Most runners can fudge their way through a half marathon, but even those who followed their plan to the letter can absolutely blow up during a full. Using a data set of NYC marathons form 1979 until 2024 (scraped from the NYRR site, found on Kaggle), I explore the answers to a few different questions, including:
Temperature: How do times compare to the hottest year (2022) vs. a year with a more optimal temperature? Is there a way to adjust time based on temperature? What age group/gender was more affected by the heat? Does optimal marathon temperature (40 - 50 degrees) line up with optimal average performance (do years with a temperature in this range show better performance than those with temperatures outside it)?
Age and gender: What does performance look like throughout the life cycle for men and women? Are the optimal ages the same? What is a fair way to age-grade a time? (Note: Since 2023, NYRR has included a nonbinary “X” option for gender.)
#cleaning to separate columns and remove letters from temps weathered <- weather_data_3 |>separate(col = min_temp, into =c("min_temp", "min_temp_c"), sep ="/") |>separate(col = max_temp, into =c("max_temp", "max_temp_c"), sep ="/") |>#removing the F from min and max temp mutate(max_temp =str_remove(max_temp, "F")) |>mutate(min_temp =str_remove(min_temp, "F")) #getting only the yearweathery <- weathered |>mutate(date =str_sub(date, start =-4))#selecting only the columns we want and formatting as numerictemps <- weathery |>select("Year"= date, min_temp, max_temp) |>mutate(Year =as.numeric(Year)) |>mutate(min_temp =as.numeric(min_temp)) |>mutate(max_temp =as.numeric(max_temp))
Exploratory analysis: temperature
Exploratory analysis of a very hot year (2022) versus a more normal year (2021). Did performance differ overall?
The peaks for the two years are significantly different, indicating there is a difference in finish time based on temperature.
Joining the marathon table with temperature table
#converting time to minutesnyc_marathons$Finish.Time_parsed <-hms(nyc_marathons$Finish.Time)nyc_marathons$Finish_Minutes <-as.numeric(nyc_marathons$Finish.Time_parsed, "minutes")#joining with tempmarathon_joined <-left_join(nyc_marathons, temps, by ="Year")
Exploring trends in finish time, temperature, and participation
Let’s look how the number of participants has changed over the years.
#number of participants over the yearsparticipants <- marathon_joined |>count(Year)participants |>mutate(n = n/1000) |>ggplot(aes(x = Year, y = n, color = Year)) +geom_point(shape =1) +geom_line() +labs(title ="Number of Participants Over the Years", y ="Participants (thousands)")
Numbers have generally climbed over the years. There are dips in 2001 (Sept 11) and 2021 (Covid-19). The 2012 marathon was canceled due to Hurricane Sandy.
Let’s look at how the average time has changed.
mins_by_year <- marathon_joined |>filter(Year >1985) |>#when the marathon moved to November (1986)group_by(Year, max_temp) |>summarise(mean_time =mean(Finish_Minutes))
`summarise()` has grouped output by 'Year'. You can override using the
`.groups` argument.
#the mean time has generally gone up over the yearsmins_by_year |>ggplot(aes(x = Year, y = mean_time)) +geom_point() +labs(title ="Average Marathon Time by Year", y ="Mean Time (Minutes)") +theme_minimal()
#average time plotted by temperature (as the temperature goes up, does time go down?)mins_by_year |>ggplot(aes(x = max_temp, y = mean_time)) +geom_point() +geom_smooth(method ="lm", se =FALSE, color ="blue") +labs(x ="Max Temperature", y ="Mean Time", title ="Average Times by Temperature")
`geom_smooth()` using formula = 'y ~ x'
The mean time has gone up over the years, likely due to the wider range of participants. I’m puzzled by the jump in average time that happened around 2003-2005. Those were not hot years, though the race did get larger.
As for the time by temperature, I believe some of the lower averages are from when the marathon was smaller.
Trends by gender
#by men, women, and nonbinary peoplemins_by_year_gender <- marathon_joined |>filter(Year >1985) |>#when the marathon moved to November (1986)group_by(Year, max_temp, Gender) |>summarise(mean_time =mean(Finish_Minutes))
`summarise()` has grouped output by 'Year', 'max_temp'. You can override using
the `.groups` argument.
