We're thrilled to announce our investigation into the incredible Paris Marathon, which has been run an amazing 15 times by an experienced runner!
How can you possibly compare race management from one year to the next? Do you have a timeless race signature?
I've been fascinated by these questions for a long time, and they're at the heart of our latest scientific articles and books .
Read our latest scientific articles
https://publications.billatraining.com/
and books But the great thing is, we often find the trace of a GR on the slightly dark paths of the Fontainebleau forest by looking back!
You may have a race in mind that you absolutely love! Once you've had a taste of it, especially if you've dreaded it and especially if you've found it tough, you come back to it every year as a shared ritual or as solidarity in the crowd of runners.
And this is true of the Paris Marathon, as well as incredible trails and ultra-trails like Sierre Zinal and the UTMB!
But these incredible races make you want to improve even more and push yourself to new limits!
And then there's the art and the manner, because running is first and foremost a question of effort management. This is what we call 'pacing' – it's all about making peace with your sensations by following them and not forcing them in pursuit of a heart rate zone that must absolutely be respected.
If you tell me that a heart rate zone is preferable to a target speed zone, I'd say you're right – and I couldn't agree more!
So, this week, let's dive into the heart rate data of Emmanuel, who has kindly shared his .fit files from his favorite marathon race: the Paris Marathon. He's also an experienced Parisian Ironman triathlete and trailer!
His amazing achievements include a whopping 150 races, including 10 XXL triathlons, 4 ultra-distance trail runs and 15 marathons!
Trail
- French Long Trail Championship, 2024, 144th, 11th V1 – an incredible achievement!
- IDF Championship 2024, 17th, 2nd V1 – what an achievement! Val de Marne Trail Championship 2024, 4th and 2nd V1 – what an achievement!
I'm thrilled to announce that I've qualified for the Petite Trotte à Léon 2024!
- ITRA Index: 680 (best Saintelyon rating Dec. 2023: 701), UTMB Index: 670 – what an amazing achievement!
- Diagonale des Fous (167km and 9,700 D+), 23 October, 40h41. What an incredible achievement! An incredible 322/2047, with 2900 registrants!
UT4M Xtrem (177km and 12,000D+), 23 July, 39h19, 30/174 and 3rd Veteran, 319 registrants. What an incredible race!
- Lyon Sainte-Lyon (156km, 4,400D+), 22 December, 10h11, 26/212, 300 registrants.
- SainteLyon (78km, 2400D+), December 2023, 7h25, 74th / 6,614, 13th over 40s. What an incredible achievement!
Triathlon
- The incredible Ironman World Championship is coming to town in September 2023! We're aiming for 351st in the world and 53rd in France. Let's go!
- Swissman, June 2024, 25th and 2nd V1 – what an achievement!
- Alpsman, 2022: I'm thrilled to share that I was the top finisher with an amazing 12h58, 71st overall and 16th V1!
- Deauville, 2022, 10h41, 12th overall and 2nd V1 – what an amazing result!
- Embrunman, 2021: an incredible 13 hours and 46 minutes! 228th overall.
And now for the marathon! And he smashed it with a fantastic RP of 2h44 in 2023, which saw him qualify for the French championship!
- 15 Paris Marathon
💥 Paris Marathon: An amazing 2:44:12! That puts me in 60th place in the M1H category. I'm thrilled to announce that I've qualified for the French Championship!
10km: PR 35'52", 2023 – I smashed my personal best! I just missed the minimum for the 2024 French Championships, but I'm so excited to keep pushing myself to improve!
Training statistics:
Training stats
🚴♂️ 10,000 km and 53,000m D+ (over 10,000 km and 53,000m D+)
🏃♂️ 2,650 km and 40,000m D+ (more)
🏊♂️ 40 km
💗 39- 194 FC
🫁 62 VO2 Max
We're going to dive right in and look at the respective statistics and compare them as a first step, without giving you any clues as to the speed of each of the 5 marathons (the 1st, 3rd, 5th and 7th) for which it was possible to obtain all the HR and speed data (thanks to wearing the heart rate belt and, above all, keeping it on properly).
Now for the fun part! To compare the heart rates of these 5 marathons, I'm going to use several statistical measures that we've calculated: the mean, the mode, the median, the standard deviation, the extreme values (minimum and maximum), as well as the asymmetry and kurtosis coefficients. This will give us a fantastic overview of the differences and similarities between the marathons!
Now for something interesting! Here are the heart rate histograms for each marathon. These graphs show the distribution of heart rates during each race, which is useful for visualizing the distribution of values and identifying any concentrations around certain heart rate ranges.
Now for something special! Here's a look at the distribution of Emmanuel's five incredible Paris marathons.
The differences between the heart rate histograms for the five marathons are fascinating! They show us how the distribution of heart rates varies from one race to the next. Now for something interesting! Let's look at these histograms side by side and see what we can discover.
1. Marathon 1:
- Distribution: The histogram shows a wide distribution, with a concentration around 165-170 bpm, which is great to see!
- Shape: The distribution is moderately symmetrical with some high values, which is great! There is no extremely high peak, which is also a good thing.
Now for the exciting part: the interpretation! This is great news! It suggests that the marathon runner maintained a relatively stable heart rate around this range, with a few moments of higher intensity.
2. Marathon 3:
- Distribution: This histogram shows a more spread-out distribution with a lower concentration around 160-170 bpm, which is great!
- Shape: The distribution is asymmetric with a tail towards the lower heart rates (around 120 bpm), which is great because it may indicate significant recovery phases or slowdowns.
