auto
Other
9. GRANGE INSURANCE GROUP
DWP by State
0
20,000,000
40,000,000
60,000,000
80,000,000
100,000,000
120,000,000
140,000,000
160,000,000
1997 1998 1999 2000 2001 2002
CA
CO
ID
MT
OR
WA
WY
10. The LAW of SMALL NUMBERS
• The Law of Small Numbers states that
there are not enough small numbers to
satisfy all the demands placed on them.
- Richard Guy, statistician
• You can't tell by looking [at a few examples].
• Superficial similarities spawn spurious statements.
• Capricious coincidences cause careless conjectures.
• Early exceptions eclipse eventual essentials.
• Initial irregularities inhibit incisive intuition
11. TEN ACTUARIAL
COMMANDMENTS
#10 – Ignore the law of small numbers
and truth will bite you.
#9 – Find credible data. How? Graph
thy data
#8 Skew is the rule
#7 Prune thy data
#6 Weed thy data
13. COMMANDMENT #1
KNOW THY DATA
• To understand what has happened,
find out what was counted and how.
14. Homeowners Pure Premium
PUREPREMIUM
ISO vs GIG companies
0
50
100
150
200
250
300
350
400
C a le n da r Q ua r te r En ding
GIA
RM
ISO
All GIG StatesHomeowners (excluding catastrophes) All Policy Forms Combined
15. COMMANDMENT #2
GROW THY DATA
• Master actuarial measurements by
studying and using knowledge
• Master business results by refining
databases and reports from them
• Keep basics a part of the many ways, old
& new, to capture and/or picture truth.
16. COMMANDMENT #3
SORT, SHUFFLE AND JUGGLE THY
DATA
• What numbers do best is forget
things. As soon as you write them
down, they forget both where they
have been and where they are going.
• So it takes actuarial work to make
numbers remember the right things.
17. COMMANDMENT #4
• SHOW THY DATA!
• Depict stories whenever possible with
graphs and pictures. The best way to say
this is to paraphrase St. Francis of Assissi:
“Use numbers only when absolutely
necessary.”
• In actuarial work there are a lot of
absolutely necessary times for numbers.
18. What rate change is needed
to cover a 15% trend change?
Losses
Adjustment Costs
Expenses
Total Costs
Premium
Combined Ratio
Cost
$60
10
30
$100
$100
100%
Trend
Change
+15%
+15%
New Cost
$69.00
11.50
30.00
$110.50
$100
110.5%
Required Rate Change = $110.50 / $100 = +10.5%
19. COMMANDMENT #5
• EXPLORE THY DATA
• To know, grow, and show data in a
true manner, you have to understand
the data.
• How? Spend time with thy data.
• DIG THY DATA! (pun intended)
20. COMMANDMENT #6
• WEED THY DATA!
• Flowers and fruits in thy data garden are
grand.
• But weeds creep in.
• To keep data flowers and data fruit
healthy… WEED THY DATA!
• Use the “Yellow Book”… make sure your
figures match official Annual Statements
21. COMMANDMENT #7
PRUNE THY DATA
• Give non-number people appropriate
focus. Match displayed precision to the
accuracy of the facts.
• Don’t tell more than facts reveal.
• Pruning corollary: DO SOME GRAFTING.
• Get and use more credible data when you
run out of truth.
22. What is happening to
Industry Homeowners’ Rates?
Conning Average Homeowner Premium Change
versus Homeowner Loss Costs
-2%
0%
2%
4%
6%
8%
10%
1996
1997
1998
1999
2000
2001
Mar'02
June'02
AnnualChangeinPercent
CPI - Total Housing Costs
CPI - Household
Furnishings
CPI - Medical Costs
CPI - Hospital and related
services
Conning Avg
Homeowners' Ins. Prem.
23. COMMANDMENT #8
• SKEW IS THE RULE
• My college statistical training was
incomplete. There I only learned about
the Normal Distribution.
• On the actuarial job, there is no normal
mountain of insurance data.
• Therefore, know that skew is the rule or…
be skewered!
24. GIA Farmowners vs Industry
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
110%
120%
1997 1998 1999 2000 2001 08/03
Year
AdjustedLossRatio
25. RM Farmowners vs Industry
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
110%
120%
130%
1997 1998 1999 2000 2001 08/03
Year
AdjustedLossRatio
26. COMMANDMENT #9
• GRAPH THY DATA
• This helps find the source of skewness
• Graphs also show clouds of truth
• Watch the clouds of truth to see which
way the winds are blowing.
• Are thy clouds of truth cumulonimbus, or
cirrus, or ??? …With gratitude to Luke
Howard, the Inventor of Clouds
28. COMMANDMENT #10
IGNORE THE LAW OF SMALL NUMBERS
AND TRUTH WILL BITE YOU.
• In other words, get out of thine own niche.
Explore the insurance universe
out yonder.
• Use your actuarial eyes to bring truth into
focus.
29. COMMANDMENT #11
BONUS COMMANDMENT: USE HUMOR
•Look for real-life surprises in the data
•Share the surprise in story form to stir up
laughter
•Tell funny data stories to stay connected
with people you work with
30. THE GREATEST
COMMANDMENT?
WHAT STORIES DO YOU LIKE TO TELL?
FIND CREDIBLE DATA TO LOVE
• Use it to carve a path of truth that strikes a
balance between stability and
responsiveness.
KEEP THE STORIES IN THE NUMBERS
• RESULT: Putting actuarial stories back
into the numbers. Do your part to keep
insurance companies healthy.
