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. 2023 Apr 19;18(4):e0283851. doi: 10.1371/journal.pone.0283851

Data-driven evaluation of the Boston marathon qualifying times

Laura Albrecht 1,*, Ross Ring-Jarvi 1, Dorit Hammerling 1
Editor: Chris Harnish2
PMCID: PMC10115302  PMID: 37075050

Abstract

The Boston Marathon is one of the most prestigious running races in the world. From its inception in 1897, popularity grew to a point in 1970 where qualifying times were implemented to cap the number of participants. Currently, women’s qualifying times in each age group are thirty minutes slower than the men’s qualifying times equating to a 16.7% adjustment for the 18-34 age group, decreasing with age to a 10.4% adjustment for the 80+ age group. This setup somewhat counter-intuitively implies that women become faster with age relative to men. We present a data-driven approach to determine qualifying standards that lead to an equal proportion of qualifiers in each age category and gender. We had to exclude the 75-79 and 80+ age groups from analysis due to limited data. When minimizing the difference in proportion of men and women qualifying, the women’s times for the 65-69 and 70-74 age groups are 4-5 minutes slower than the current qualifying standard, while they are 0 to 3 minutes faster for all other age groups.

Introduction

Every year on Patriots Day thousands of runners line up to take part in the historic Boston Marathon. From its inception in 1897, popularity grew to a point in 1970 where qualifying times had to be implemented to cap the total number of participants [1]. Runners must achieve a certain qualifying time at a previous marathon to be eligible to register for the Boston Marathon. The increase in popularity of both the Boston Marathon and marathon running in general has caused the Boston Athletic Association (BAA) to make the time standards more stringent three times in the last twenty years. The most recent time standard drop of five minutes in each age group, implying faster qualifying times, went into effect in 2020. A runner’s age on the date of the Boston Marathon and the gender they self-identified at the time of their qualifying race determines their required qualifying time [2]. We utilize this definition of gender in our analysis and only use the term sex in reference to previous work.

The new qualifying standards, given in Table 1, start at 3 hours for men and get slower on a sliding scale across each subsequent age group. The women’s qualifying times (QTs) are 30 minutes slower than the men’s times in every age group. This time gap of 30 minutes equates to a 16.7% adjustment for the 18–34 age group decreasing with age to a 10.4% adjustment for the 80+ age group implying women become faster with age relative to men.

Table 1. 2020 Boston qualifying times.

Times are presented in H:MM format.

Age Group 18–34 35–39 40–44 45–49 50–54 55–59 60–64 65–69 70–74 75–79 80+
Men’s QT 3:00 3:05 3:10 3:20 3:25 3:35 3:50 4:05 4:20 4:35 4:50
Women’s QT 3:30 3:35 3:40 3:50 3:55 4:05 4:20 4:35 4:50 5:05 5:20
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The effects of sex or age on running performance have been the topic of much previous research. Performance for elite and average runners has been found to decline around age 35 and 50, respectively [3, 4]. The difference between the average male and female runner has been estimated to be about 11.6% [5]. However, not much research has assessed if this gap is consistent between men and women’s times as they age. One study of the Berlin Marathon times speculated the decline in performance with aging may be different for men and women [6]. When the BAA was considering updating the qualifying times in 2013, Smith et al. [7] investigated the potential effect of changing the qualifying times by different amounts based on the age-sex distribution of runners that qualify. They observed a substantially lower percentage of female qualifiers compared to male qualifiers in the 60 and over age groups.

Women were first allowed to enter the Boston marathon in 1972 and at the time had to achieve the same qualifying time as the men. Small changes between the men’s and women’s times were introduced over the next 15 years and in 1987 the static 30-minute time difference between men and women was introduced. While the time standards themselves have changed multiple times since then, the 30-minute gap between men’s and women’s times in all age groups has remained consistent. The 70–74, 75–79, and 80+ age groups were added in 2002, again adopting the same 30-minute time gap that existed at the younger age groups. To the best of our knowledge, the decision to use this fixed time difference in every age group was not informed by data.

First, we investigate the effect of this 30-minute time gap and the distribution of runners at different age groups and genders. Then, we present one potential data-driven approach to suggest a more quantitatively justified method for setting future qualifying times. We aim to determine qualifying times leading to an equal proportion of qualifiers across genders. That is, if, for example, 7% of men 18–34 reach the qualifying time, we seek a qualifying time for women leading to 7% of women 18–34 qualifying as well. Seeking a fixed proportion of qualifiers across one race or after combining results from all races would be relatively simple. However, the proportion of qualifiers in each marathon and year are highly impacted by different features of that race. The proportion of runners qualifying in the same marathon in different years is influenced by factors such as weather and the individual runners participating in a given year. When comparing different marathons, other factors are also introduced such as elevation, course profile, and prize money. To control for this variability, we seek to find qualifying times that minimize the difference in the proportion of qualifiers conditioning on each individual marathon and year. Boston marathon qualifying times have historically been set at integer values in minutes, which we adopt. Therefore, our goal is to find integer qualifying times for women that minimize the difference in the proportion of qualifiers across all age groups, genders, marathons, and years using a large sample of popular Boston-qualifying marathons for a time period of 20 years.

Materials and methods

Data

We developed a web-scraper in Python to collect results from www.marathonguide.com [8] for 10 different marathons from 2000–2019; Chicago, New York, Los Angeles, Twin Cities, Houston, Philadelphia, California International, Marine Corps, Grandma’s, and Honolulu Marathon. We chose these marathons to get a good geographic sample of races across ten of the top largest marathons in the US [9]. Additionally, all marathons except for Honolulu are listed as top qualifying marathons or as one of the marathons with the most Boston qualifiers [8, 10]. We used the Selenium package [11] to cycle through all pages of results and then use the Beautiful Soup package [12] to change the HTML race content into a Python string object. R Tidyverse [13] was used to clean and organize the data. A few marathon observations are missing or excluded in our analysis; New York 2012 was canceled due to super-storm Sandy, Twin Cities in 2003 and 2005 as well as Grandma’s in 2006 are excluded due to age being missing from the results. Additionally, the 75–79 and 80+ age groups have very few women runners and have been excluded from our analysis. This data is publicly available from Marathon Guide and our analysis complied with the websites terms of service [8].

