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Guidelines:1. This exam is open-note, open-readings, open-slides, but closed Internet. NO ONLINE RESEARCH. YOU CAN USE course lecture slides and readings only!! (Please view attached documents / slides.)2. Use the Word template provided. Please also bold any class terms in the write-up.3. As usual, no need for introduction, background, or conclusion. You can waste a max of
100 combined words on these superfluous parts.Questions:Part I: Descriptive Evaluate the decision making described in this case. Focus on the following four questions (but
some sections will be longer than others). A. Analyze the JCP shopper’s experience using course concepts, both before and after
the changes described in the case. (Hint: This is asking about JCP shoppers’ judgments and decisions).B. Analyze the weaknesses in JCP’s decision making process (errors, biases, etc.). Be
specific about identifying the psychological drivers underlying these shortcomings. C. Analyze the strengths in JCP’s decision making process, if any, and what decision
errors these strengths reduced or eliminated. (Hint: B & C are about organizational
decisions, not about shopper psychology). D. The CEO is not the only player in this story. What organizational factors either
exacerbated or reduced decision errors? (Hint: This is about Week 8 topics)Part II: Prescriptive Based on your Part I analyses, how can JCP (or a similar company) improve their decision
making process in this type of scenario? E. Suggest one or two prescriptions that would help a company like JCP make better
decisions in such situations. Be as specific as possible about what you would do and
what biases or problems you are trying to combat. Be concrete about how these
prescription(s) would be implemented. Take into account the costs (money, time, and
psychological) associated with your suggested changes and be realistic. Feel free to be creative here, but please make sure to rely on only concepts from this class.F. Be aware that executives may not be particularly receptive to your advice. What are
the sources of resistance and how would you overcome them?HINTS (READ CAREFULLY!):1. Please restrict yourself to the information provided in the case. There are many articles
about the company and these events in the news and online, but they are not relevant for
the final. Evidence from outside the case will NOT count. 2. This is not a research paper. Searching the Internet will NOT help you on the exam but
CAN hurt you by distracting you with irrelevant information. I’m interested in YOUR
application of our course concepts to a specific case, not your research abilities. 3. Assume we understand the class concepts (don’t waste words explaining them), but
indicate why the concepts are relevant. Use your application to show your understanding. 4. Do not just laundry list every bias you think applies to the situation. Thoughtful analysis
and justification are required. I would rather you concentrate on making a few points well
than listing a number of points and not elaborating on any of them in depth. 5. Do not just regurgitate stuff from class. Provide evidence from the case to support the
psychology, not examples from other companies or life. 6. Use only the concepts from this class to analyze the case! Do not base your response on
your knowledge from other business classes, especially marketing, or OB, or strategy. 7. I discourage direct quotes from the case. A few quotes may be useful, but you can usually
make the point more succinctly in your own words. You should definitely not directly
quote or even paraphrase from readings other than the case. 8. Use the principles we discussed in the week on organizational decision making to
maximize the efficacy of working with a partner. Do not just split up writing for Parts I
and II. Your prescriptions (Part II) should flow from your descriptive analysis (Part I)! 9. Finally, remember that hindsight is 20/20. It is natural to conclude that every bad
outcome results from a bad decision, but we discussed in class how good decisions can
still have bad outcomes due to inherent risks and uncertainty (and vice versa). It is
important for you to show that you are able to delineate good decisions from bad ones.
The case may not always have all the detailed information you would need to identify a
decision error definitively. However, do your best to convince us that your analysis does
not reflect a hindsight bias.PLEASE DO FOLLOW INSTRUCTIONS ABOVE ^ AND USE THE ATTACHED DOCUMENTS.
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BUS143 Winter 2019 Final Exam
Word Count:
123456789 123456790
Part I. Descriptive Analysis
A.
The Psychology of the JCP shopper’s experience: Before and After Changes
Your text here.
B.
