Goal Attainability and Performance: Do You Run Faster When You Can Run Slower? Mariya Burdinaa, R. Scott Hillerb, and Neil E. Metzc
Abstract
In this paper we test the importance of goal attainability by measuring whether performance improves when setting a more realistic goal. Goal-setting literature suggests that workers respond to challenging but achievable goals with increased performance. Empirical evidence supports the notion of goals increasing performance, however the evidence on how attainability of goals affects performance is mixed. This study uses publicly available marathon data from
1970-2015 to directly analyze the effect of a realistic goal on performance. For many non- professional runners the goal is to qualify for the Boston marathon, which involves running a certified marathon within a specified amount of time, where qualifying time depends on runner’s gender and age group. We test whether runners increase their effort, and consequently improve their performance if they enter a new age group, and as a result have a more attainable goal. We find that runners who enter a new age group and as a result have a more relaxed qualifying time, perform better than the runners whose qualifying time did not change. We also observe a non- linear relationship between the attainability of a goal and performance, as the goal becomes relatively easy, performance decreases.
Keywords: goal setting, performance, effort
JEL Classification: D84, J22, L83, Z20
a Assistant Professor of Economics, College of Business, University of Central Oklahoma, 100 North University Dr., Edmond, OK, 73034. [email protected], (405)974-2829. b Corresponding Author, Assistant Professor of Economics, Fairfield University, 1073 North Benson Rd., Fairfield, CT, 06824. [email protected], (203)254-4000, ext. 2795. c Assistant Professor of Economics, College of Business, University of Central Oklahoma, 100 North University Dr., Edmond, OK, 73034. [email protected], (405)974-5326.
1. Introduction
Incentive literature in economics often focuses on the efficacy of monetary rewards.
Improving productivity and results can be a function of the financial incentives, but non- pecuniary rewards are also important in many cases. These rewards are much more difficult to measure, and their mechanisms harder to understand, but in many cases, may be as important to personal incentives as monetary rewards. In a business environment, Corgnet, Gómez-
Miñambres, and Hernán-Gonzalez (2015) test the importance of goal-setting using an experimental setting. Hsiaw (2013) provides a theory model of goals as internal motivation, with realistic goals being important for achievement. In this paper we follow in the same line of literature by empirically exploring the importance of setting challenging while realistic goals.
Specifically, we test the effect of attainable goals on results, using the qualification of marathon runners for the Boston Marathon. Qualifying for the Boston Marathon could be the ultimate goal for many runners, yet it is elusive to most. In order to qualify for Boston, one must run a marathon on a certified course within a specific time limit determined by the Boston
Athletic Association.1 This qualifying time is based upon an individual runner’s gender and age group. Runners in younger age groups have faster qualifying times than runners in older age groups and males have faster qualifying times compared to females. This qualification structure makes runners more capable of qualifying once they age into the next cohort.
Figure 1 shows the number of finishers by age for the Boston Marathon in years 2012-
14.2 There is a noticeable spike in the number of runners who finish the race at the start of their
1 For the full list of rules on qualifying for Boston Marathon please see http://www.baa.org/Races/Boston- Marathon/Participant-Information/Qualifying.aspx 2 We examine the number of finishers as information is not available on age and runners starting the race. While there will be slightly less finishers than starters, an examination of finishers still allows us to see patterns by age. Also, in 2013 the number of runners finishing is low due to the very unfortunate bombing near the finish line.
2 age group. Ages 40, 45, and 50 have many more finishers than those just one year younger at ages 39, 44, and 49. The increase in the number of finishers at the beginning of a new age group could be explained by the qualifying standards becoming easier. However, data shows that the number of finishers drops one year into each age group, which suggests that runners may be willing to put effort into qualifying once they know their goals become more attainable.
[Insert Figure 1 here]
We suggest that runners entering a new age group have a more attainable goal because of the slower qualifying time, and thus may put in more effort to improve their finish time.
Generally, as in Hsiaw (2013) the easier the goal the less inclined a runner may be to stop early, maintaining a training schedule that allows for better results. This paper tests whether marathon runners improve their performance as their goal of qualifying for the Boston Marathon becomes more realistic when entering a new age group.
Running experts suggest setting specific, challenging, yet realistic goals in order to improve running times (for examples on running advice from experts see Frazier 2012, Johnson
2013, Keflezighi and Douglas 2015). This advice is largely based on goal-setting theory developed by Locke in (1968), which has been examined by researchers in the fields of psychology, weight loss, athletic performance, as well as economics. Goal-setting literature suggests that specific yet challenging and realistic goals improve performance.3 While much of the research supports the notion of goals needing to be specific and challenging, very few studies have examined whether or not attainability plays a key factor in improved performance.
Our paper attempts to further clarify the relationship between goal attainability and performance. We investigate how adjusting the goals from unattainable to more realistic affects
3 See Locke and Latham (1990) and (2002) for a more complete review of the literature.
3 performance. Using public data obtained from many well-known and sizeable marathons, we investigate whether marathon runners improve their performance as their goal of qualifying for the Boston Marathon becomes more realistic when entering a new age group or if their performance suffers due to the changes that make qualifying more challenging. We are able to collect data that allows us to determine how far from the BQ time the runner was in the past, and whether their past performance combined with the transition into a new age group affects their future performance.