Overall, our collected data set contains 3.2 million runners, 1.9 million men (59%) and 1.3 million women (41%). Fig 1 shows the number of runners and the percentage that qualify for Boston in each age group in our data. The majority of runners in our data are in the 18–34 age group. The proportion of women runners starts at 49.5% for the 18–34 age group and decreases to approximately 21% for the 70–74 age group. The percentage of runners that qualify for Boston in each age group ranges from about 4–9%. Other than the 18–34 age group, women qualify at a higher rate for all ages 50 and under. For age groups 55 and over, the percentage of men that qualify is greater and the gap between the proportion of men and women qualifying increases in each subsequent age group (Fig 1).

Fig 1. Number of men and women runners in each age group and percentage that qualify for Boston under the 2020 qualifying times across all marathons collected.

Fig 1

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Our collected data are used to analyze the distribution of runners that qualify for Boston at the current qualifying times and compare those times with different potential qualifying standards. As an initial evaluation of the current 30-minute time gap between men’s and women’s qualifying times, we looked at the difference between men’s and women’s times at fixed percentiles in our data set. We determined the time in our data correlated with the top 4–9% of men and women, respectively, at each 0.1% increment. This covers the range of the percentage of runners that qualify in each age group at the current Boston Qualifying Times as seen in Fig 1.

Minimizing the difference in the proportion of qualifiers

Using our collected marathon results, we kept the men’s qualifying times set at the current Boston qualifying times and determined from the data the proportion of men that qualify in each age group (AG), marathon, and year. That is, the proportion of men qualifying is specified from the data and considered fixed. The proportion of men qualifying at time t is calculated as shown in Eq 1. The proportion of women qualifying is found in the same manner.

propMijk(t)=#ofMenQualifyinginAGi,marathonj,yeark,atqualifyingtimet#ofMeninAGi,marathonj,andyeark (1)

We minimized the difference in the proportion of men and women qualifying across each marathon and year as shown in the objective function given in Eq 2. We performed a grid search at every one minute interval between the age-group-specific Men’s QT plus twenty minutes and plus forty minutes, and evaluated the objective function within this range for each age group. For example, for the 18–34 age group with a Men’s QT of 3 hours, we evaluated the objective function (Eq 2) with t equal to every minute between 3 hours and 20 minutes and 3 hours and 40 minutes. We refer to the value of t that minimized this objective function as the optimized difference in proportions qualifying time (Optimized QT). The term ‘optimize’ in this context specifically refers to the process of determining the women’s qualifying times that minimize the absolute differences in proportions of male and female qualifiers, as defined by the chosen objective function in Eq 2. We inspected all plots of the objective function versus qualifying times to ensure a true minimum was reached.

OptimizedQT=mint∑jk|propWijk(t)-propMijk| (2)

Systematic differences in marathons such as cut-off time, elevation, and prize money can affect the field of runners in each marathon. To ensure our results are robust and not sensitive to the choice of the sample of marathons included, we repeated this analysis ten times excluding one marathon at a time and compared the resulting ten qualifying times to the qualifying times found with all marathons included.

Proportion analysis

We used a two proportion z-test to determine if the differences in proportions between men and women are significant in each marathon and year. We set a threshold on the proportion test to a p-value less than 5%. We performed the proportion test at both the current women’s Boston qualifying times and at the times found when minimizing the difference in proportions for comparison.

Results

The distribution of the differences between men’s and women’s times for the top 4–9% of runners are shown in the boxplot in Fig 2. The red line indicates the 30-minute time gap currently used in each age group. A difference of less than 30 minutes exists for the 35–39, 40–44, and 45–59 age groups and the time difference is greater than 30 minutes for all of the 60+ age groups.

Fig 2. Difference between men’s and women’s times for the top 4–9% of runners at each 0.1% increment in each age group.

Fig 2

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The red line indicates the 30-minute difference which is currently used in each age group.

The qualifying times found from minimizing Eq 2 over t are shown in Table 2. When compared to the Current QTs, the Optimized QT for the 18–34 age group was 1 minute slower, the 65–69 age groups was 4 minutes slower, and the 70–74 age group was 5 minutes slower. All other age groups were between 0 and 3 minutes faster than the Current qualifying times. Using the Optimized QT instead of the Current QT has a large effect on the absolute and relative change of the number of women qualifying in some age groups. For example, a decrease of 3 minutes for the 35–39 and 40–44 age groups would lead to over 1900 fewer qualifiers in each age group (approximately a 17% relative decrease). An increase of 4 minutes at the 65–69 age group and 5 minutes in the 70–74 age groups would increase the number of qualifiers by 110 and 38 runners respectively (17.9% and 22.8% relative increase). In all age groups except 60–64, the difference in proportions of men and women that qualify are closer to zero using the Optimized QTs.

Table 2. Optimized women’s qualifying times found from Eq 2.

The difference in minutes between the Current QTs and the Optimized QTs are given in the second row. The absolute difference in the number of qualifiers at the Current QTs compared to the Optimized QTs is shown in the third row with the relative percent change displayed in parentheses. The last row gives the percent difference of the proportion of men and the proportion of women that qualify at their respective qualifying times. A negative value indicates a higher proportion of men qualify relative to women.

