Suboptimal Strategy in Performing Coincident Timing Task under

Risk

Keiji Ota

, Masahiro Shinya

1,2

and Kazutoshi Kudo

Laboratory of Sports Sciences, Department of Life Sciences, Graduate School of Arts and Sciences,

The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan

Japan Society for the Promotion of Science, Tokyo, Japan

Keywords: Decision-making, Risk-sensitivity, Response Variance.

Abstract: The best performance often goes hand in hand with risk in many sports. Players are engaged in considering

how much risk they take. Some studies reported that movement strategy is modified by risk-sensitivity.

Here, we investigated how people responded under risk to which high gain got closer to zero gain. We

designed new coincident timing task in which participants were rewarded with the highest score if they

pressed a button just at a target time (2300 ms) but they did not get a score if they responded after the target

time. In this task, the participants should take the variability of their response into account and take a risk-

neutral strategy to get the highest total score that was theoretically calculated. However, we found out that

the participants took a risky response compared with an estimated optimal response. This risk-seeking

strategy degraded a task performance. These results suggest that not only small variability in response but

also taking an optimal strategy is important to get higher performance under risk.

1 INTRODUCTION

The best performance often goes hand in hand with

risk in many sports. For example, probability of

scoring a point would be highest if a tennis player

succeed to hit a ball on line, but he or she loses a

point if the ball is out of the line by 1 mm. In such

situations, beginners should not aim for edge of the

line because they cannot control the ball accurately

enough. To take an appropriate strategy, players

should take risk as well as variability in their motor

output into account. Thus, players are engaged in

making a decision about where in a court they

should aim under risk.

Classical economic lotteries task have been used

to study about decision-making under risk. An

example would be a choice between (0.5, $100; 0.5,

$0) and (1, $50); a 50%:50% chance at $100 or

nothing versus a certain (100%) gain of $50. If

people are asked to choose either of two lotteries,

most people would averse the 0 outcome and choose

the second sure lottery. The expected utility theory

(von Neumann and Morgenstern, 1944) claimed that

people make a decision to maximize expected utility,

predicting that most people prefer the second lottery

even though on average the two lotteries have the

same mean payoff.

However, in the field of behavioural economics,

deviation from the expected utility theory has been

repeatedly demonstrated, which indicated that

human decision-making under risk is not always

rational (Kahneman and Tversky, 1979). Referring

this concept in behavioural economics, recent

research has been focusing on human selection

behaviour in motor task under risk.

For example, Wu et al., (2009) showed that

participants tended to be risk-averse in deciding

between classical economic lotteries, but they tended

to be risk-seeking in deciding between same lotteries

presented in stochastically equivalent motor form.

O’Brien and Ahmed (2013) showed that risk-

sensitive behaviour transferred across different

movements. They found that participants showed

same direction of risk-sensitivity between two

movements, that is, they tended to be risk-seeking in

performing both arm reaching movement and whole-

body movement. It has been suggested that

participants underestimated their own motor

variability, and then tended to be risk-seeking. (Wu

et al., 2009); (O’Brien and Ahmed, 2013);

(Nagengast et al., 2011). In contrast, Nagengast et al.,

Ota K., Shinya M. and Kudo K..

Suboptimal Strategy in Performing Coincident Timing Task under Risk.

DOI: 10.5220/0004640600130018

In Proceedings of the International Congress on Sports Science Research and Technology Support (icSPORTS-2013), pages 13-18

ISBN: 978-989-8565-79-2

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

(2010) indicated that participants are more risk-

averse in the face of increased uncertainty induced

by experimentally added large Brownian noise, but

they are risk-neutral when an added Brownian noise

is small. This result indicated that the direction of

risk-sensitivity could be changed according to

situation. These studies suggested that movement

decision-making is not always optimal under risk,

which is inconsistent with previous works claiming

models of optimal movement planning

(Trommesäusher et al., 2003a; 2003b; 2005).

In this study, we developed new coincident

timing task in which high gain and risk goes hand in

hand. The first purpose of this study is to investigate

relationship between risk-sensitivity and a task

performance. The second purpose is to investigate

inter-individual differences based on trial-by-trial

analysis. First, we compared a observed response in

the task with a theoretically calculated risk-neutral

response. We demonstrated that the participant’s

behaviour was not optimal under risk and then

discussed the relationship between risk-sensitivity as

well as response variability and a task performance.

Second, we demonstrated that there is an inter-

individual difference in responses following to miss

trials.

2 METHODS

2.1 Experimental Task

Twelve right-handed, healthy adults (6 male, 6

female; mean age 28.8 ± 8.7 yr) participated in the

experiment. All participants were unaware of the

purpose of the experiment. This study was approved

by the Ethics Committee of the Graduate School of

Arts and Sciences, the University of Tokyo.

We showed a time sequence of the experiment in

Figure 1A. After presenting the warning tone, an

imperative stimulus (visual cue) was presented on

the screen. Foreperiod interval between the warning

tone and imperative stimulus was randomly varied

from 800 ms to 1200 ms in steps of 100 ms. The

participants were required to press the bottom at

2300 ms after visual cue. This target interval was

fixed. A score of a trial was described as a function

of response error (time difference between an actual

response interval and the target interval). We termed

it “score function”.