For each marathon, runners may be motivated by three specific goals (Arbuckle 2014):
1. To finish
2. To improve upon the last finish time
3. To qualify for the Boston Marathon
Finishing a marathon is the goal for many first-time marathoners. The runners in our study have already accomplished this goal, as only those who ran at least two marathons were included in our dataset. Among these runners, improving the previous finish time is a recurring goal regardless of whether or not they are trying to qualify for Boston. Qualifying for Boston could be the most challenging goal for those who have not been able to do so in the past. For some, this goal may not be realistic, but for those who finished previous marathons close enough to the stated qualifying time, it could be attainable. Our dataset allows us to determine how close a runner was to BQ during their previous marathon race and thus to determine if a runner is likely to set the BQ time as a goal.
This paper is organized as follows. In Section 2, we present a brief review of literature looking into goal-setting and performance. In Section 3, we discuss the data, Section 4 the
4 research methodology, in Section 5 we present the results, and in Section 6 we provide the conclusions and discuss avenues for further investigation.
2. Literature Review
The goal-setting theory developed by Locke (1968) states that setting challenging yet achievable goals increases intrinsic motivation, and as a result improves performance. Latham,
Mitchel and Dossett (1978) examined Locke’s theory in workplace production and confirmed the link between goal-setting and workplace performance. When describing the characteristics of successfully set goals, Locke and Latham (1985) suggest that in order to boost performance, goals must be specific, challenging and also attainable and/or realistic. They hypothesized that unrealistic and unreasonable goals will result in failure, which will lead to a drop in motivation and lower overall performance.
Substantial research supports the idea that goals need to be specific and challenging
(Mento, Steel, and Karen 1987; Smith, Hauenstein, and Buchanan 1996; Goerg and Kube 2012).
Easy and non-specific goals do not provide enough motivation and as a result, performance suffers while challenging goals are a stronger motivator than “do your best” goals. Locke and
Latham (1990) and Locke and Latham (2002) reviewed an extensive amount of laboratory and field studies involving over 40,000 people. In more than 90 percent of the reviewed articles, they found either strong or mostly strong support for the idea that setting challenging goals improves performance more than setting less challenging goals.
Contrary to the volume of studies supporting the notion of goals needing to be specific and challenging, very few have examined whether or not attainability plays a key factor in improved performance. To our knowledge, few studies have empirically examined the impact of
5 realistic goal setting on performance. Among them, there is no consensus on whether attainable goals have a greater effect on performance compared to unattainable goals.
A study conducted by Locke and Somers (1987) was among the first to examine the characteristics of successful goals. The authors analyzed data from a natural experiment in which emphasizing the importance of goals resulted in improved performance. In their setting, the original goals were unrealistic and not enforced. Consequently, the goals were not met.
Intervention in the form of enforcing the importance of set goals and adjusting them to be more realistic demonstrated improved performance. It is not clear which change had a greater effect on the end result. However, the findings suggest that the potential for improved performance increases when goals become more attainable.
Researchers examining the idea of realistic goal-setting often turn to the area of weight loss. These studies have produced mixed results. In most cases, overweight people are advised to set small, reasonable goals when losing weight.4 Yet there is no solid evidence to demonstrate that this method is more successful. Some studies show that setting unrealistic weight-loss goals increases the probability of participants quitting the weight loss treatment (Dalle Grave et. al.
2005), or could lead to a greater weight regain after the treatment is over (Byrne, Cooper, and
Fairburn 2004). Other studies found no significant relationship between attainability of weight goals and weight loss or regain (Ames, Perri, and Fox 2005; Gorin, Pinto, and Tate 2007). In other studies when people had more ambitious goals, more weight loss was achieved when the participants set high and unrealistic goals (Fabricatore, Wadden, and Rohay 2008; Linde, Jeffery, and Finch 2004). De Vet, Nelissen, and Zeelenberg (2012) also found that participants who set
4 The Practical Guide Identification, Evaluation, and Treatment of Overweight and Obesity in Adults, 2000. National Institutes of Health. National Heart, Lung, and Blood Institute. North American Association for the Study of Obesity. Available at http://www.nhlbi.nih.gov/files/docs/guidelines/prctgd_c.pdf
6 unrealistically high goals put more effort into the weight-loss attempt. One reason for the mixed results from these studies is their reliance on an experimental setting which lacks a substantial sample size. Further, it is not clear what determines attainability of the goals discussed in these studies.
Studies examining the relationship between goal attainability and performance in the field of athletic performance also produce mixed results when testing the hypothesis of unrealistic goals and its possible diminishing impact on performance (Weinberg, Fowler,
Jackson, Bagnall, and Bruya 1991; Garland, Weinberg, Bruya, and Jackson 1988; Bar-Eli, Levy-
Kolker, Tenenbaum and Weinberg 1993; Bar-Eli, Tenenbaum, Pie, Btesh, and Almog 1997).