Age Group 18–34 35–39 40–44 45–49 50–54 55–59 60–64 65–69 70–74
Optimized Women’s QT 3:31 3:32 3:37 3:48 3:54 4:05 4:19 4:39 4:55
Difference from Current QT (minutes) +1 -3 -3 -2 -1 0 -1 +4 +5
Change in # of Qualifiers at Optimized QT (Relative % Change) +1579 (5.9%) -1911 (-17.0%) -1997 (-17.1%) -1173 (-11.2%) -357 (-5.8%) 0 (0%) -81 (-4.5%) +110 (+17.9%) +38 (+22.8%)
% Difference proportion of men vs women qualifying at Optimized QTs (% Difference at Current QTs) -0.09% (-3.47%) -0.20% (+0.70%) -0.23% (+0.81%) -0.51% (+.33%) -0.31% (+0.06%) -0.11% (-0.11%) -1.28% (-0.95%) -1.00% (-2.18%) -1.46% (-2.66%)
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To assess the sensitivity of our approach to the choice of marathons included, we also determined the qualifying times by excluding one marathon at a time and again minimizing the difference in proportions. The frequency at which each qualifying time was obtained is shown in Fig 3. The qualifying times found when minimizing the difference in proportions across all races, as reported in Table 2, is highlighted in red. In most cases, the results when excluding one marathon are all within 1 minute of the Optimized QTs found when all marathons are included. The 70–74 age group was more sensitive to the exclusion of individual marathons with Optimized QTs ranging from 4:51–5:03.

Fig 3. Optimized difference in proportions QTs found when excluding one of the ten marathons at a time.

Fig 3

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The Optimized QTs across all marathons is highlighted in red.

Results of the two proportion z-test are shown in Fig 4. The first column of Fig 4 shows the results of the proportion test evaluated at the current women’s qualifying times and the middle column shows the results at the optimized difference in proportions women’s qualifying times. Red squares indicate a higher proportion of men qualifiers and blue squares indicate a higher proportion of women qualifiers. To represent significant differences between men and women’s proportions, we set a threshold on the proportion test to a p-value less than 5%. Dark red and dark blue squares indicate the difference is significant at a 95% confidence level. Summaries by age group of the number of results at each significance level at the Current QTs and Optimized QTs are shown in the third column of Fig 4.

Fig 4. The first column shows the results of the proportion test using the current Boston marathon qualifying times, the second column shows the results using the optimized difference in proportions qualifying times given in Table 2, and the third column shows the total number of results for each level at the current and optimized difference in proportions qualifying times.

Fig 4

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Red squares represent a higher proportion of men qualifying, blue squares represent a higher proportion of women qualifying. Dark red and dark blue indicate whether this difference is significant at a 95% significance level while light red and light blue indicate a difference in proportion that is not significant at the 95% level.

Discussion

The Boston Marathon currently uses a static 30-minute time gap between men’s and women’s qualifying times across each age group, implying women become faster relative to men as they age. We collected data to evaluate the impact of this 30-minute time gap on qualifiers across different age groups and proposed a data-driven approach to find qualifying times that maintain parity within each age group.

We collected data from ten different marathons from 2000–2019. Overall, our data set includes 3.2 million runners. Based on data provided by the BAA, the marathons in our data account for 28.6% of all qualifiers that entered the Boston Marathon in 2018 and 2019. The geographic distribution of runners’ home states in our data closely resembled that of the Boston Marathon data. We also compared our data with the report by www.runrepeat.com using their database of races which is said to include 96% of all US race results from 1986 to 2018 [14]. We observed that the average finishing times, as well as the age and sex distribution of runners in our data, are consistent with the corresponding values given in their report (S2 and S3 Figs). Thus, our data set appears to be a reasonable sample of marathon race results. For validation purposes, future work could include replicating this analysis on another data set with different marathons.

Based on our data, we find that in the 18–34 age group, the proportion of men who qualify for the Boston Marathon at the current qualifying times is slightly higher than that of women. In the 35–49 age groups, however, more women qualify proportionally than men. In the 50–59 age groups, the proportions are similar between men and women. Finally, in the 60–74 age groups, the proportion of men who qualify is higher, and the gap between the proportion of men and women continues to increase with each age group. As an alternative to a set time gap, we determined qualifying times by minimizing the difference in the proportion of men and women qualifiers across all marathons and years. Our method suggests adding 1 minute in the 18–34 age group, adding 4–5 minutes in the 65–69 and 70–74, and subtracting 3 minutes in the 35–39 and 40–44 age groups from the respective current women’s qualifying times would lead to a more equitable proportion of women to men qualifiers.

In contrast to the Boston Marathon, the New York City Marathon, which utilizes a mixture of entrants through qualifying times, lottery entries, and charity entries, has qualifying times that range from a 20 minute time gap for the 18–34 age group to 100 minutes for the 80+ age group [15]. Previous studies have indicated the decline in running performance for women is greater with age than for men [16, 17]. Fig 2 illustrates a discrepancy in finishing times between men and women in the top 4–9% of runners in our data, suggesting a time difference that increases with age may be more appropriate than a static time gap.

We kept the men’s qualifying times fixed and found qualifying times for women to minimize the difference in the proportion of women and men qualifying across each age group, marathon, and year. Many potential objective functions could be used to determine qualifying times in this manner. We chose to keep the proportion of men qualifying constant to ensure our Optimized QTs did not cause large reductions in qualifiers in the older age groups. At the current QTs, the proportion of qualifiers in the older age groups is higher than it is in the younger age groups (Fig 1). Therefore, if we allowed the men’s qualifying times to change as well and optimized to find a consistent proportion of qualifiers across all age groups, this would decrease the number of qualifiers in the older age groups and increase the number of qualifiers in the younger age groups. In 2002 the BAA altered the qualifying times to make the times easier for all runners 45 and older to accommodate more participants [18]. We infer this decision was motivated by a desire to boost participation among older runners specifically.