#broken out yearlymins_by_year_gender |>ggplot(aes(x = Year, y = mean_time, color = Gender)) +geom_point() +labs(y ="Mean Time (Minutes)", title ="Performance by Year/Gender") +theme_minimal()
#temperature and gender mins_by_year_gender |>ggplot(aes(x = max_temp, y = mean_time, color = Gender)) +geom_point() +labs(y ="Mean Time (Minutes)", x ="Max Temp", title ="Performance by Temp/Gender")
`summarise()` has grouped output by 'Year', 'max_temp'. You can override using
the `.groups` argument.
gender_by_year |>ggplot(aes(x = Year, y = mean_time, color = Gender, size = num_gender)) +geom_point(shape =1) +labs(y ="Average Time", title ="Participants by Year, Broken Out by Gender") +theme_minimal()
gender_by_year |>filter(!is.na(Gender)) |>ggplot(aes(x = Year, y = num_gender, color = Gender)) +geom_point(shape =1) +labs(y ="Participants", title ="Participants by Year, Broken Out by Gender") +theme_minimal()
Pretty consistently about 3-10k more men participate than women each year. We also see a consistent, roughly even gap between men’s and women’s performance by year. When we break things out by temperature, men/women’s times appear less consistent.
Exploring age and finish time
When does performance peak? Is it different for men and women?
`summarise()` has grouped output by 'Age'. You can override using the `.groups`
argument.
#filter out anyone younger than 18 because there aren't many/some seem like errorsgender_and_age |>filter(!is.na(Gender)) |>#filter out NAsfilter(Age >17) |>ggplot(aes(x = Age, y = mean_time, color = Gender)) +geom_point() +labs(y ="Mean Time (in Minutes)", title ="Mean Performance by Age and Gender") +theme_minimal()
It makes sense that non-binary runners are all over the map, since we don’t have many data points. The scattering at the end (80+ for men and ~70+ for women) is likely also because we have fewer data points. However, there is a very consistent, seemingly non-linear pattern to these points. Performance peaks in the late 20s and early 30s, then slowly declines (with a strange drop in time for both genders at ~50 and 60).
Does the difference between average times remain consistent over time?
gender_age_comparison <- gender_and_age |>filter(!is.na(Gender)) |>#filter out NAsfilter(Gender !="X") |>#filtering out non-binary runners, sine we don't have enough datafilter(Age >17)gender_wide <- gender_age_comparison |>pivot_wider(names_from = Gender,values_from =c(mean_time, num_gender),names_glue ="{.value}_{Gender}" )#create a new column for mean differencegender_wide <- gender_wide |>mutate(mean_diff = mean_time_W - mean_time_M)#graph it and filter out anyone over 80 because the data is too sparsegender_wide |>filter(Age <80) |>ggplot(aes(x = Age, y = mean_diff, color = Age)) +geom_point() +labs(y ="Mean Difference (Minutes)", title ="Mean Difference Between Men's and Women's Times by Age") +theme_minimal()
#by percentage of total timegender_percent <- gender_wide |>mutate(perc =round((mean_time_W - mean_time_M) / mean_time_M,3))gender_percent |>filter(Age <80) |>ggplot(aes(x = Age, y = perc, color = Age)) +geom_point() +labs(y ="Mean Difference (Percent)", title ="Mean Percent Difference Between Men's and Women's Times by Age") +theme_minimal()
The difference is not consistent, with the gap widening though about 37, dipping, and then gong back up before it dips again. Broken out by percentage, we see a similar shape, with a dip in percent difference between 37 and 47.
Mean differences and Temperatures
Comparing 2022 to “normal” year 2024, when temps were closer to ideal (between 44 and 54).
Look at two different groupings: gender/age and pace groups
#putting the histograms for 2024 (regular year) and 2022 (warm year) together ggplot(subset(nyc_marathons, Year %in%c(2024, 2022)), aes(x = Finish_Minutes, fill =as.factor(Year))) +geom_histogram(position ="identity", alpha =0.5, bins =30) +scale_fill_manual(values =c("2024"="#69b3a2", "2022"="#404080")) +labs(fill ="Year", title ="2022 vs. 2024 Finish Times") +theme_minimal()
years_2022_2024 <- marathon_joined |>filter(Year %in%c(2022, 2024))#calculating the average time by genderyears_2224 <- years_2022_2024 |>filter(Age >17) |>filter(Gender !="X") |>group_by(Age, Gender, Year) |>summarise(mean_time =mean(Finish_Minutes), num_gender =n())
`summarise()` has grouped output by 'Age', 'Gender'. You can override using the
`.groups` argument.
gwide_again <- years_2224 |>pivot_wider(names_from = Year,values_from =c(mean_time, num_gender),names_glue ="{.value}_{Year}" )#calculate how much slower, on average, people of different ages were in 2022pace_comparison_24 <- gwide_again |>mutate(diff = mean_time_2022 - mean_time_2024) #eliminating data for people over 75 because it becomes less consistentpace_comparison_24 |>filter(Age <75) |>ggplot(aes(x = Age, y = diff, color = Gender)) +geom_point() +theme_minimal() +labs (y ="Difference", title ="Gross Mean Difference in Finish Time", subtitle ="Versus a Colder Year")
Men, who tend to be faster overall, seem to have been more affected by the heat, with overall differences by age looking slightly larger.