Decision Making Process: Weaknesses
Your text here.
C.
Decision Making Process: Strengths
Your text here.
D.
Organizational Factors
Your text here.
Part II. Prescriptions
E.
One or Two Concrete Prescriptions and Why
Your text here.
F.
How to Overcome Resistance to Prescribed Changes
Your text here.
Personal bests as reference points
Ashton Andersona,b,1,2 and Etan A. Greenb,c,3
a
Department of Computer Science, University of Toronto, Toronto, ON, Canada M5S 3G8; b Microsoft Research New York City, New York, NY 10011;
and c Department of Operations, Information and Decisions, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104
Edited by Jose A. Scheinkman, Columbia University, New York, NY, and approved January 9, 2018 (received for review April 19, 2017)
Personal bests act as reference points. Examining 133 million chess
games, we find that players exert effort to set new personal best
ratings and quit once they have done so. Although specific and
difficult goals have been shown to inspire greater motivation than
vague pronouncements to “do your best,” doing one’s best can
be a specific and difficult goal—and, as we show, motivates in a
manner predicted by loss aversion.
reference points | personal bests | loss aversion | motivation | goals
There is nothing noble in being superior to your fellow man; true
nobility is being superior to your former self.
Attributed to Ernest Hemingway
A
long line of research suggests that small differences in outcomes are felt disproportionately when they bridge a reference point separating psychological losses from psychological
gains (1–3). This phenomenon of loss aversion explains a number of empirical puzzles: aversions to gambles in which losses
are possible (4), aversions to parting with randomly endowed
objects (5), and aversions to selling investments at a loss (6, 7).
Reference points provoke aversions to losses, thereby distorting
important decisions. But where do reference points come from?
One source of reference points is externally generated goals
(8), such as round numbers. For instance, baseball players, students, and marathon runners exert effort to outperform roundnumbered batting averages, standardized test scores, and race
times, respectively (9, 10). However, reference points can also
be internally generated, as when they correspond to expectations
(11, 12) or sunk costs (13). In this paper, we propose that the
internally generated goal of one’s personal best, or past peak
performance, acts as a reference point. For example, real estate
agents may try to beat their biggest sales, auctioneers may try to
beat their highest bids, and teachers may try to beat their best
evaluations.
We study personal bests in the context of chess ratings. We
hypothesize that players will stop playing once they set a new
personal best rating, out of an aversion to falling behind, and
that they will play longer and try harder when a personal best is
in reach, hoping to eclipse it. We ground these hypotheses in a
simple utility model, which we detail in Materials and Methods. In
our model, players choose whether to play and how much effort
to exert if they do. The loss-averse player experiences a positive
shock when her rating eclipses the reference point (10). In SI
Appendix, we model how reference-dependent risk preferences
affect opponent selection, but we find no support for the theorized relationship in the data.
A principal difficulty in testing these hypotheses is that individuals are typically far from their best, and hence behavior near
personal bests is rarely observed. We overcome this difficulty
by using a massive dataset comprising 133 million online chess
games played by 70,000 players, in which we observe 284,000
instances of new personal bests being set.
We find that a player’s best rating acts as a reference point.
First, win rates increase as players approach their personal best
ratings, suggesting that players exert effort to set new personal
bests. Second, players quit at discontinuously higher rates after
setting new personal best ratings, consistent with an aversion to
falling back into the domain of losses. For comparison, we con1772–1776 | PNAS | February 20, 2018 | vol. 115 | no. 8
duct comparable tests for round-numbered ratings. Whereas personal bests influence both decisions over whether to play and
how much effort to exert during games, round numbers only
influence decisions over whether to play.
The literature on goal setting concludes that specific and
appropriately difficult goals inspire greater motivation than
vague pronouncements to “do your best” (14, 15). Yet, when
performance is quantifiable, doing one’s best is a specific goal.
