To use the calculator below, enter the runner’s age in years, select their gender, and enter their finish time in the format H:M:S (i.e. 3:45:42).
The results will include:
- the age graded time and performance level percentage
- the percentile closest to their finish time
- the z-Score of their finish time relative to the mean for their age group
Continue reading below for some additional context.
Note: The underlying tables are only calculated for runners up to age 79. This will not return useful data for runners in their 80’s or 90’s. The age graded results currently incorporated in this calculator are based on the 2023 age grade tables. The percentiles and z-Scores are based on data I collected from 2023.
Error:
Age Grade Results
| Age | |
| Gender | |
| Time | |
| Age Graded Time | |
| Age Grade (PLP %): | |
| Percentile | |
| Mean | |
| Standard Deviation | |
| Z Score |
If you'd like to host a similar calculator on your own website, let me know. I've considered turning this into a WordPress plugin, but I'm not going to bother unless someone is going to use it. Leave a comment, and I'll follow up.
What Does This Calculator Do?
Recently, I've been writing a series of articles on Medium exploring how to best compare race results between runners of different ages.
Traditionally, the age grading system has been used to calculate an age graded time for the purpose of comparisons. This system uses an age factor to predict how much time you would slow down - compared to a younger runner.
I've been exploring two alternative methods of comparisons - percentiles and z-scores. I'll link below to the original articles to more fully explain things, but here's the gist of it.
The percentile shows what percent of runners in a given age group finish slower than a given time. So a percentile of 92% means that 92% of runners fail to meet that time - and the result is in the top 8% for that category of runner.
The z-score is a measurement of how far above or below a given finish time is compared to the mean finish time for that group. A result of -1 means that the time is one standard deviation below the mean.
You can use the calculator above to put in race results for a marathon and see how the age grading system, percentiles, and z-scores stack up.
Methodology and Context
If you haven't been following the series on Medium, here's a little more context. The links below will grant you access to each individual article behind the Medium paywall.
In the introductory article, I laid out some of my issues with the current age grading system. In short, it's a valuable tool and it's better than nothing. But unless you're at the very top levels of performance, there's very little difference in individual performance. The system may also may advantage certain age groups over others.
In the next two articles, I lay out the sample of data I will use for my analysis and conduct a brief exploration of the data. My analysis is based on finish times from all American marathons with over 500 runners that took place from September to November, 2010 to 2019. Collectively, this provided a large enough sample to identify stable distributions for most age groups - although things get a little funny when you start getting into the 70-74 and 75-79 age groups.
In the next two articles, I laid out an argument for using percentiles to compare efforts and then conducted some analysis of how this system works. The system is not perfect, and it is hard to distinguish between efforts at the very top end of the distribution. However, it does seem to do a great job of distinguishing the regular efforts of above average runners. Some tweaking could help fine tune things.
Finally, this article lays out how z-scores could be used to compare results. Conceptually, I liked this. But once I dug into the data, I'm not all that satisfied with it. The way the distributions are set up, it clearly advantages some groups (mostly young women) over others. Although the mean finish times vary in a clear and predictable way, the standard deviations don't - making z-scores a less useful tool than percentiles.
I gathered new data from 2023, and I updated the percentiles. The current version of the calculator reflects this new data.
Nice calculator, but it doesn’t seem to accept ages greater than 79. In particular I get no results for ages 80 and &1.
Good catch, Tony.
The dataset I was working with didn’t have enough data on runners 80+ to reliably calculate percentiles and z-scores for them. So it can’t return those results.
I can still calculate the traditional age grading values – I just need to fix the calculator to fail more gracefully. Once I update things with the 2023 data, I’ll also see if I can add percentiles and z-scores for the 80-84 age group
Great insights! Your age-grade calculator offers a fresh take on comparing marathon performances using age-grading, percentiles, and z-scores. The alternative methods add depth, especially for non-elite runners.
Additionally, the z-score analysis highlights potential biases, offering room for further refinement. This balance of methodologies makes your calculator a versatile option for runners seeking a more comprehensive performance analysis.
I am a male, 66 with a recent marathon of 3:45:17. My age-graded percentile is 68.59, my percentile is 92.95 and my z score is -1.26. I assume a minus z score 1.26 standard deviations faster than normal. Is that correct?