Garland et. al. (1988) proposed a theory which contradicted Locke (1968), stating that performance and goal difficulty exhibit a monotonically positive relationship, suggesting performance can only improve with increased difficulty of set goals. Locke (1991, 1994) responded to the criticism of his theory by pointing out shortcomings of the studies which could not confirm the link between goal attainability and performance. Bar-Eli et al. (1997) also suggested that the length of the performed experiments could have been too short in order to see significant differences in the outcomes of those with realistic and those with unattainable goals.
Bar-Eli et al. (1997) used field experiments to examine how goal difficulty and attainability affect performance. In their setting, competitive high school track athletes were given four different goal conditions: ‘do’ or ‘do your best’ (no goals), ‘improve by 10%’ (easy),
‘improve by 20%’ (difficult/realistic) and ‘improve by 40%’ (improbable/unattainable). The results show that those with specific goals performed better than those without set goals.
Additionally, those with difficult yet realistic goals increased their performance more than those with unrealistic goals or goals that were too easy. The major downside to most athletic
7 performance studies, similar to weight loss studies, is their reliance on experiments which often contain a relatively small number of observations which may not produce robust results. Our study uses a natural experiment setting and involves a large dataset over many years.
The closest study to our work is one conducted by Harding and Hsiaw (2014) who developed a theoretical model of consumer demand for an energy conservation program that involves non-binding, self-set goals. They also present empirical evidence supporting the notion that goals must be realistic in order to motivate performance. In their study, consumers who chose realistic goals when it came to energy conservation consistently saved more, achieving savings of nearly 11% more than those choosing very low or unrealistically high goals.
Finally, it is worth noticing that marathon data has received recent attention as it presents researchers with an opportunity to study goal setting and performance in a real-world, non- experimental setting. Markle, Wu, White, and Sackett (2015) use marathon data to study
Prospect Theory and found that setting a goal before running a marathon improved a runner’s performance on average by 6 minutes. Even though their study found that goal setting improves performance, they did not find the Boston marathon qualifying time to be an influence on participant satisfaction from running a marathon.5
3. Data
To investigate the relationship between goal attainability and performance, we use publicly-available data on finish results from many marathons over 45 years. We obtained this data by taking the finishers of three BQ marathons: Oklahoma City Memorial Marathon (2001-
2014), California International Marathon (1990-2013), and Grandma’s Marathon (2001-2014),
5 There are other recent papers on behavioral biases using marathon running data, see Allen, Dechow, Pope, and Wu (2014).
8 and finding all race results from these finishers on the website Athlinks.com, a vast repository of race data. All three marathons are certified as BQ marathons, and the California International and
Grandma’s marathon are among those BQ marathons cited as “good for qualifying”.6 We used these races because of their status and with their racing histories we could collect names of marathon runners who are likely to be eager to qualify for Boston. Complete racing histories were obtained for most of these finishers from 1970-2015, providing repeat observations and experience data.
The following variables were included in the race results of each observation: the participant’s first and last name, age, gender, race name, year, date, and finish time. We were able to match participants by their name and city of residence from year to year in each marathon and determine participants who ran two or more marathons. Some marathons in certain years were missing either age or gender variables, yet, we were able to reconstruct most of the missing data for marathoners participating in two or more races. We also had to exclude runners from our final data set who had a common first and last name as it was impossible to determine which individual participated in which race.
The key information in our analysis is the Boston qualifying standards which are determined by the Boston Athletic Association and differ based upon the participant's gender as well as the age of each participant on the date of the Boston Marathon for which they are qualifying. Table 1 presents BQ standards based on athlete’s age and gender. The most recent
6 Currently there are more than one thousand certified marathon courses which runners can use to Boston Qualify. The Boston Athletic Association reports which marathons are usually known as the best to BQ, based either on the number of qualifying individuals or percent of qualifying individuals. Usually these marathons are flatter and have more favorable running weather conditions.
9 standards were adopted for the 2013 Boston Marathon. Prior to 2013, all age group qualifying times were five minutes longer.7
[Insert Table 1 here]
The cutoff date to attempt qualifying is the second week of September, slightly more than half a year prior to the Boston Marathon.8 This means any officially certified marathon held between the third week of September and the second week of the next September is considered to be a qualifier for the Boston Marathon in the following year. For example, those running a marathon in December 2011, if qualified will be eligible to participate in the 2013 Boston
Marathon. Those running in April 2012, if qualified, are also eligible to run the Boston Marathon in 2013.
The timing of the qualification process along with the change in the qualifying time by age groups leads to some complex age issues which we must consider in our study. The main challenge in our investigation is presented by the absence of a birthday date for each participant.
The rules of qualifying state that the qualifying marathon finish time should be less than the predetermined qualifying time for the age group the runner is in during the Boston Marathon, not during the qualifying marathon. We can estimate BQ time for most of the participants, but for some who are close in their age to their next age group it may not be possible. For example, a female who turned 34 in September 2015 and will be 35 in April 2017 for the Boston Marathon for which she is trying to qualify, may use results from a December 2015 marathon race. Thus,
7 Once every several years the BQ times are adjusted to limit the number of runners in the field. As the number of runners that BQ each year increases, the organizers make the qualifying time more difficult (faster time) to limit the size of the field. Prior to 2013, the standards were adjusted once in 2003, but only for those runner over the age of 55. The BQ times in Table 1 are correct for all runners since 2003, but they are different for this small portion of runners in our sample who are over age 55 and ran prior to 2003. http://www.baa.org/news-and- press/news-listing/2011/february/boston-athletic-association-announces-new-registration-process.aspx. 8 The Boston Marathon is usually held on the third Monday of April.