It is also calibrated to be appropriately difficult (cf. ref. 16)—
rarely impossible, and, if too easy, quickly surpassed and reset.
We show that people exert effort to do their best and quit once
they have done so, consistent with loss aversion around personal
best reference points.
Results
To test our theoretical predictions, we conduct an empirical analysis of behavior around personal bests in the context of chess ratings on the Free Internet Chess Server (FICS). A chess player is
assigned a rating, updated after every game she plays, that estimates her skill level. The FICS rating system is simple: when a
player wins, her rating goes up, and when she loses, it goes down.
How many rating points each player would gain with a win or
lose with a loss depends on the difference in the players’ ratings (see Materials and Methods for further details on the rating system). Ratings fluctuate around a player’s true skill, and,
when these fluctuations reach a new peak, the player sets a new
Significance
Research in psychology, economics, and neuroscience suggests
that small differences in outcomes are felt disproportionately
when they bridge a reference point separating psychological losses from psychological gains. However, knowledge of
where reference points come from is limited. We propose that
one’s personal best, or past peak performance, acts as a reference point by inducing effort when current performance
would otherwise fall short. Analyzing a massive dataset of
online chess games, we find that players exert effort to set
new personal best ratings and quit once they have done so.
In education, fitness, and other domains, technology is making performance quantifiable. Our results suggest that these
advances will motivate individuals to compete with their
past selves.
Author contributions: A.A. and E.A.G. designed research, performed research, analyzed
data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This open access article is distributed under Creative Commons AttributionNonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).
Data deposition: The data reported in this paper have been deposited in the Open Science Framework (https://osf.io/tsfgv/?view only=e9e1c483aa3d488797f2e70de86abea1).
1
To whom correspondence should be addressed. Email: [email protected]
2
Present address: Department of Computer Science, University of Toronto, Toronto, ON,
Canada M5S 3G8.
3
Present address: Department of Operations, Information and Decisions, The Wharton
School, University of Pennsylvania, Philadelphia, PA 19104.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1706530115/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1706530115
A
Number of observations
1e+06
5e+05
0e+00
−200
−150
−100
−50
0
Rating after game Personal best
5e+05
4e+05
3e+05
2e+05
1e+05
0e+00
−30
−20
−10
0
Rating after game Personal best
Fig. 2. Histogram of the difference between current ratings and personalbest ratings (zoomed in near the reference point on the right).
only 1 in 750 player-games results in a new personal best, we
still observe 284,000 instances of personal bests being set.
We observe how behavior changes as players approach and
surpass their personal best ratings. In the main text, we report
average outcomes for each rating point difference between a
player’s current rating and her personal best rating. Where comparisons are made between players whose ratings are just shy of
their personal bests and those who just set a new personal best
by winning the previous game, we restrict the sample to the 101.5
million player-games that follow a win. This restriction ensures
that observations on either side of the reference point are
comparable.
To observe how behavior changes as players approach their
personal bests, we compare behavior when players’ ratings are
close to their personal bests with behavior when players’ ratings are farther away. One concern with this approach, however,
is that certain types of players may be close to their personal
bests more often than other types of players. Thus, differences in
behavior may be confounded by differences in player attributes.
To address this concern, we run comparable regressions with
player fixed effects, which we report in SI Appendix. These estimates reflect only within-player differences in behavior, rather
than differences between players.
Quitting. What happens when players set new personal bests?
Fig. 3A shows how the probability of quitting varies with the distance between a player’s current rating and her personal best rating from before her last game. We define quitting as not playing
another game within 1 h of finishing the most recent game; in
SI Appendix, Fig. S8, we show qualitatively identical results for
a 24-h threshold. The probability of quitting jumps across the
B
Fig. 3.
Anderson and Green
Probability of quitting for at least 1 h around personal bests (A) and round numbers (B), with 95% confidence intervals.