We minimized the sum of the absolute differences in proportions as it is robust to outliers and ensures an equal proportion of qualifiers across genders in each age group. However, this approach resulted in fewer women qualifying in some of the younger age groups than under the previous time standards. To address this issue, future research could consider adding constraints to hold the number of female qualifiers fixed. However, such constraints could have unintended consequences, such as favoring the current qualifying times, particularly in the younger age groups. Therefore, any future work should carefully consider these trade-offs when attempting to mitigate the issue of having fewer women qualifiers.

The Optimized QTs still result in faster times for women relative to men as they age but the differences are slightly less extreme than at the Current QTs. This could be explained by the lower popularity of recreational marathon running with older women than men. Additionally, cut-off times used in many races could disproportionately discourage women in older age groups from participating. In general, it has been observed that more older men than women participate in sports activities [19]. Women were not even allowed to participate in marathons fifty years ago [20]. However, the relative participation of women in marathon running has been increasing in recent years and on average, women are improving faster relative to men [14, 17, 21]. We also observe this in our data set over the past 20 years (S3 Fig). As running continues to become more popular, this dynamic may change over time.

The BAA utilizes a rolling enrollment system which allows the faster participants relative to their qualifying times to register first. In all but one year since the rolling system was implemented in 2012, not all runners who qualified were accepted into the race [18]. The effect of these faster cut-off times is outside the scope of our analysis. The number of qualifiers does appear to be sensitive to small changes in qualifying times, which could have a significant effect on the proportion of qualifiers and would be useful to include in a future study.

The Boston Marathon was canceled for the first time in history in 2020 due to the COVID-19 pandemic [22]. We only collected data and explored marathons for the 20 years prior to the pandemic but hypothesize it may take awhile for road racing to rebound to pre-pandemic popularity. For the first time since 2013, all runners who qualified and entered Boston were accepted to run it in 2022 and 2023, despite the fact the field size remained unchanged compared to 2015–2019 [18]. The abundance of cancelled or postponed races in 2020 and 2021, which limited the opportunities for runners to achieve a qualifying time, may have contributed to the easier entrance times. The effect of the pandemic on road race participation across genders and age groups will be important to consider to compare future data against our results. A dynamic perspective could be applied to monitor changes in the proportion of qualifiers over time, particularly in response to external events like the pandemic, and to examine the differential impacts across genders and age groups.

Qualifying for Boston is the goal of many amateur runners who may run multiple marathons in an effort to achieve this goal. Runners training to qualify for Boston are likely to have finishing times clustered around their respective qualifying times. Thus, small changes have a large impact on the number and proportion of women that qualify (Table 2). Due to the popularity of the race, the BAA has repeatedly altered the qualifying times to limit the size of the field. We utilized a data-driven approach to setting new qualifying times that maintain parity within each age group. Overall, the qualifying times found using our method and data set are similar to the current qualifying times suggesting the static 30-minute time gap is consistent with our data-driven approach. However, we find modest changes to the women’s qualifying times would lead to a more equal proportion of qualifiers across genders. Our method could be easily adapted to other potential objective functions to determine qualifying times specific to the race organizer’s goals and desired distribution of qualifiers.

Conclusion

In our data set, we observe the proportion of men that qualify at the current Boston qualifying times is slightly higher than women in the 18–34 age group in our data, in the 35–49 age groups more women qualify proportionally than men, in the 50–59 age groups the proportions are similar, and at the 60–74 age groups the proportion of men qualifying is higher and the gap between the proportion or men and women grows in each age group. As an alternative to the 30-minute fixed time gap currently used, we determined qualifying times by minimizing the difference in the proportion of men and women qualifiers across all marathons and years. Our analysis shows adjusting the qualifying times by adding 1 minute to the 18–34 age group, adding 4–5 minutes in the 65–69 and 70–74 age groups, and subtracting 3 minutes from the 35–39 and 40–44 age groups from the current women’s qualifying times could result in a more equal proportion of women to men qualifiers. Our methodology could easily be applied to other potential objective functions to determine data-informed qualifying times specific to the race organizer’s desired size and distribution of qualifiers.

Supporting information

S1 Fig. Distribution of finishing times by marathon.

The total number of runners observed in each marathon is shown in parentheses. The orange vertical line indicates the cut-off time for each marathon. Some marathons are strict with their cut-off times while others are more lenient. An interesting feature to note, in each marathon except for Honolulu we see a bump right around the 4 hour mark, a popular goal time for many runners.

(TIF)

Click here for additional data file. (516.3KB, tif)
S2 Fig. Distribution of all finishing times by age group and gender.

The number of runners in each age group and gender are shown in parentheses. The distribution of times does not change much between the 18–34, 35–39, and 40–44 age groups. We then see a shift towards slower times in each subsequent age group, particularly in the oldest age groups.

(TIF)

Click here for additional data file. (339.2KB, tif)
S3 Fig. Percentage of women runners by age group from 2000–2019.

The 18–34 age group increased towards 50% and then appears to have leveled off around that 50% split. All other age groups are increasing on average each year. We observe a sharper increase in the percentage of Women in many age groups in 2012 due to New York not being held that year. New York has a lower percentage of women runners than most other marathons so it’s exclusion leads to the spike observed.

(TIF)

Click here for additional data file. (581.1KB, tif)
S1 Table. Number of participants by marathon and age group.

(PDF)

Click here for additional data file. (54.9KB, pdf)
S2 Table. Cut-off times and average number of participants by marathon.

Differences in cut-off times may be responsible for the variation in the proportion of qualifiers across different marathons. Also, each marathon has different levels of enforcement with cut-off times which could impact the distribution of finishers.

(PDF)

Click here for additional data file. (51.1KB, pdf)

Data Availability

All data was taken from a public website (www.marathonguide.com). The clean version of our data is uploaded to zenodo currently. doi: 10.5281/zenodo.6959864.