10 she needs to run under 3 hours and 40 minutes to BQ, as that's the qualifying time for the 35-39 age group. A different female runner who turned 33 in March 2015 and is also using December
2015 marathon to qualify for Boston, also needs to run that marathon under 3 hours and 40 minutes to qualify as she also will be 35 during the 2017 Boston marathon. Even though one female was 34 during December qualifying marathon and another one was still 33, both of them were using the same qualifying standards. So, without knowing a person's birthday it is challenging to determine what their qualifying time is and if they qualified or not. For consistency purposes we assumed that those of age 34, 39, 44, 49, 54, 59, 64, 69, 74, and 79 are qualifying using the next age group qualifying times. While this introduces inevitable measurement error, there is no other way for us to estimate the age of each runner at the next
Boston Marathon. In order to address the potential for bias, we conduct age falsification tests to ensure our results are not driven by any measurement error.
Our dependent variable is the marathon finish time, measured in minutes. We estimate several models using different independent variables. The main independent variables in each model indicate if a runner entered a new Boston Qualifying age group and if her qualifying standards became more challenging, stayed the same, or got easier. Initially we use a variable showing if the runner entered a new qualifying age group. Since runners entering the new BQ age group have more realistic qualifying goals, they may put more effort into qualifying, and as a result improve performance. Thus, we expect this variable to have a negative significant coefficient. The modification of this variable is a set of dummy variables indicating if the qualifying time increased or decreased, and by how much. Using the runner’s age and current qualifying time, we are also able to determine by how much the qualifying standards have changed. Boston qualifying standards get easier by either 5, or 10, or 15 minutes. At the same
11 time, since qualifying standards have changed in 2013, we had a group of runners for whom standards became more challenging by 5 minutes.
Additional examination of the data provided us with guidance for the econometric specifications. Looking at the average finish times by age, we did not observe a significant difference between those that changed Boston Qualifying age group. Performance should improve the most when the goals are challenging yet realistic. If we consider a sample of those for whom the qualifying time changes then three scenarios are possible. First, there will be some runners which are already close to qualifying for Boston and thus, lowering the qualifying standards for them will make the goal more attainable but relatively easy. There are also those who are quite far away from qualifying and adjusting their qualifying time by 5-15 minutes will not make the goal of qualifying more realistic. Finally, there are runners who are somewhat close to qualifying, thus their goal is still challenging and adjusting qualifying times will make it more realistic. We expect to see the last group improve their performance the most compared to any other group.
When it comes to running marathons, there is no single scheme that will determine how much one can improve, which makes it difficult to determine for which groups of runners it will be “easy” or “challenging” to qualify for Boston (Gaudette 2013). Bar-Eli et al. (1997) used
10%, 20%, 40% improvement targets as a measure of goal difficulty, but in a marathon, a 10% improvement is a difficult goal to attain (i.e. a 10% improvement from the most common finish time of 4 hours would be 24 minutes). The improvement target is based on the number of minutes by which a runner missed her qualifying time in the previous marathon. Of course, it is entirely possible that a 5 minute improvement may be very difficult for some and quite easy for
12 others. For this reason, we include a runner’s previous personal record (or personal best) marathon finish time to control for overall ability.
Table 2 shows the difference in finish time between runners for whom qualifying standards did not change, and for whom qualifying standards either decreased by 5 minutes or increased by 5, 10, and 15 minutes respectively. All differences are compared to runners for whom the qualifying standards did not change, whom we excluded from the table. Each column groups runners based on how close they were to qualifying for Boston in the previous race. Each row groups runners according to the change in qualifying time based on them entering a new age group. The difference in finish time is measured in minutes.
[Insert table 2 here]
The patterns in each column and across columns show that runners have interesting reactions to their change in BQ time relative to their previous finish time. The most noticeable thing about the results is that regardless of their previous finish time, all runners for whom qualifying standards became more challenging, had a slower finish time compared to those for whom those standards did not change. This observation is consistent with goal setting theory and suggests that once the goal became more challenging, the runners performed worse. We also notice that runners who missed their qualifying time by less than 5 minutes and gained 5 minutes of qualifying time, on average, were slower than those for whom qualifying time did not change.
While for runners who missed qualifying time by more than 5 minutes the result is reversed.
Those who gained 5 minutes of qualifying time were on average faster than those for whom qualifying time did not change. This suggests that runners near the BQ time that experienced a more attainable, but still difficult goal (they needed to improve by 5-10 minutes to BQ), tended to improve more than most other runners. At the same time, for those who missed qualifying by
13 less than 5 minutes and at the same time gained 5 minutes of qualifying time, the goal became too easy, and thus, there was no need for those runners to try harder.
Finally, we observe that those who gained 10 or 15 minutes were on average slower than those for whom qualifying time did not change. Even though this observation is somewhat contradictory to the goal setting theory, it is important to keep in mind that those runners are usually older than the average runner for whom the qualifying time did not change. Thus, without controlling for the age it is difficult to conclude whether these runners were faster or slower than those for whom qualifying time did not change.