PNAS | February 20, 2018 | vol. 115 | no. 8 | 1773
PSYCHOLOGICAL AND
COGNITIVE SCIENCES
personal best. The rest of the time, her current rating trails her
personal best.
Chess ratings are highly visible. Fig. 1 shows an example user’s
information page, which publicly and prominently displays the
player’s current rating and best past rating. Current ratings are
also shown beside players’ names when playing a game, and
players receive text and sound notifications when they reach a
new personal best.
We construct our dataset from the complete set of blitz games
(which are expected to last between 6 min and 30 min) played
on FICS between 2000 and 2015. Our unit of analysis is the
“player-game,” of which there are two per game: one for the
white pieces and one for the black pieces. The complete set
of blitz games comprises 313 million player-games across 156.5
million games. To produce the dataset for our main analyses,
we carry out a series of filtering steps. For example, we filter out player-games before a player’s 200th game, to allow
players to establish a meaningful personal best; we filter out
player-games where the player’s rating is too uncertain; and we
filter out player-games where the player has achieved a personal best in the last 20 games, so as to consider instances in
which beating a personal best is a meaningful goal (see Materials
and Methods for more details). After filtering, our dataset comprises 212 million player-games across 133 million games. Our
results do not depend on these filtering restrictions; as described
in SI Appendix, we replicate our empirical results with different filtering parameters and obtain meaningfully unchanged
results.
Fig. 2 shows a histogram of games at each value of the difference between a player’s current rating and her personal best
before her last game. Players are typically far from their personal best ratings—the median difference is −118 points, and
only 3.7% of games are played within 30 points of the player’s personal best. For reference, in most cases, a win against an equally
rated player adds 8 points, a loss to an equally rated player subtracts 8 points, and the greatest possible rating change from a single game is 16 points. In the histogram, values to the right of 0 represent instances of players setting new personal bests. Although
Number of observations
Fig. 1. Example user information display. RD measures the variance of a
player’s rating.
2e+06
A
B
Fig. 4.
Performance short of personal bests (A) and round numbers (B), with 95% confidence intervals.
reference point—a 4.5 percentage point, or 20%, increase. As
predicted, players are discontinuously more likely to quit after
setting a new personal best.
This effect is more pronounced for more-frequent players
and for long-standing personal bests. Among the half of players
whose median time between games is less than 10 min, the probability of quitting jumps 29% (a 4.6 percentage point increase
from a baseline of 15.7 percentage points), compared with a jump
of 14% (a 4.1 percentage point increase from a baseline of 30.5
percentage points) among less frequent players. Breaking a personal best that is fewer than 20 games old is associated with a
9% jump in the probability of quitting (a 2.0 percentage point
increase on a baseline of 22.2 percentage points), compared with
a 20% jump in the probability of quitting (a 4.5 percentage point
increase on a baseline of 21.9 percentage points) for personal
bests that have stood for at least 20 games.
Achieving a personal best precipitates not only a higher rate
of quitting but also longer quitting spells. Among those who quit
with ratings one point short of their personal bests, the median
duration between games is 752 min. Among those who quit after
eclipsing their personal bests by one rating point, the median
duration between games is 816 min.
For comparison, we measure quitting near round numbers,
which have been shown to act as reference points in other domains
(9, 10). Fig. 3B shows how the probability of quitting varies with
the distance to the nearest multiple-of-100 rating (where all ratings ending in 51 to 99 are to the left of 0, and all ratings ending in 01 to 50 are to the right of 0). As with personal bests,
players are discontinuously more likely to quit after breaking a
century marker—players with ratings ending in 01 quit 3.5 percentage points more often than players with ratings ending in 99.
This relative increase of 20% is the same as the corresponding relative increase around personal bests. (There is also a smaller discontinuous jump around the round number of 50—players with
ratings ending in 51 quit 0.6 percentage points, or 3.3%, more
often than players with ratings ending in 49.) By this comparison,
personal bests motivate as powerfully as round numbers.
