Round Numbers as Goals: Evidence from Baseball, SAT & ‘the Lab’ - PowerPoint Presentation

Slide1

Round Numbers as Goals:Evidence from Baseball, SAT & ‘the Lab’

(with

Devin

Pope,

In press,

Psychologial Science)

Slide2

The Paper in one slide

Rosch (Cog Psych 1975): ‘Cognitive Reference Points’Focal values in categories used to judge other valuesOur question: in a JDM way?Focus on performance scalesPrediction:P1: more effort just below RNP2: more f() just above RNFindings:Baseball: ‘Too many’ batters with a .300 batting averageSAT: ‘Too many’ retake with __90 vs. __00Lab: More likely to keep trying _9 vs. _0

8

7.7

Slide3

Study 1: Baseball

Background

Balls are thrown

Batters take turns (“at-bats”)

If ball is hit ~ >“hit”

Batting average

: “hits” / “at-bats”

BA is a good DV because:

Granular

Paid attention to by players

BA ~ {.200-.400}

Slide4

Study 1: Baseball (2)

Sole ‘round’ number: .300

Hypothesis: batters disproportionately prefer .300 to .299

Predictions:

1) ‘too many’ .300 season averages

2) Try hard to get/keep .300

Slide5

Data

All player-seasons 1975-2008

N=11,430

Granularity: > 200 at-bats

N=8,817

Graphs will focus on those with .280-.320

N=3,083

Slide6

Graph: Batting Averages(raw freqs)

At the end of the season

With 5 plate-appearences left

Z

= 7.35,

p

<.001

Slide7

How do batters achieve that?

Next, look at last play of season.HitsWalksSubstitutions

Slide8

Do .300 players substitute more out of their last at-bat?

Slide9

Do .299 players ‘walk’ less?

Slide10

Do .299 hit more on their last at-bat?

Endogenous exit for sure.

Better actual performance, maybe.

Slide11

Summary Study 1

“too many” .300 season averages

Achieved by

Fewer walks at .299

S

ubstitutions at .300

Maybe: greater hitting %.

Slide12

Limitations

One round number

 got lucky?

It is a small effect

Not in p-value

Not in SD

In terms of consequences

(just one play in the season)

Agents, managers, advertisers?

Slide13

Study 2: SAT re-taking

Many round numbers

Stakes are larger

Third party problem remains

But addressed empirically

Also: see Study 3

Slide14

Background on the SAT

Scored 400-1600

Intervals of 10

Retaking is allowed

(about 50% do)

HS Juniors and Seniors take it

Prediction: “too many” retake it if

__90 vs __00

Slide15

Data

College Board Test Takers Database

N= 4.3 million; 1994-2001

Last test only

Did individual retake it?

D/K!

Infer retaking rates from score distributions

Slide16

Inferring Retaking Rates

Don’t observe key DV

But:

Juniors can easily retake

Much more difficult for seniors

Juniors (but not seniors) should have

“too few” __70,__80,__90 scores

“too many” __00, __10 __20

Slide17

Let’s see

Graph with raw frequencies next

Slide18

SAT by Juniors and Seniors

Slide19

A better graph

Plotting the slope

F(x)/F(x-10)

(Uri: Explain Ratio=1)

Slide20

Graph with F(x)/F(x-10)

Explain the effect is not ONLY at __90

Slide21

Interpretation and Alternative Explanations

Find

: big jumps in F(x) at _00 (for juniors)

Infer

: disproportionate retaking below _00

Interpret

:

_00 is a goal

BUT

1) Maybe _00 really

is

discontinuously better

Version 1. Same effect, different agent

(can live with)

Version 2.

Arbitrary thresholds

(less so)

2) Maybe _00 is

perceived

as discontinuously better by test-taker

Next, look at (1) & (2) empirically.

Slide22

1) Is it discontinuously better to get a _00 than _90 in the SAT?

Compare admission with _90 and _00

Data 1:

(JBDM 2007) “Clouds Make Nerds Look Good”

N=1100 undergrad admission decisions

Null:

pr

(

admit|SAT

=1000) -

pr

(

admit|SAT

=990)=

pr

(

admit|SAT

=1010)-

pr

(

admit|SAT

=1000)

Tested at:

1200,

p

=.96

1300,

p

=.99

1400,

p

=.20

1500,

p

=.92

Small N, but nothing there directionally.

SAT not that important.

Slide23

Same test, different dataset

Data 2: ‘Ongoing’ project with Francesca Gino

MBA admission decisions & GMAT (<800)

GMAT=600, p=.09 (wrong sign)

GMAT=700, p=.93

Slide24

Alternative Explanations

1) Maybe _00 really is discontinuously better2) Maybe _00 is perceived as discontinuously better by test-taker

Slide25

Back to SAT dataset

Score sending reveals info.

If _00 disc. better than _90

 scores sent to disc. different schools.

Next: the graph

Schools predicted by score

Slide26

Slide27

Summary

Too many _70,__80,__90 retake SAT

About 10%-20% percentage-points too many

No effect on admission decisions

No effect on score sending decisions

We interpret:

_00 (becomes) a goal influencing retake decision if met/not-met.

Slide28

Motivation of Study 3

Studies 1 & 2 show large effects in the field

Alternative explanation: third party

Keep in mind though, that:

Baseball managers think locus is players

Also,

here

3

rd

party locus

is

interesting.

Does not predict admissions

Does not predict where SATs are sent

Study 3, eliminate by design

Slide29

Study 3

Scenarios inspired by Heath Larrick and Wu (

Cog

Psyc

1999)

“Imagine your performance is x”

“how motivated to do more”? 1-7

X is

below round number

just below

round number

above

round number.

Slide30

Study 3: Design

Three scenarios

Same order

Performance between subject

E.g. all three “just below”

Analyze scenarios combined

Slide31

Scenario 1

Imagine

that in an attempt to get back in shape, you decide to start

running

laps at a local track.

After

running for about

half an hour and having

done

[

18/19/20 ; 28/29/30

]

laps

you start feeling quite

tired

and are thinking that you might have had enough.

How

likely do you think it is that you would run

one more

lap

?

Slide32

Results for 3 scenarios combined