Funding Statement

The authors received no specific funding for this work.

References

Decision Letter 0

Chris Harnish

23 Jun 2022

PONE-D-22-13227Evaluating the fairness of the Boston Marathon qualifying timesPLOS ONE

Dear Dr. Albrecht,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

In order to resolve the differences between reviewers, I have read the paper and recommend significant revision. Please review each reviewers comments and address their concerns. In addition, I recommend the following:

  • I believe reviewer 2 makes a legitimate case for the use of fairness. While I believe you have defined the word, I question whether fairness is relevant in a scientific paper. I believe you should reposition your paper as evidence-based for qualifying times. This is a more direct way to direct your argument; Are the current standards evidence-based? It doesn't appear so. Is your approach better? I can't say, but we should establish standards based on the evidence, not arbitrary fixed numbers. That is the case the authors should make and a suggestion on how to get there!  

  • There is inconsistent grammar, language use (like many in areas where present not past tense is used). The paper feels disjointed as if written by different individuals and then combined without regard to flow.

  • There are insufficient references for a paper of this magnitude. In particular, much of the (limited) discussion is more extended conclusions and speculation and lacks any meaningful literature to support it. I recommend several references to review:

  • The introduction is extensive and well written but should end with a clear purpose and hypotheses. 

  • The Methods are very confusing and poorly structured, and should be written in the past tense. The general writing is completely different from the intro and much of the methods are actually results. I recommend streamlining and reorganizing to clearly identify who the participants were, where the data came from, how it was analyzed with details on stats, and specific criteria for exclusion of data. I envision much of the data with figures should move to results.

  • Results are extensive but should be streamlined and flow based on the story you with to tell in the discussion. 

  • Figures are at times confusing with superfluous text on the figures. Titles need to be concise where possible and clearly identify what the figure is showing without excess story or text. I'm just having a hard time following the story you're telling.
    • ​I recommend identifying the key 3 or 4 figures and moving the rest to supplements to tell your story. 
  • The discussion is inadequate for the paper and data you present. Two big paragraphs do little to help the paper and largely just try to tell us how much better your optimized times are. However, you haven't really made that case, and really should leave it to the conclusion and future rec's for research. It also needs to lean into supporting references. I suggest:
    • Restating the purpose and hypotheses then reviewing what you found. Then each subsequent paragraph targets a single finding.
    • An additional paragraph can cover unexpected findings and then perhaps one more paragraph to note the limits of this study and future recommendations.

  • Now hit the conclusion with the overarching findings and message. Avoid over speaking your results.

Please utilize the time available and perhaps request an independent reader prior to resubmission. We look forward to reading your revised work.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: No

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: No

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: This study presents the results of primary scientific research. To this reviewer’s knowledge, the results reported in this manuscript have not been published elsewhere. Statistics and other analysis are performed to a high technical standard and are described in sufficient detail. Conclusions are presented in an appropriate fashion and are supported by the data. This article is presented in an intelligible fashion and is written in standard English. In addition, the researchers meet all applicable standards for the ethics of experimentation and research integrity.

I am curious on why those ten races were selected for data analysis. It is not noted in the methods. When looking at the top qualify races for Boston, several of them are not even listed (e.g. Honolulu, Houston, LA). Top Qualifying Races | Boston Athletic Association (baa.org). Please provide more information on this.

This reviewer suggests providing a shorter summary after each Figure. The current summaries are very lengthy and are what is exactly in the text of the article. In addition, the color coding is helpful but many readers will be looking at this article in black/white (especially if print). This reviewer would suggest looking at different ways to express the data so can be viewed by all. Since, this study looked at data prior to the pandemic, do the authors feel that this has now changed the outcome of their data. Boston has now opened up the race for more athletes to be able to run. This might be something to mention in the discussion. Overall, I enjoyed reading this article. As a runner myself this is always great to see how investigators are looking at marathon data.

Reviewer #2: Dear authors,

The study aimed to investigate whether the Boston Marathon qualifying times are “Fair”. Although this is an interesting topic and deserves attention, in a way that future marathons' qualifying times seek to include a more homogenous number of qualifiers across genders, I have some concerns about the way the manuscript was presented and reported.

First, I believe that if authors want to evaluate fairness, they should include a proper definition of the term and how this affected their research question. Fairness in sports is a rather complicated matter, involving several other factors that were not considered in the study and not discussed properly. In my opinion, the study simply aimed to analyse whether the current Boston qualifying times include a similar percentage of women and men, and whether the times could be changed by applying a mathematical model in a way that the difference in proportion of qualifiers across genders is smaller (although the authors do not report how much this difference is).

Second, it is not clear from the introduction and the aims of the study what is the current differences in the number of women and men that qualify in each race. This is a piece of very important information, that would allow us to know if there is indeed a large difference in the proportion of qualifiers across genders.

Also, the methods section is quite complicated to follow and there is some information that is not relevant to the aims of the study. For example, the authors surprisingly collected data from 10 different other marathons, and it is not clear why they did that. I believe most of the data that were analysed and presented are not relevant to the aims of the study which was to analyse whether the Boston qualifying times include a similar proportion of runners across genders. I believe the authors should then focus on the “Proportion Analysis” assessing the Boston qualifying times and how changing it would minimize the difference in the proportion of qualifiers across each race. The authors also included in the methods sections, several results from their analysis that should be included only in the “Results” section.

Finally, the “Discussion” section does not represent all the data that was analysed. The authors previously presented the results from several different analyses, yet the discussion had only two paragraphs and only included one reference. The authors should aim to discuss the results of their study comparing it with previous published studies, making sure that all the data that was analysed, is discussed as well.

Kind regards.