Let’s bucket these into age groups and look it it by percentage, because raw numbers don’t account for general differences in time.
pace_comparison_percentage <- gwide_again |>mutate(diff_percent =round((mean_time_2022 - mean_time_2024) / mean_time_2024, 4))#Adding an age groupgwide_grouped <- gwide_again |>mutate(age_group =cut(Age, breaks =c(18, 25, 35, 45, 55, 65, Inf), labels =c("18-24", "25-34", "35-44", "45-54", "55-64", "65+"), right =FALSE))#using weighted mean so the number of runners in each age cat are accounted forgroup_diffs <- gwide_grouped |>group_by(Gender, age_group) |>summarise(mean_2022 =weighted.mean(mean_time_2022, num_gender_2022, na.rm =TRUE),mean_2024 =weighted.mean(mean_time_2024, num_gender_2024, na.rm =TRUE),.groups ="drop" )#adding a percent differencegroup_diffs <- group_diffs |>mutate(diff_percent =round((mean_2022 - mean_2024) / mean_2024, 4))group_diffs |>ggplot(aes(x = age_group, y=diff_percent, fill = Gender)) +geom_col(position ="dodge") +scale_fill_brewer(palette ="Set2") +labs(x ="Age Group", y ="Percent Difference", title ="Heat Impacts by Gender and Age Group")
Again, the impacts are significantly different between men and women in every age group. Heat impact peaks for men in the 25-34 age group at almost 10%. This makes sense because muscles make heat and make it harder to regulate your temperature; men in the 25-34 age group tend to have more muscle. Women also tend to have better thermoregulation in general.
Men also tend to go out too hot, and it’s harder to recover from that when it’s hot out. I don’t have a citation for that, but it feels true.
This finding conflicts with this study, which suggests older athletes struggle more in the heat.
I also wonder if heat heat impacts you more if you’re faster or slower. This is complicated by the fact that people tend to start later in the day if they are slower.
Age- and temperature-grading
I found an age-grading system that expresses your performance as the percentage of the world record time for your age and gender. It called anyone below 50% a casual/beginner runner, which didn’t feel right (these people are still finishing a marathon). So, I decided to create something else.
Introducing the incredibly flattering Sam Barbaro age- and temperature-grading system.
This system takes your percentage in your age and gender (so, if you’re 45, you will be ranked with other 45-year-old women) and gives you the corresponding time in the top-performing age group in an ideal year.
Ideal marathon temperature for regular runners is 40-50 degrees. However, temperatures for the NYC marathon haven’t hit that range since 2014, which was kind of a while ago. I’ve used a more recent year, 2024, where temperatures were between 44 and 54.
We can also see which year in the past 15 years had the lowest mean time for men and women to see if this holds.
`summarise()` has grouped output by 'Year', 'Gender'. You can override using
the `.groups` argument.
mean_times
# A tibble: 26 × 4
# Groups: Year, Gender [26]
Year Gender max_temp Mean_Time
<dbl> <chr> <dbl> <dbl>
1 2024 M 54 258.
2 2010 M 51 258.
3 2013 M 55 259.
4 2011 M 54 259.
5 2014 M 48 264.
6 2019 M 54 264.
7 2017 M 61 266.
8 2016 M 59 266.
9 2021 M 53 267.
10 2023 M 65 267.
# ℹ 16 more rows
The best year for men was when temperatures reached a high of 54 in 2024. For women, it was when temperatures reached a high of 54 in 2011. We will go with 2024, since it is more recent and reflects the current popularity of marathons.
The worst year for everyone was 2022.
Let’s check the size of the 25-34 age group (peak performance bracket) in an ideal year:
#Filter out peak performers in the 25 -34 age groupage_scale_2024 <- marathon_joined |>filter(between(Age, 25, 34), Year ==2024)count(age_scale_2024)
n
1 18613
There are 18k participants in this bracket, about 40% of all participants, which seems like too much. Let’s narrow it down further. What are peak performance ages for men and women?
library(gt)
Warning: package 'gt' was built under R version 4.5.2
# A tibble: 76 × 4
# Groups: Age [76]
Age Gender mean_time num_gender
<int> <chr> <dbl> <int>
1 24 M 245. 12095
2 26 M 245. 18996
3 25 M 246. 15595
4 28 M 246. 24760
5 27 M 246. 22044
6 23 M 247. 8402
7 29 M 247. 27935
8 30 M 248. 31942
9 31 M 248. 31978
10 33 M 249. 33386
# ℹ 66 more rows
For men, it’s also 24-26.
