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

(with Devin Pope, In press, Psychologial

Science)

The Paper in one slide• Rosch (Cog Psych 1975): ‘Cognitive Reference Points’

– Focal values in categories used to judge other values

• Our question: in a JDM way?• Focus on performance scales• Prediction:

P1: more effort just below RNP2: more f() just above RN

Findings:• Baseball:

– ‘Too many’ batters with a .300 batting average• SAT:

– ‘Too many’ retake with __90 vs. __00• Lab:

– More likely to keep trying _9 vs. _0

87.7

Study 1: BaseballBackground• 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}

Study 1: Baseball (2)• Sole ‘round’ number: .300

• Hypothesis: batters disproportionately prefer .300 to .299

• Predictions:1) ‘too many’ .300 season averages2) Try hard to get/keep .300

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

Graph: Batting Averages(raw freqs)

At the end of the seasonWith 5 plate-appearences left

Z = 7.35, p<.001

How do batters achieve that?

• Next, look at last play of season.

– Hits–Walks– Substitutions

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

Do .299 players ‘walk’ less?

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

Endogenous exit for sure.Better actual performance, maybe.

Summary Study 1• “too many” .300 season averages• Achieved by– Fewer walks at .299– Substitutions at .300–Maybe: greater hitting %.

Limitations1. One round number got lucky?2. It is a small effect – Not in p-value– Not in SD – In terms of consequences • (just one play in the season)

3. Agents, managers, advertisers?

Study 2: SAT re-taking

• Many round numbers• Stakes are larger• Third party problem remains– But addressed empirically– Also: see Study 3

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

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

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

Let’s see

Graph with raw frequencies next

SAT by Juniors and Seniors

A better graph

Plotting the slopeF(x)/F(x-10)

(Uri: Explain Ratio=1)

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

Explain the effect is not ONLY at __90

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.

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.

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

Alternative Explanations1) Maybe _00 really is discontinuously better

2) Maybe _00 is perceived as discontinuously better by test-taker

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

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.

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 3rd party locus is interesting.– Does not predict admissions– Does not predict where SATs are sent

• Study 3, eliminate by design

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.

Scenario 1Imagine 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?

Results for 3 scenarios combined