**********

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Reviewer #1: No

Reviewer #2: No

**********

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While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PLoS One. 2023 Apr 19;18(4):e0283851. doi: 10.1371/journal.pone.0283851.r002

Author response to Decision Letter 0

3 Aug 2022

Editor #1, comment #1

I believe reviewer 2 makes a legitimate case for the use of fairness. While I believe you have defined

the word, I question whether fairness is relevant in a scientific paper. I believe you should reposition your

paper as evidence-based for qualifying times. This is a more direct way to direct your argument; Are the

current standards evidence-based? It doesn’t appear so. Is your approach better? I can’t say, but we should

establish standards based on the evidence, not arbitrary fixed numbers. That is the case the authors should

make and a suggestion on how to get there!

Our response #0.1

We think this is an excellent suggestion. We agree presenting our method as an evidence-based alternative

is clearer and less subjective. We have repositioned our paper as the editor suggested and have removed the

discussion of the word fairness.

Editor #1, comment #2

There is inconsistent grammar, language use (like many in areas where present not past tense is used).

The paper feels disjointed as if written by different individuals and then combined without regard to flow.

Our response #0.2

We have edited the paper to make sure the tense is consistent throughout each section and have added

some transitions to try and make the paper flow better.

Editor #1, comment #3

There are insufficient references for a paper of this magnitude. In particular, much of the (limited)

discussion is more extended conclusions and speculation and lacks any meaningful literature to support

it. I recommend several references to review: Bagley DOI: 10.1111/sms.13404 Tanaka DOI: 10.1113/jphysiol.

2007.141879 Nicolaidis doi: 10.3390/ijerph16101777Waldvogel doi: 10.3390/ijerph16132377 https://runrepeat.com/stateof-

running https://runnerclick.com/marathon-finishing-times-study-and-statistics/

Our response #0.3

Thank you so much to the editor for taking the time to include these references as a starting point. We

have expanded the discussion to incorporate more references, including several of those suggestions, that are

relevant to our hypothesis and results.

Editor #1, comment #4

The introduction is extensive and well written but should end with a clear purpose and hypotheses.

Our response #0.4

Thank you. An additional paragraph has been added to the end of the introduction to make our purpose

more clear and help ease the transition into the methods section.

Editor #1, comment #5

The Methods are very confusing and poorly structured, and should be written in the past tense. The

general writing is completely different from the intro and much of the methods are actually results. I

recommend streamlining and reorganizing to clearly identify who the participants were, where the data

came from, how it was analyzed with details on stats, and specific criteria for exclusion of data. I envision

much of the data with figures should move to results.

Our response #0.5

Thank you for bringing this to our attention. We have revised the methods section to try and make it

more clear and hope the tone fits better with the rest of the paper now. Most of the figures and exploratory

data analysis have been moved to either the results section or the supplemental information.

Editor #1, comment #6

Results are extensive but should be streamlined and flow based on the story you with to tell in the

discussion.

Our response #0.6

We have updated the results section to to better focus our story. Fig 6 has been moved to the supplemental

information section.

Editor #1, comment #7

Figures are at times confusing with superfluous text on the figures. Titles need to be concise where

possible and clearly identify what the figure is showing without excess story or text. I’m just having a hard

time following the story you’re telling. I recommend identifying the key 3 or 4 figures and moving the rest

to supplements to tell your story.

Our response #0.7

We have updated all the figure captions to be more concise. We really appreciate the suggestion to

identify the key figures. This really helped us focus our story and improved the flow of our paper. We

have moved four of the figures into the supplemental section. While we believe these figures give interesting

insight into our data set, we agree the supplemental section is probably a better place to include them.

Editor #1, comment #8

The discussion is inadequate for the paper and data you present. Two big paragraphs do little to help

the paper and largely just try to tell us how much better your optimized times are. However, you haven’t

really made that case, and really should leave it to the conclusion and future rec’s for research. It also

needs to lean into supporting references. I suggest: Restating the purpose and hypotheses then reviewing

what you found. Then each subsequent paragraph targets a single finding. An additional paragraph can

cover unexpected findings and then perhaps one more paragraph to note the limits of this study and future

recommendations.

Our response #0.8

Thank you for this very specific outline on how to improve our discussion. We have thoroughly reorganized

the discussion to follow this outline. We have expanded our discussion to include more references and

added a discussion about the limitation of our work and potential directions of future work.

Editor #1, comment #9

Now hit the conclusion with the overarching findings and message. Avoid over speaking your results.

Our response #0.9

We have revised the conclusion in this way. We truly thank you for taking the time to provide such

detailed and useful suggestions for each section of our paper.

Reviewer #1, comment #1

I am curious on why those ten races were selected for data analysis. It is not noted in the methods. When

looking at the top qualify races for Boston, several of them are not even listed (e.g. Honolulu, Houston, LA).

Top Qualifying Races — Boston Athletic Association (baa.org). Please provide more information on this.

Our response #1.1

Thank you for bringing it to our attention that we failed to explain our choice of marathons. We chose

these 10 marathons to get a good geographic sample of marathons that are 10 of the top 15 largest marathons

in the US. Additionally, all marathons except for Honolulu are listed as top qualifying races for Boston. We

have added an explanation of this in the Data section.

Reviewer #1, comment #2

This reviewer suggests providing a shorter summary after each Figure. The current summaries are very

lengthy and are what is exactly in the text of the article. In addition, the color coding is helpful but many

readers will be looking at this article in black/white (especially if print). This reviewer would suggest looking

at different ways to express the data so can be viewed by all.

Our response #1.2

Thank you for the suggestion. The figures summaries have been shortened on all figures. The color

choices in our figures all come from color blind friendly color palettes and as this is an online only journal,

we believe they should be readable to readers.