Noting that there’s conflicting information about peak marathon age, but it’s generally cited as 30-34. There could be many reasons for this discrepancy (which is not a sample size issue). Maybe lifelong runners tend to participate at 24-26, while most people get into running in their 30s. Perhaps hillier marathons, like NYC, are better-suited to the 24-26 age group.
The new scale:
scale_2024 <- marathon_joined |>filter(between(Age, 24, 26), Year ==2024)count(scale_2024)
n
1 4832
summary(scale_2024)
Year Race Name Gender
Min. :2024 Length:4832 Length:4832 Length:4832
1st Qu.:2024 Class :character Class :character Class :character
Median :2024 Mode :character Mode :character Mode :character
Mean :2024
3rd Qu.:2024
Max. :2024
Age State Country Overall
Min. :24.00 Length:4832 Length:4832 Min. : 25
1st Qu.:24.00 Class :character Class :character 1st Qu.:13390
Median :25.00 Mode :character Mode :character Median :24936
Mean :25.13 Mean :25430
3rd Qu.:26.00 3rd Qu.:37339
Max. :26.00 Max. :55473
Finish.Time Finish Finish.Time_parsed
Length:4832 Min. : 8236 Min. :2H 17M 16S
Class :character 1st Qu.:13655 1st Qu.:3H 47M 34.75S
Mode :character Median :15377 Median :4H 16M 17S
Mean :15673 Mean :4H 21M 13.0658112582787S
3rd Qu.:17423 3rd Qu.:4H 50M 23.25S
Max. :33762 Max. :9H 22M 42S
Finish_Minutes min_temp max_temp
Min. :137.3 Min. :44 Min. :54
1st Qu.:227.6 1st Qu.:44 1st Qu.:54
Median :256.3 Median :44 Median :54
Mean :261.2 Mean :44 Mean :54
3rd Qu.:290.4 3rd Qu.:44 3rd Qu.:54
Max. :562.7 Max. :44 Max. :54
4832 times (under 10% of participants), ranging from 2 hours 17 mins to 9 hours 22 mins. The fastest time is an elite and the slowest time is probably someone who walked. I am keeping the outliers because some people are elite and some people walk. I also recognize that this logic may break down in older age groups: someone 80 years old may rank #1 for their age out of fewer participants, but may have never been capable of a 2:17 marathon; someone 40 years old may come in last for their age, but finish in less than 9 hours 22 minutes; a 34-year-old elite may have a better time than 2:17.
One fix for this could be to include a case statement saying if your time is < 2:17 or the top women’s time, 2:32, then the age-graded time should just be your time. Or, if your time is less than the age-graded time, the result should be your time.
To find your age percentage, find your rank in your age (year)
age_index <- marathon_joined |>filter(Gender =="W", Age ==42, Year ==2022)|>arrange(Finish_Minutes) |>mutate(age_index =row_number())count(age_index)
n
1 679
let’s say the age index is 363 (finished in ~5 hours, 1 min)
index_42 <-as.data.frame(round(363/count(age_index),2)*100)#this returns the actual timeactual_time <- age_index |>filter(age_index ==363) |>select(Finish_Minutes)actual_time
Finish_Minutes
1 300.95
age_graded_42 <- index_42 |>left_join(women_percentile, by =c("n"="Percentile")) |>mutate(Mean_Time =pmin(Mean_Time, actual_time$Finish_Minutes))age_graded_42
n Mean_Time
1 53 272
This person’s age- and temperature-graded time is 4 hours and 32 minutes.