We account for the attainability of a qualifying goal by including a variable measuring how much a runner missed qualifying in the previous race. A runner may also estimate their qualifying chances by the amount of time it took them to run their best race, so we take into account the runner’s personal best marathon time and use it as another proxy to control for a runner’s qualifying chance. As a result, we lose the first observation of each runner, but this allows us to better control for personal ability.
The other independent variables include runner characteristics such as age and gender. In order to control for a runner’s experience, we use the number of marathon and non-marathon races completed by the runner in the past. We use the number of races in the particular year as a proxy measuring runner’s preparedness for the marathon. Training for a marathon requires a serious commitment from a runner, but we have no way of observing if the runner was actually seriously training (i.e. completing their scheduled runs). Those who participate in numerous races may also be more likely to complete their training plan for the marathon. Additionally, we construct the variable showing if the runner has a potential to qualify based on her previous marathon finish time and her current Boston qualifying time.
14
The initial dataset of all runners, from all years and all races contains more than 5.5 million observations, but this includes many races which are not marathons. When cleared of all races but marathons and narrowed to the range of finishing times between three and five hours with multiple observations for each runner, the final sample contains 145,544 observations, but given the need to establish an initial race time, the observations in each regression are less.9
Variable definitions are presented in Table 3. Summary statistics are included in Table 4.
[Insert Table 3 here]
[Insert Table 4 here]
The average time for a runner in our dataset is 240 minutes, which is 20 minutes less than the reported overall average marathon time10, but that is largely due to the fact that we excluded races in which a marathoner finished in over 5 hours as the chances of qualifying are minimal.11
We also observe that 17% of our sample qualified for Boston at some point. The average time by which the runners missed their BQ time is 25 minutes and the average time by which a runner’s personal best race missed their BQ time is 12 minutes. Both of these statistics in our sample allow us to believe that qualifying is within reach for an average runner in our sample.
4. Methodology
9 We have also determined participants who had the same last and first name, yet were either from a different city or showed a large gap in the age while participating in marathons. We have assumed that these participants happened to have the same first and last name but were actually different people and thus are considered separate runners. 10 http://runrepeat.com/research-marathon-performance-across-nations 11 If we kept slower runners in the dataset, the average finish time was 261 minutes which is close to the 264 minutes average reported finish time for marathon runners http://www.livestrong.com/article/1002323-average- time-run-marathon/
15
We estimate the effect of a change in goal attainability on two separate models measuring performance. First, we estimate the effect of a change in age group on a runner’s performance during the marathon. The model uses the following general form:
푅푎푐푒_푡𝑖푚푒푖푗푡 = 훼0 + 훼1 ∑ 퐵푄_푐ℎ푎푛𝑔푒푖푡 + 훼2퐴𝑔푒푖푡 + 훼3퐺푒푛푑푒푟푖 + 훼4푀𝑖푠푠푒푑푖푗푡−1
+ 훼5퐸푥푝푒푟𝑖푒푛푐푒푖푡 + 훼6퐸푥푝푒푟𝑖푒푛푐푒_푆푞푖푡 + 훼7푅푎푐푒푠_𝑖푛_푦푒푎푟푖푡
+ 훼8푅푢푛푛𝑖푛𝑔_푃푅푖푡 + 훼9푀𝑖푛_푅푎푐푒_푇𝑖푚푒푖푡 + 훼10 ∑ 푀표푛푡ℎ푖푗 휖푖푗푡
Where 푅푎푐푒_푡𝑖푚푒푖푗푡 is athlete i’s finish time in year t at marathon j. 퐵푄_푐ℎ푎푛𝑔푒푖푡 is a set of variables showing if an athlete aged into a new Boston qualifying age group. We use several regression specifications to estimate the effect of a new age group on marathon finish time. In the first specification, we use 퐵푄_𝑔푟표푢푝_푐ℎ푎푛𝑔푒푖푡 variable indicating if a runner simply entered a new age group. In the second specification we add a dummy variable
퐵푄_푐ℎ푎푛𝑔푒_푛푒𝑔5푖푡 indicating if qualifying standards got tougher for a runner as a result of change in change in qualifying structure for the 2013 Boston Marathon. In the third specification we use a set of dummy variables 퐵푄_푐ℎ푎푛𝑔푒_푛푒𝑔5푖푡, 퐵푄_푐ℎ푎푛𝑔푒5푖푡, 퐵푄_푐ℎ푎푛𝑔푒10푖푡, and
퐵푄_푐ℎ푎푛𝑔푒15푖푡. These variables indicate if the qualifying standards for a runner decreased by 5 minutes, did not change, increased by 5, 10, or 15 minutes respectively.