Reviewer #1, comment #3

Since, this study looked at data prior to the pandemic, do the authors feel that this has now changed

the outcome of their data. Boston has now opened up the race for more athletes to be able to run. This

might be something to mention in the discussion.

Our response #1.3

This is an interesting point we hadn’t considered yet. We have added a paragraph in the discussion

regarding the effect of the pandemic on marathons and how this will impact future data. We only collected

data on and explored marathons prior to the pandemic but hypothesize it may take a few years for road

racing to rebound to pre-pandemic popularity. For the first time since 2013, all runners who qualified and

entered Boston were accepted to run it this year. The field size for the 2022 race was the same as the previous

5 years before the pandemic. We assume the abundance of canceled or postponed races in 2020 and 2021,

which limited the opportunities to achieve a qualifying time, may have been a big contributing factor to the

easier entrance criteria this year. The effect of the pandemic on road race participation across genders and

age groups will be interesting to look at in the coming years.

Reviewer #2, comment #1

First, I believe that if authors want to evaluate fairness, they should include a proper definition of

the term and how this affected their research question. Fairness in sports is a rather complicated matter,

involving several other factors that were not considered in the study and not discussed properly. In my

opinion, the study simply aimed to analyse whether the current Boston qualifying times include a similar

percentage of women and men, and whether the times could be changed by applying a mathematical model

in a way that the difference in proportion of qualifiers across genders is smaller (although the authors do not

report how much this difference is).

Our response #2.1

We agree that the discussion of fairness is complicated and have instead reframed our paper, as suggested

by the editor, away from fairness. In Fig 4 we show a side by side bar plot of the results of the proportion test

at the current Boston qualifying times and our optimized times to try and show that our optimized times

lead to a more equal proportion qualifiers. We have edited the explanation of this plot to try and highlight

that result more explicitly. We have also added a row to Table 2 showing the difference in proportions

between men and women across all races at the current and optimized times.

Reviewer #2, comment #2

Second, it is not clear from the introduction and the aims of the study what is the current differences in

the number of women and men that qualify in each race. This is a piece of very important information, that

would allow us to know if there is indeed a large difference in the proportion of qualifiers across genders.

Our response #2.2

Thank you and we agree we skimmed over detail and it needs to be more clear. In the second row of

Fig 1 we show the proportion of men and women that qualify in our data in each age group. Other than

the 18-34 age group which has a slightly higher percentage of men qualifying than women, women qualify at

a higher rate for all ages 50 and under. For age groups 55 and over, the percentage of men that qualify is

greater and the gap between the proportion of men and women qualifying increases in each subsequent age

group. This explanation has been added to the Data section.

Reviewer #2, comment #3

Also, the methods section is quite complicated to follow and there is some information that is not

relevant to the aims of the study. For example, the authors surprisingly collected data from 10 different

other marathons, and it is not clear why they did that. I believe most of the data that were analysed and

presented are not relevant to the aims of the study which was to analyse whether the Boston qualifying

times include a similar proportion of runners across genders. I believe the authors should then focus on

the “Proportion Analysis” assessing the Boston qualifying times and how changing it would minimize the

difference in the proportion of qualifiers across each race. The authors also included in the methods sections,

several results from their analysis that should be included only in the “Results” section.

Our response #2.3

Thank you for this feedback. We have edited the methods section to hopefully make it easier to follow.

We have also moved any results in the methods section into the results section. As described above, we have

added an explanation to why these 10 marathons were chosen. Many of the exploratory data pieces were

moved to the supplemental information as we think it may be of interest to reader, especially those in the

running community, but agree it detracts from the story we are trying to tell.

Reviewer #2, comment #4

Finally, the “Discussion” section does not represent all the data that was analysed. The authors previously

presented the results from several different analyses, yet the discussion had only two paragraphs and

only included one reference. The authors should aim to discuss the results of their study comparing it with

previous published studies, making sure that all the data that was analysed, is discussed as well.

Our response #2.4

Thank you for this suggestion. We have expanded the discussion section to ensure all of the results presented are included. The discussion has been expanded as described in response to the editor’s comments

to include a more thorough comparison with previous literature.

Attachment

Submitted filename: Response to Reviewers.pdf

Click here for additional data file. (90.5KB, pdf)

Decision Letter 1

Chris Harnish

23 Aug 2022

PONE-D-22-13227R1Data-driven evaluation of the Boston marathon qualifying timesPLOS ONE

Dear Dr. Albrecht,

Thank you for submitting your revised manuscript to PLOS ONE. While I believe the manuscript has merit, reviewers could come to a consensus on this. Therefore, after careful review I enlisted a third non-academic reviewer with significant expertise in statistics and data analysis. It has been enlightening to read a fresh review from a unique point of view. I believe reviewer 3 has offered the authors a clear pathway forward while improving the overall value of the manuscript. Therefore, we invite you to submit a revised version of the manuscript that addresses the key areas recommended below.

  • Please give careful consideration to the statistical methods provided.

  • Consider carefully reviewing several databases on running, like that of run repeat. 

  • Addressing the Fairness question; reviewers struggled with this concept and I would decide on one clear path and stay with it. Reviewer 3 offers some ideas.

  • Be clear on what your messaging is on the results. Editor note: I believe you've overplayed the grand outcomes and missed some key points, like the Boston qualifier really breaks down as a specific age. 
    • ​I believe reviewer 3 has offered some of the best advice to tackle the results issues, but it is a bit of work.

I appreciate your understanding and I look forward to reading the next revision. Please submit your revised manuscript by Oct 07 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

  • A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

  • A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

  • An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Chris Harnish, PhD

Academic Editor

PLOS ONE

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: (No Response)

Reviewer #3: (No Response)

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Partly

Reviewer #3: Partly

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: Yes

Reviewer #3: No

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: Dear authors,

Thank you for considering my previous comments and making the necessary adjustments. Although I appreciate the authors’ efforts to address all points, there are still some important key points that need to be clarified and properly addressed.