There were two conditions tested with different

score functions. One was No Risk condition that had

a symmetric score function (Figure 1B). When the

participants responded within the target interval,

they receive a score for a trial as a positive linear

function of response interval. In addition, when the

participants responded after the target time, they

received a score as a negative linear function of

response interval. The maximum possible score of

100 point was associated with responding to the

target time perfectly.

The other was Risk condition that had an

asymmetric score function (Figure 1C). In Risk

condition, the highest gain (100 point) got closer to

zero. Within the target interval, the same score

function as that in No Risk condition was applied.

However, no score was given if the participants

responded after the target time. We termed it “miss

trial” in which they were cautioned by an unpleasant

alarm and flashed red lamp on the screen.

Figure 1: Experimental task. (A) Illustration of time

sequence. First waning tone was ringed. After randomized

foreperiod duration, visual cue was presented. The

participants were required to press the bottom at the target

time (2300ms) after the visual cue. A response error (time

difference between a response interval and the target

interval) was given to the participants in every trial. (B)

Symmetric score function in No Risk condition. A score

for a trial was given when the participants responded over

the target time. (C) Asymmetric score function in Risk

condition. A score for a trial was not given (i.e., 0 point),

if they responded after the target time. This “miss trial”

was cautioned.

We provided the participants with response error,

score for a trial and accumulated total score in each

trial. We also gave verbal instructions describing the

score function before each condition. The

participants performed 10 trials training, 100 trials in

No Risk condition and lastly 100 trials in Risk

condition. The participants were instructed to

maximize total score in each condition.

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2.2 Definition of Risk-sensitivity

We applied the score function of Risk condition to

the obtained distribution of response time in No Risk

condition (Figure 2Upper panel). We then calculated

the optimal mean response time by simply shifting

the distribution until the highest total score was

obtained (Figure 2Middle panel). The estimated

optimal mean response time was always smaller than

the target time given each participant’s own variance

in response time. This can be regarded as a

theoretical risk-neutral optimal response. Finally, we

defined risk-sensitivity as the difference between the

observed mean response time and the optimal mean

response time (Figure 2Lower panel).

Figure 2: Procedure of estimating risk-sensitivity. (Upper

panel) We applied the score function of Risk condition to

the obtained distribution of response time in No Risk

condition. (Middle panel) We shifted the distribution until

the highest total score was obtained. Left solid line means

the estimated optimal mean response time. (Lower panel)

We showed the distribution of response time in Risk

condition. Right solid line means the observed mean

response time. Risk-sensitivity was defined as the

difference between the observed and the optimal responses.

Positive risk-sensitivity value indicates that the

participants pressed the button later than the optimal

timing (risk-seeking response), and negative risk-

sensitivity value indicates that the participants

pressed the button sooner than the optimal timing

(risk-averse response).

2.3 Inter-individual Differences

In addition to the risk-sensitivity based on all the

trials, it would be interesting to see inter-individual

differences based on trial-by-trial analysis. We

focused on presages of miss trials and recovery from

miss trials in Risk condition. Trial-by-trial analysis

would explain inter-individual difference in

performing the task. We compared histograms of

response time in trials which are previous to miss

trials and that in trials which are preceded by success

trials. We also compared histograms of response

time from the trials following to miss and success. In

this paper, examples of two participants are

discussed.

3 RESULTS

All the participants took an inappropriate risk for

their own variance in response time. Observed

response time and estimated optimal response time

are plotted against standard deviation (SD) of

response time in No Risk condition for all twelve

participants (Figure 3). The observed response time

was higher than the estimated optimal response time

for all the participants, and thus positive risk-

sensitivity was observed.

Figure 3: Risk seeking strategy taken by the participants.

Theoretically, optimal response time (filled squares) must

be smaller than the target time as a function of one’s

variability in response time (x axis shows SD of response

time in No Risk condition as an index of the variability).

However, observed response time (open squares) was

higher than the estimated response time for all the

participants, which indicates that they took higher risk for

their own variability.

SuboptimalStrategyinPerformingCoincidentTimingTaskunderRisk

Figure 4: The results of correlation analysis. Negative correlation between SD of response time in Risk condition and total

score in Risk condition (A), negative correlation between risk-sensitivity and total score in Risk condition (B), positive

correlation between risk-sensitivity and SD of response time in Risk condition (C).

We then analyzed the effect of the variance in

response time and the risk-sensitivity on the total

score by calculating Pearson’s correlation coefficient

between them. The total score was affected not only

by response variance but also by suboptimal risky

strategy. The risk-sensitivity, as well as SD of

response time, had a strong negative correlation

between the total score (Figures 4 A&B; r = -0.75, p

< .01; r = -0.73, p < .01, respectively). Moreover,

there was strong positive correlation between SD of

response time and risk-sensitivity (Fig. 4C; r = 0.78,

p < .01). The result suggests that the larger response

variance is (i.e., less accurate in response time), the

higher value of positive risk-sensitivity the

participants had. The participants responded closer

to the target time even though they had large

response variance, thus, the value of risk-sensitivity

was high.