퐴𝑔푒푖푡 and 퐺푒푛푑푒푟푖are athlete i’s corresponding age and gender (equal to 1 if female, and
0 if male) during the year t. We expect both, 퐴𝑔푒푖푡 and 퐺푒푛푑푒푟푖 variables to be positively related to marathon finish time on average, older runners and females have slower finish times compared to younger runners and males respectively. Variable 푀𝑖푠푠푒푑푖푗푡−1 measures by how much the runner missed the BQ time in their previous marathon, giving the improvement necessary if the qualifying time is not lowered. The E푥푝푒푟𝑖푒푛푐푒푖푡 term counts the total number
16 of races the runner has completed before race j in our dataset. This includes marathons and other races shorter than marathons. The variable 퐸푥푝푒푟𝑖푒푛푐푒_푠푞푢푎푟푒푑푖푡 is the square of
퐸푥푝푒푟𝑖푒푛푐푒푖푡. The variable 푅푎푐푒푠_𝑖푛_푦푒푎푟푖푡 provides the total races the runner completes in year t. The 푅푢푛푛𝑖푛𝑔_푃푅푖푡 and 푀𝑖푛_푅푎푐푒_푡𝑖푚푒푖푡 variables are intended to capture the racer’s maximum potential to that point, considering the best marathon time and the best overall time of the runner prior to the current race. ∑ 푀표푛푡ℎ푖푗 is a set of dummy variables indicating in which month runner i participated in the marathon j. We use month dummies to control for seasonal differences in races.
The error term is assumed to be normally distributed, and estimation is performed with a random-effects least squares regression. Several models are estimated with the independent variables slightly altered as described above.
5. Results
Table 5 provides the results of a random effects least-squares regression. Our dependent variable in each of the specifications is the marathon finish time in minutes for each runner in an individual race. Coefficients on month are excluded for space considerations.
[Insert Table 5 here]
In each of the regressions we observe that age is positively and significantly related to a runner’s marathon finish time. That is not a surprise as we expect older runners to have slower marathon finish times. The gender variable also has a predicted positive sign, indicating that on average, females have slower finish times by more than 11 minutes compared to the male racers.
The experience variable is positive and significantly related to the finish time, while the square of experience is negatively related to the finish time. This result is somewhat surprising as it
17 suggests that past participation in numerous races hurts one performance. One possible explanation for such a result is that the experience variable consists of all races a runner participated in, including 5-Ks and Half Marathons, which are less strenuous and require less training. Thus, it is possible that slower runners may choose to participate in these races more often. However, the negative sign on Experience_sq indicates there is a level of experience from which time begins to improve. As a group the experience terms indicate that experience does not help finish time initially, but leads to an improvement in time as experience increases. Another interesting observation is that the number of races a marathoner had during that particular year
(Races_in_year) is negatively related to their finish time, which indicates that runners who compete in many races may be more serious about their training and thus perform better while running a marathon. Running_PR and Min_Race_time variables are both positively related to the finish time, indicating that runners with faster personal records will have faster marathon finish times.
Column (1) presents the results of an econometric specification in which our main variable of interest, BQ_group_change shows what we would expect, a significant negative relationship with the finish time. As the qualifying for Boston Marathon becomes more attainable, runners will put more effort in finishing a marathon in faster time. On average, entering a new age group decreased finish time by 0.67 minutes.
Since qualifying standards became more challenging for those trying to qualify for the
2013 Boston Marathon, we wanted to see if that change had an effect on finish times of the runners. Column (2) presents the results of that regression, in which BQ_change_neg5 is the dummy variable indicating if the qualifying time decreased by 5 minutes, that is in order to qualify a runner must run 5 minutes faster. This change would be applicable to all runners who
18 did not change age groups and who ran qualifying marathons after September 2011. What we observe is a positive and significant relationship between this variable and finish time, which indicates that as the goal became more challenging, on average, runners had a greater marathon finish time. The runners who experienced an increase in qualifying standards on average slowed down by 1.41 minutes compared to runners that did not experience this change.
Column (3) expands on the simplest regression form and includes a set of dummy variables indicating if Boston qualifying standards got harder by five minutes or got easier by either five, ten, or fifteen minutes. The results suggest that for those who experienced more difficult qualifying standards, finish time was slower by about 1 minute compared to those for whom finish times did not change. Results also show that those who entered a new age group and as a result received five-minute slower qualifying standards were more likely to decrease their finish time, on average by 1.9 minutes compared to those for whom qualifying standards did not change. Those for whom qualifying standards got easier by 10 minutes also had faster finish times compared to the “no-change” group. The results also indicate that the runners for whom qualifying standards changed by 15 minutes did not have significantly faster times than those for whom the standards did not change. There are two things that can explain this result.
First, those who have a 15 minute reduction in qualifying time are older than those that have a 5 or 10 minute advantage. Second, it suggests that as the goal becomes not only attainable but also somewhat easy, runners did not put as much effort into accomplishing it. These results suggest that there is a non-linear relationship between goal difficulty and effort as we observe the goal becoming easier, at first runners tend to speed up, but when the goal becomes relatively easy, runners tend to slow down. This finding supports the hypothesis of improved performance under challenging, yet realistic goals.
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We further investigate how changes in qualifying time affects runners who are close to accomplishing their goal of qualifying for Boston Marathon by excluding slower runners who did not show potential for qualifying. Table 6 presents the results of the estimation, where runners who have a finishing time with a difference from qualifying greater than two standard deviations away from the sample average maximum improvement are dropped. This is intended to ensure that the results are not being driven by runners with little chance of ever qualifying for
Boston. This specification means that in our sample if a runner began their marathon career by missing qualifying by 56 minutes or more, they were deemed unlikely to ever qualify, and dropped from the sample. The results show that runners with the best chance of qualifying experience the same reduction in finish time from more realistic qualifying standards. Results are qualitatively similar to the baseline regression, with the coefficient on BQ_group_changes slightly lessened, and the individual 5 and 10 minute change variables strengthened marginally.
