round numbers as goals: evidence from baseball, sat & ‘the lab’
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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? - PowerPoint PPT PresentationTRANSCRIPT
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Round Numbers as Goals:Evidence from Baseball, SAT & ‘the Lab’
(with Devin Pope, In press, Psychologial
Science)
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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
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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}
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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
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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
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Graph: Batting Averages(raw freqs)
At the end of the seasonWith 5 plate-appearences left
Z = 7.35, p<.001
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How do batters achieve that?
• Next, look at last play of season.
– Hits–Walks– Substitutions
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Do .300 players substitute more out of their last at-bat?
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Do .299 players ‘walk’ less?
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Do .299 hit more on their last at-bat?
Endogenous exit for sure.Better actual performance, maybe.
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Summary Study 1• “too many” .300 season averages• Achieved by– Fewer walks at .299– Substitutions at .300–Maybe: greater hitting %.
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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?
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Study 2: SAT re-taking
• Many round numbers• Stakes are larger• Third party problem remains– But addressed empirically– Also: see Study 3
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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
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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
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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
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Let’s see
Graph with raw frequencies next
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SAT by Juniors and Seniors
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A better graph
Plotting the slopeF(x)/F(x-10)
(Uri: Explain Ratio=1)
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Graph with F(x)/F(x-10)
Explain the effect is not ONLY at __90
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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.
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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.
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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
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Alternative Explanations1) Maybe _00 really is discontinuously better
2) Maybe _00 is perceived as discontinuously better by test-taker
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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
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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.
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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
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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.
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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?
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Results for 3 scenarios combined