I believe the manuscript is still a bit hard to follow and the message is still not clear. The aim of the study was to analyse how adjusting (not sure if “optimising” is adequate) the qualifying times of the Boston marathon would result in a more equal proportion of men and women across age groups. Yet, there is a lot of information that is not relevant to the aims of the study. For example, I believe most of the figures included in the supplemental material are irrelevant and should be excluded from the study. The introduction has improved and is properly written, clearly stating the problem and how you aim to solve it. However, the other sections are still quite confusing. In the methods section, I had a difficult time trying to understand how the demographics from the other 10 marathons would help you achieve your aim. The study adopted a pretty robust and complicated analysis, so every step of the data collection and analysis needs to be clearly explained. It is also important to report how many runners took part in each race you analysed and also split by age groups.

I still think there are too many figures that do little to help you deliver your message. The authors also did not attach figure 1 to their submission. In your results, you found that decreasing the qualifying times for the 35-39, 40-44, 45-49, 50-54 and 60-64 age groups would “optimise” the distribution of men and women across age groups. However, this approach, at the same time, substantially lowers the overall absolute number of qualifiers in the race, which will, in fact, exclude more runners. For this reason, I don’t think your approach will “optimise” the qualifying times, as you would essentially exclude more people from taking part in the race.

The discussion should start by stating the aims of the study and providing a comprehensive summary of the main findings. The following paragraphs should then expand the main findings comparing your results with previous studies. I think the discussion is quite speculative and not supported by adequate evidence. For example, reference number 17, although interesting, is a blog post that probably was not peer-reviewed. There are also a couple of paragraphs (lines 199 to 214) including information not relevant to the study.

Reviewer #3: This is an interesting piece of work that I think should be published with revisions. Please see attachment: the 'no' under #3 is because 'partly' was not option.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

Reviewer #3: Yes: Gregory P. Swinand

**********

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While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Attachment

Submitted filename: Review PONE-D-22-13227R1 GS.docx

Click here for additional data file. (263.2KB, docx)
PLoS One. 2023 Apr 19;18(4):e0283851. doi: 10.1371/journal.pone.0283851.r004

Author response to Decision Letter 1

24 Feb 2023

We address the reviewers comments point by point in the attached document. Thank you for your feedback and suggestions to improve our manuscript.

Attachment

Submitted filename: BQ_PLOS_Response_Letter_2.pdf

Click here for additional data file. (202.7KB, pdf)

Decision Letter 2

Chris Harnish

20 Mar 2023

Data-driven evaluation of the Boston marathon qualifying times

PONE-D-22-13227R2

Dear Dr. Albrecht,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. In addition, I ask that you address one minor suggestion by our reviewer to highlight the specific impacts on qualifying among women. This can be particularly helpful for those researchers who may wish to build on your research.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Chris Harnish, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #3: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #3: my main concerns were over the sample selection and how they dealt with that. The comparing to the larger database on what i presume are the only available covariates -- age, sex, and time, seems reasonable. the other concern was toning down the idea that this procedure was better or whatever and it is clearly explained that optimal is only with regards to minimising the objective function; which is fine. there is still a curious issue that the proposed new way would lead to fewer women qualifying for certain age categories. for future research, if they want to include, the final note that qualifying has become less difficult in the immediate aftermath of the pandemic is quite interesting, and how these things evolve over time or react to other such world-impacts; maybe a dynamic or prescriptive perspective could be considered next!

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #3: Yes: Dr Gregory P. Swinand

**********

Acceptance letter

Chris Harnish

29 Mar 2023

PONE-D-22-13227R2

Data-driven evaluation of the Boston marathon qualifying times

Dear Dr. Albrecht:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

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Thank you for submitting your work to PLOS ONE and supporting open access.

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PLOS ONE Editorial Office Staff

on behalf of

Dr. Chris Harnish

Academic Editor

PLOS ONE

Associated Data

    This section collects any data citations, data availability statements, or supplementary materials included in this article.

    Supplementary Materials

    S1 Fig. Distribution of finishing times by marathon.

    The total number of runners observed in each marathon is shown in parentheses. The orange vertical line indicates the cut-off time for each marathon. Some marathons are strict with their cut-off times while others are more lenient. An interesting feature to note, in each marathon except for Honolulu we see a bump right around the 4 hour mark, a popular goal time for many runners.

    (TIF)

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    S2 Fig. Distribution of all finishing times by age group and gender.

    The number of runners in each age group and gender are shown in parentheses. The distribution of times does not change much between the 18–34, 35–39, and 40–44 age groups. We then see a shift towards slower times in each subsequent age group, particularly in the oldest age groups.

    (TIF)

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    S3 Fig. Percentage of women runners by age group from 2000–2019.

    The 18–34 age group increased towards 50% and then appears to have leveled off around that 50% split. All other age groups are increasing on average each year. We observe a sharper increase in the percentage of Women in many age groups in 2012 due to New York not being held that year. New York has a lower percentage of women runners than most other marathons so it’s exclusion leads to the spike observed.

    (TIF)

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    S1 Table. Number of participants by marathon and age group.

    (PDF)

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    S2 Table. Cut-off times and average number of participants by marathon.

    Differences in cut-off times may be responsible for the variation in the proportion of qualifiers across different marathons. Also, each marathon has different levels of enforcement with cut-off times which could impact the distribution of finishers.

    (PDF)

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    Attachment

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    Attachment

    Submitted filename: Review PONE-D-22-13227R1 GS.docx

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    Attachment

    Submitted filename: BQ_PLOS_Response_Letter_2.pdf

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    Data Availability Statement

    All data was taken from a public website (www.marathonguide.com). The clean version of our data is uploaded to zenodo currently. doi: 10.5281/zenodo.6959864.

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