One noticeable difference is that for runners who had a chance to qualify and for whom qualifying standards changed by 15 minutes, finished on average 1 minute slower than those for whom qualifying standards did not change. These results once again confirmed our assumption of improved performance under realistic and challenging goals.
[Insert Table 6 here]
Concerns may still remain that we are not identifying the age change effect on marathon results. In results available by request, we create falsification tests that replace the
BQ_group_change variable with ages both 1 and 2 years before the original variable. For example, whereas a runner who is 34 is counted as changing age groups in the main specification, we try ages 33 and 32 to try to find a similar effect. In the basic regression with these falsification tests, we find a significant, small increase in finish times from moving into
20 these age groups in the years prior to the change in age group. These results account for the standard controls, including an increase in age, and show an opposite effect to the changing of the age bracket, indicating that our data is not suffering from measurement error, and if there is any bias in our results, it is toward attenuation.
6. Discussion
The goal of this paper is to examine the relationship between realistic goals and performance. Using the data from numerous different marathons and analyzing the difference in performance of runners over the course of many years, we find strong support to the hypothesis that performance improves as the goals change from unattainable to realistic. We see that lessening qualifying standards had a strong positive relationship with performance and that in cases in which the standard became more challenging, we see a strong negative relationship with performance. From an economic standpoint, this is an interesting result as it relates to effort and performance. As managers seek to create policies to maximize effort from their employees, our paper suggests performance goals need to be carefully chosen, and that managers should implement attainable goals. Goals that are too easy or difficult may cause a drop or no change in performance.
Some of the difficulty in measuring attainment of goals arises from small sample sizes and an inability to control for external influences. In using marathons, we can observe years of a running career, controlling for the level of experience and previous results. Additionally, because of the varying changes to the Boston qualifying time, we have variation in goals that allows identification of improvement with attainability.
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In addition to the large sample used, our study benefits from the clarity and simple measurement of the goal of BQ. The goal is clear and the runner can always be sure of what they need to achieve, and by how much they must improve to achieve their goal. Past empirical studies on the importance of the attainability of goals may have suffered from less of a clear path to goal attainment. For example, setting an attainable weight loss target may not be enough if the person does not know how to achieve it. Improvement in running may be more straightforward, and in this process realistic goals prove important.
The collection of such a large dataset creates the potential for measurement error, but our results are robust to sensitivity and falsification tests. Our empirical results are clear, but future research could focus on different stages of the marathon. For example, we would like to see if the results hold when instead of measuring performance by the marathon finish time, we use the time it took a marathoner to complete an early stage of the marathon, the 5 or 10 kilometer mark.
These stages may help to remove some of the problems which are unknowable to the researcher, but could affect finishing times, and potentially strengthen our results.
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Figures
Figure 1: Boston Marathon Finishers by Age in 2012-14 1400
1200
1000
800 2014 600 2013
400 2012 NumberFinishers of 200
0 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Age
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Tables
Table 1: Boston Qualifying times in minutes by age and gender before and after 2013 Before 2013 (Minutes) After 2013 (Minutes) Age group Men Women Men Women 18-34 190 220 185 215 35-39 195 225 190 220 40-44 200 230 195 225 45-49 210 240 205 235 50-54 215 245 210 240 55-59 225 255 220 250 60-64 240 270 235 265 65-69 255 285 250 280 70-74 270 300 265 295 75-79 285 315 280 310 80 and over 300 330 295 325
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Table 2: Average finish time difference by previous results and qualifying changes
Missed Boston Qualifying time in the previous race Change in Boston Qualifying time by 5 minutes by 5-10 minutes by 10-15 minutes by 15-20 minutes Lost 5 minutes 4.67 4.48 4.23 4.70
Gained 5 minutes 0.67 -1.90 -0.95 -0.86
Gained 10 minutes 3.93 2.78 5.20 3.01
Gained 15 minutes 16.44 18.31 13.79 15.49
The table shows the difference in marathon finish times between runners for whom qualifying time stayed the same and runners for whom qualifying time has either decreased by 5 minutes, or increased by 5, 10, or 15 minutes. The runners are grouped according to number of minutes by which they have missed BQ in the previous race.