We also investigated inter-individual differences

based on trial-by-trial analysis. Examples of two

participants were shown in Figure 5. The histogram

of response time on the whole trials in Risk

condition are shown in Figures 5A and 5B. The

response times are normally distributed in both

histograms. The histograms from the trials before

miss (filled bars) and success (open bars) are shown

in Figures 5C and 5D. The shape of the histograms

from the trials before miss was similar to that from

the trials before success. It was not also different

between participants. This would suggest that miss

responses randomly occurred: miss responses were

independent on the response in the previous trials.

However, the histogram of response time from the

trials following to miss (filled bars) had obviously

different shape with that from the trials following to

success (open bars) in participant 2 (Figure 5F).

Earlier responses to the target time were shown after

miss trials more than after success trials. This would

indicate that participant 2 made a large

compensation after miss trials. He might strongly

avoid consecutive miss. On the contrary, such

tendency was not shown in participant 1 (Figure 5E).

In Figure 5E, some responses after miss trials were

plotted over the target time in contrast to Figure 5F,

which indicated that consecutive misses were shown

in participant 1.

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Figure 5: Inter-individual differences in trial by trial

compensation. Examples of two participants are shown.

(A, B) Histograms of response time on the whole trials in

Risk condition. Both histograms are normally distributed.

(C, D) Histograms of response time from the trials before

miss (filled bars) and success (open bars). Histograms

have a similar shape between them and between the

participants. (E, F) Histogram of response time from the

trials following to miss (filled bars) and success (open

bars). In participants 2, earlier responses to the target time

are shown after miss trials more than after success trials.

In participants 1, consecutive misses were shown.

4 DISCUSSION

This is the first study to assess the relationship

between risk-sensitivity and task performance. We

showed that the participants tended to be risk-

seeking under a risk situation where high gain and

zero gain are joining to each other. This risk-seeking

strategy, as well as response variability, had a

significant effect on degrading the task performance.

In Risk condition, the observed response time

was closer to the target time than the theoretically

calculated optimal response time, that is, all the

participants tended to be risk-seeking. Cumulative

prospect theory (Tversky and Kahneman, 1992)

would explain that this tendency might be due to

underestimation of their own response variance (Wu

et al., 2009); (O’Brien and Ahmed, 2013);

(Nagengast, et al 2011). The participants might

believe themselves to have smaller response

variability than they actually have, which would

likely influence them to respond closer to the target

time.

The asymmetric score function was applied in

Risk condition. Wu et al., (2006) found that

participants performed suboptimally when pointing

in the asymmetric expected gain landscape. On the

other hand, Trommershäuser et al., (2003a; 2003b)

showed risk-neutral and optimal movement planning

in the symmetric expected gain landscape. Our

participants might not be able to perform a

theoretically optimal strategy under the asymmetric

score function. This was confirmed by calculating

the difference between the observed total score and

the theoretically calculated total score. From the

typical example in Figure 2, this participant could

improve 924 points that was calculated by

subtracting the observed total score (i.e., 7582

points) from the optimal total score (i.e., 8596

points).

Risk-seeking behaviours are sometimes observed

in real sports fields. For example, professional NBA

basketball players attempt consecutive three point

shots after they successfully scored three points even

though the probability of taking points is decreased

(Neiman and Lowenstein, 2011). They may believe

they will succeed again. Therefore, suboptimal

decision-making would have the effect on degrading

a performance of beginners as well as experts in a

variety of sports.

We also investigated inter-individual differences

in responses following miss trials. In participants 2

in Figure 5F, earlier responses to the target time

were shown after miss trials more often than after

success trials. This indicated that he made a large

compensation with a different strategy. This

tendency was not shown in participants 1 (Figure

5E). The histogram of the response time from the

trials following to miss had similar shape to that

from the trials following to success. In contrast to

Figure 5F, some responses were plotted over the

target time, which indicated that consecutive misses

were shown. For this participant, the total score will

surely increase by responding within the target time

with surely strategy to avoid consecutive miss. The

behaviour following to miss would be an important

factor to explain the individual response pattern.

Thus, we need to investigate how these differences

are produced in future studies.

As implication for real sports field, our results

suggest that it is important to evaluate and improve

optimal strategy depending on each player’s skill

level. Coaches and trainers often instruct how to

move a body focusing on a form itself. In addition to

SuboptimalStrategyinPerformingCoincidentTimingTaskunderRisk

such instruction, instruction based on the

improvement of risk-handling strategy leads to

organize better training.

5 CONCLUSIONS

Under risk situation where high gain and zero gain

are joining to each other, optimal strategy can be

calculated depending on the player’s variability.

However, the participants tended to take higher risk,

possibly because of their underestimation of

variability. This suboptimal decision-making

resulted in reducing the total score. Therefore,

improving the risk-handling strategy can contribute

to improve task performance both for beginners and

experts in a variety of sports.

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