### Round Numbers Are Goals: Evidence from Baseball SAT takers and

```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 RN
P2: more f() just above RN
Findings:
• Baseball:
– ‘Too many’ batters with a .300 batting average
8
– ‘Too many’ retake with __90 vs. __00
Lab: 7.7
• SAT:
•
– More likely to keep trying _9 vs. _0
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}
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
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 season
With 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 %.
Limitations
1. 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)
Study 2: SAT re-taking
• Many round numbers
• Stakes are larger
• Third party problem remains
– Also: see Study 3
Background on the SAT
• Scored 400-1600
– Intervals of 10
• Retaking is allowed
• 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 slope
F(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”
– Null:
- 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 Explanations
1) 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 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 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