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Table 3: Variable Descriptions Variable Description Race time Marathon finish time BQ group change =1 if participant changed Boston qualifying age group BQ change neg 5 =1 if Boston qualifying time decreased by 5 minutes BQ change 0 =1 if Boston qualifying time stayed the same BQ change 5 =1 if Boston qualifying time increased by 5 minutes BQ change 10 =1 if Boston qualifying time increased by 10 minutes BQ change 15 =1 if Boston qualifying time increased by 15 minutes Age Participant’s age Gender =1 if female Missed Time by which the participant missed qualifying for Boston in the previous race Experience Number of races participant competed in Experience squared Experience squared Running PR Fastest previous marathon finish time Race in a year Number of races participant competed in during particular year Min race time Fastest previous 5k race Month_t =1 if ran a marathon in month t (January t=1, February = 2, etc.) Missed_index_1 = 1 if qualified for Boston in the previous year Missed_index_2 = 1 if missed qualification by less than 5 minutes Missed_index_3 = 1 if missed qualification by 5-10 minutes Missed_index_4 = 1 if missed qualification by 10-15 minutes Missed_index_5 = 1 if missed qualification by 15-20 minutes Missed_index_6 = 1 if missed qualification by more than 20 minutes
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Table 4: Summary Statistics Variable Mean Std. Dev Min Max Race time 240.8440 30.3984 180 300 BQ group change 0.1584 0.3651 0 1 BQ change neg 5 0.0414 0.1991 0 1 BQ change 0 0.7347 0.4415 0 1 BQ change 5 0.1181 0.3228 0 1 BQ change 10 0.0677 0.2513 0 1 BQ change 15 0.0269 0.1619 0 1 Age 42.4854 10.4931 17 82 Gender 0.3318 0.4709 0 1 Missed 25.1605 30.9526 -125.017 114.7333 Experience 29.0423 38.7165 1 377 Experience squared 2342.4130 6481.7850 1 142129 Running PR 228.2195 29.6390 180 300 Race in a year 6.0743 6.2478 1 30 Min race time 47.5014 54.7675 10 297.2167 Month_ind_1 0.0253 0.1572 0 1 Month_ind_2 0.0215 0.1450 0 1 Month_ind_3 0.0557 0.2293 0 1 Month_ind_4 0.1043 0.3057 0 1 Month_ind_5 0.0747 0.2629 0 1 Month_ind_6 0.1386 0.3455 0 1 Month_ind_7 0.0237 0.1521 0 1 Month_ind_8 0.0108 0.1035 0 1 Month_ind_9 0.0338 0.1808 0 1 Month_ind_10 0.2479 0.4318 0 1 Month_ind_11 0.0760 0.2651 0 1 Missed_ind_1 0.1742 0.3793 0 1 Missed_ind_2 0.0428 0.2025 0 1 Missed_ind_3 0.0461 0.2098 0 1 Missed_ind_4 0.0464 0.2103 0 1 Missed_ind_5 0.0459 0.2093 0 1
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Table 5. Regression results
(1) (2) (3)
BQ group change -0.671*** -0.619*** (0.179) (0.180)
BQ change neg5 1.392*** 1.096*** (0.336) (0.337)
BQ change 5 -1.945*** (0.210)
BQ change 10 -1.829*** (0.268)
BQ change 15 -0.495 (0.423)
Age 0.757*** 0.759*** 0.767*** (0.0108) (0.0108) (0.0110)
Gender 11.72*** 11.73*** 11.82*** (0.251) (0.251) (0.250)
Missed 0.219*** 0.220*** 0.224*** (0.00378) (0.00378) (0.00379)
Experience 0.172*** 0.170*** 0.172*** (0.00615) (0.00618) (0.00618)
Experience squared -0.000484*** -0.000477*** -0.000483*** (0.0000278) (0.0000279) (0.0000279)
Running PR 0.315*** 0.314*** 0.313*** (0.00467) (0.00467) (0.00467)
Races in a year -0.236*** -0.234*** -0.254*** (0.0179) (0.0179) (0.0181)
Min Race Time 0.0369*** 0.0369*** 0.0367*** (0.00230) (0.00230) (0.00229)
_cons 118.4*** 118.3*** 118.4*** (1.024) (1.024) (1.023) N 110835 110835 110835 R squared 0.4168 0.4169 0.4184 Standard errors in parentheses *p< .10, **p< 0.05, ***p< .01
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Table 6. Results excluding athletes unlikely to qualify
(1) (2) (3)
BQ group change -0.460** -0.395** (0.200) (0.200)
BQ change neg5 1.606*** 1.471*** (0.372) (0.374)
BQ change 5 -1.168*** (0.236)
BQ change 10 -1.109*** (0.286)
BQ change 15 1.168*** (0.423)
Age 0.936*** 0.938*** 0.935*** (0.0135) (0.0135) (0.0137)
Gender 16.37*** 16.38*** 16.42*** (0.327) (0.327) (0.327)
Missed 0.189*** 0.190*** 0.191*** (0.00528) (0.00529) (0.00531)
Experience 0.154*** 0.151*** 0.153*** (0.00751) (0.00754) (0.00755)
Experience squared -0.000330*** -0.000321*** -0.000324*** (0.0000352) (0.0000352) (0.0000352)
Running PR 0.304*** 0.303*** 0.303*** (0.00664) (0.00665) (0.00665)
Races in a year -0.316*** -0.314*** -0.325*** (0.0225) (0.0225) (0.0226)
Min Race Time 0.0387*** 0.0387*** 0.0386*** (0.00281) (0.00280) (0.00280)
_cons 108.4*** 108.4*** 108.7*** (1.363) (1.363) (1.363) N 64650 64650 64650 R squared 0.4973 0.4977 0.4984 Standard errors in parentheses *p< .10, **p< 0.05, ***p< .01 This regression excludes runners who have a finishing time with a difference from qualifying greater than two standard deviations away from the sample average maximum improvement
34