What if we gender-grade?
age_graded_42_m <- index_42 |>left_join(men_percentile, by =c("n"="Percentile"))age_graded_42_m
n Mean_Time
1 53 240
Four hours and eight minutes,
An age-grading shiny dashboard
This does not account for temperature.
library(shiny)# takes a scale of people age 24-26 in 2024scale_2024 <- marathon_joined |>filter(between(Age, 24, 26), Year ==2024)#creates a scale for menmen_percentile <- scale_2024 %>%filter(Gender =="M") %>%mutate(Percentile =ntile(Finish_Minutes, 100)) %>%group_by(Percentile) %>%summarize(Mean_Time =round(mean(Finish_Minutes, na.rm =TRUE), 0))#creates a scale for womenwomen_percentile <- scale_2024 %>%filter(Gender =="W") %>%mutate(Percentile =ntile(Finish_Minutes, 100)) %>%group_by(Percentile) %>%summarize(Mean_Time =round(mean(Finish_Minutes, na.rm =TRUE), 0))# SHINY UIui <-fluidPage(titlePanel("NYC Marathon Age Grader"),sidebarLayout(sidebarPanel(numericInput("user_age", "Your Age:", value =39, min =18, max =99),selectInput("user_gender", "Gender:", choices =c("W", "M")),numericInput("user_time", "Your Finish Time (Minutes):", value =301),hr(),helpText("This grades your performance against the peak age bracket (24-26).") ),mainPanel(h3("Your Results"),uiOutput("graded_results") ) ))# --- 3. SHINY SERVER ---server <-function(input, output) { output$graded_results <-renderUI({# 1. Get the user's cohort from the full dataset cohort <- marathon_joined |>filter(Gender == input$user_gender, Age == input$user_age, Year ==2022) |>arrange(Finish_Minutes)# 2. Find user's percentile rank in that cohort# We find how many people in their age/year they beat rank <-sum(cohort$Finish_Minutes <= input$user_time) user_percentile <-round((rank /nrow(cohort)) *100, 0)# 3. Pull the "Graded" time from the 2024 Peak lookup lookup_table <-if(input$user_gender =="W") women_percentile else men_percentile graded_val <- lookup_table$Mean_Time[lookup_table$Percentile == user_percentile]# Format minutes back to H:MM format_time <-function(mins) {paste0(mins %/%60, "h ", sprintf("%02d", mins %%60), "m") }tagList(h4(paste("Your Percentile in Cohort:", user_percentile, "%")),h2(paste("Age-Graded Time:", format_time(graded_val))),p("Wow, you were fast!") ) })}shinyApp(ui, server)
Shiny applications not supported in static R Markdown documents
Creating a slider
This slider shows average NY marathon performance from age 18 onward for men and women.
gender_means_clean <- gender_and_age |>filter(!is.na(Gender)) |>filter(Age >17| Age <90) |>filter(Gender !="X")
ui <-fluidPage(theme = bslib::bs_theme(bootswatch ="flatly"),titlePanel("NYC Marathon: Mean Time by Age and Gender"),sidebarLayout(sidebarPanel(sliderInput("age_slider", "Select Age:", min =18, max =90, value =25, step =1),hr(),helpText("Compare the average finish times for men and women by age.") ),mainPanel(# Large display for the mean timesfluidRow(column(6, uiOutput("men_box")),column(6, uiOutput("women_box")) ),br(),# Plot showing the context of that age in the full datasetplotOutput("dist_plot") ) ))# --- SHINY SERVER ---server <-function(input, output) {# Reactive data for the selected age selected_data <-reactive({ gender_means_clean |>filter(Age == input$age_slider) })# Helper to format minutes to H:MM format_time <-function(mins) {if(is.na(mins)) return("No Data")paste0(mins %/%60, "h ", sprintf("%02d", round(mins %%60, 0)), "m") }# UI Box for Men output$men_box <-renderUI({ val <-selected_data() |>filter(Gender =="M") |>pull(mean_time)wellPanel(style ="background: #f7da9c; border-left: 5px solid #fab520;",h4("Men (Average Time)"),h2(format_time(val)) ) })# UI Box for Women output$women_box <-renderUI({ val <-selected_data() |>filter(Gender =="W") |>pull(mean_time)wellPanel(style ="background: #cffce0; border-left: 5px solid #4bfab7;",h4("Women (Average Time)"),h2(format_time(val)) ) })# Plot showing the trend with a highlight on the selected age output$dist_plot <-renderPlot({ggplot(gender_means_clean, aes(x = Age, y = mean_time, color = Gender)) +geom_line(alpha =0.5, linewidth =1.5) +geom_point(data =selected_data(), size =5) +# Highlight the selected pointscale_color_manual(values =c("M"="#fab520", "W"="#4bfab7")) +labs(title =paste("Age", input$age_slider, "selected"),y ="Mean Time (Minutes)") +theme_minimal() })}shinyApp(ui, server)
Shiny applications not supported in static R Markdown documents
Citations
For Shiny code: Google Gemini. (2026). Gemini 3 Flash [Large language model].
https://gemini.google.com. Accessed May 6, 2026.