We find evidence of a goal gradient, or the increase in intensity often observed when a goal is imminent (17–19), for roundnumbered ratings but not for personal bests. The probability of
quitting decreases as ratings approach a multiple of 100 but stays
flat as ratings approach personal bests. We suspect that this disparity follows from differential awareness of the two reference
points, rather than differential motivation. Players receive notifications of their personal best ratings only after they eclipse their
1774 | www.pnas.org/cgi/doi/10.1073/pnas.1706530115
previous best. Current ratings, by contrast, are shown beside
player names during every game they play. Hence, players whose
ratings trail their personal best ratings are likely more aware of
their proximity to round-numbered reference points than to their
personal bests.
Effort. Do players try harder when a personal best is within
reach? Effort is difficult to observe directly, so we measure effort
indirectly as performance relative to expectations. Specifically,
we compare observed win rates to predicted win rates, where the
predicted win rate is the empirically observed probability of a win
for a given difference in ratings between the player and her opponent. (We treat a draw as half a win.) In our data, players win
50% of games against equally rated opponents, they win 62% of
games against opponents whom they outrate by 100 points, and
they win 73% of games against opponents whom they outrate by
200 points. Do players win more often than these expectations
when they are close to their best ratings?
If effort enhances performance, and if players try harder when
a personal best is in reach, then win rates will outperform expectations when current ratings are just short of personal bests.
However, ratings fluctuate around a player’s true skill, implying that higher ratings overestimate ability. Hence, regression to
the mean predicts that win rates will underperform expectations
as current ratings approach personal bests. Jointly, these effects
predict that regression to the mean will subside, and may even
reverse, near personal bests.
Fig. 4A shows the difference between observed and predicted
win rates as a function of a player’s rating distance from her personal best. Away from the reference point, performance declines
as ratings increase, in line with regression to the mean. However, the trend abates about 10 rating points from the reference
point—approximately the distance at which a win could realistically set a new personal best rating. At the reference point,
performance is ∼1 percentage point higher than if the prevailing trend had continued unabated. This suggests that players try
harder when near their personal best—so much so as to reverse
the regression to the mean. Although we cannot identify the
mechanism by which performance improves (whether by heightened concentration, computer assistance, selection of overrated
opponents, or other means), the improvement implies that players find some way to exceed expectations when a personal best is
within reach.
Does effort subside just after setting a new personal best rating? In SI Appendix, Fig. S9, we estimate the same performance
Anderson and Green
Discussion
Quantitative measures of performance are ubiquitous, and peak
performance along these measures is often salient. Many students
care about their highest test scores (20), and many athletes care
about their fastest times (21). Moreover, quantitative measures
of performance are proliferating. Recent educational programs
in the United States expanded the use of test scores to evaluate
schools and teachers (22), and new devices quantify performance
along dimensions hitherto ignored. For instance, the proliferation
of accelerometers on wrists and in pockets has created a sudden
awareness of, and competitiveness over, the most steps one has
taken in a day (23). When performance can be tracked, peak past
performance becomes a salient benchmark for comparison.
Previous research shows that peak events factor disproportionately in experienced utility (24) and self-perceptions (25). We
show that peak performance acts as a reference point. Individuals exert effort to achieve new personal bests and quit once
they’ve done so.
Materials and Methods
The Rating System. FICS assigns a rating to every player at every point in
time using the Glicko algorithm, which is an extension of the popular Elo rating system used by official chess federations (26). The algorithm is Bayesian
and models a player’s rating as a Gaussian belief distribution characterized
by a mean and a variance, with an initial mean of 1,720 points and an initial
variance of 350 points.
The mean is the player’s rating and is updated from game results according to the ratings of the players. The amount the player gains from winning
a game is a logistic function of the rating difference between the player and
the opponent. For a rating difference D = ratingplayer − ratingopponent , the
victory reward is ∆ = k(1 − 1/(1 + 10−cD …
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