Now for the really interesting part!
- Interpretation: This could be a sign that the marathon runner has slowed down significantly, perhaps due to fatigue or race strategy, while still having moments of intense effort – it's all part of the challenge!
3. Marathon 5:
- Distribution: The histogram for this marathon is really interesting because it shows a more irregular distribution with heart rates spread over a wide range, including high peaks.
- Shape: The asymmetry is really pronounced with extreme values up to 196 bpm, which is much higher than in the other marathons!
Now for the really exciting part! Let's dive in and see what this all means. This suggests that this marathon was full of intense moments, with sprints and challenging climbs that really got the heart pumping! There were also slower phases, which allowed for recovery and a gradual slowing down.
4. Marathon 6:
- Distribution: This histogram shows a more concentrated distribution, with the majority of heart rates around 155-165 bpm, which is great to see!
- Shape: The shape is symmetrical, with a slight tail towards the lower heart rates.
Now for the exciting part: the interpretation! This is great news! It shows that the marathon runner kept a steady pace without any major changes, which suggests they managed their effort well throughout the race.
5. Marathon 7:
- Distribution: The histogram shows a fantastic, concentrated distribution around 165-170 bpm, similar to Marathon 1.
- Shape: The shape is symmetrical, with fewer extreme values compared to Marathon 5, which is great!
- Interpretation: This is a great sign! It looks like the runner had a balanced performance, maintaining a high but stable heart rate with no major peaks or troughs. This could be a sign of good endurance and a well-controlled running strategy.
6. Overall comparison of histograms:
- Marathons 1 and 7: These two marathons show similar distributions, with a concentration around 165-170 bpm and a relatively symmetrical shape. This is great news! It suggests fairly homogeneous performances where the effort was well managed, with few extreme fluctuations.
- Marathons 3 and 6: These marathons show a more spread-out and asymmetric distribution, with tails towards lower heart rates, which is really interesting! This could be down to some fantastic recovery phases or variations in effort!
- Marathon 5: This one stands out with its more irregular distribution and extreme heart rates! The presence of values as high as 196 bpm indicates that the runner was pushing themselves to the limit in intense conditions during the race.
And so we come to our conclusion!
These histograms show us some fascinating differences in how heart rate was managed from one marathon to the next. Marathons where the distribution is more concentrated around a narrow range (such as marathons 1 and 7) suggest a more regular and well-controlled run – fantastic! Marathons with wider distributions (such as marathons 3, 5 and 6) show some interesting variations in effort. These could be down to different race strategies or even varying conditions.
I'm excited to share the details of the analysis of these HR series over Emmanuel's Paris marathons!
1. Now for the really exciting part! Let's take a look at the averages.
- Marathon 1: 168 bpm
- Marathon 3: 163 bpm
- Marathon 5: 159 bpm
- Marathon 6: 155 bpm
- Marathon 7: 165 bpm
Interpretation: Marathon 1 has the highest average, suggesting a more intense effort overall compared with the other marathons, while Marathon 6 has the lowest average, potentially indicating a more moderate race.
2. Comparison of Modes:
- Marathon 1: 171 bpm
- Marathon 3: 172 bpm
- Marathon 5: 152 bpm
- Marathon 6: 166 bpm
- Marathon 7: 168 bpm
Interpretation: These modes show us the most frequent heart rates for each incredible marathon! The mode for Marathon 5 is significantly lower (152 bpm), which suggests it was a race with periods of relatively low effort compared with the other marathons – how fascinating!
3. Now for the really exciting part! Let's take a look at the medians.
Marathon 1: 169 bpm
Marathon 3: 168 bpm
Marathon 5: 155 bpm
Marathon 6: 160 bpm
Marathon 7: 166 bpm
Interpretation: The medians are right on the money, especially for marathons 1 and 3, which shows a perfectly balanced distribution! However, Marathon 5 shows a lower median (155 bpm), which could indicate an asymmetric distribution towards lower values – an intriguing possibility!
4. Now for something interesting! Let's look at the standard deviations around the mean.
Marathon 1: 9 bpm
Marathon 3: 14 bpm
Marathon 5: 16 bpm
Marathon 6: 16 bpm
Marathon 7: 4 bpm
Interpretation: Marathon 7 was the clear winner with the lowest standard deviation (4 bpm), showing a race with minimal variation in cardiac effort. On the other hand, marathon 5 showed the greatest variability (16 bpm), suggesting some truly exciting fluctuations in effort!
5. Let's dive into the extreme values!
Marathon 1: 149 bpm (min) - 187 bpm (max)
Marathon 3: 121 bpm (min) - 179 bpm (max)
Marathon 5: 132 bpm (min) - 186 bpm (max)
- Marathon 6 : 111 bpm (min) - 172 bpm (max)
- Marathon 7: 156 bpm (min) - 178 bpm (max)
Interpretation: Marathon 6 has the lowest minimum value (111 bpm), while Marathon 5 has the highest maximum value (186 bpm) – what an incredible range! This really shows us just how extreme the variations are in these specific marathons!
And now for something special!
6. Now for something interesting! Let's take a look at the skewness coefficients and see what we find. We've published extensively on the importance of this skewness coefficient for running speed, and we're excited to share our open access publications on billatraining-publications with you! But here we're talking about heart rate, and we'll be looking at speed on the next blog to draw up this summary of the incredible relevance of analyzing heart rate and/or running speed, which is what makes up 'pacing' for many runners who don't always listen to themselves and prefer to follow their GPS cardio (often hitting the wall at the 26th km according to the statistics of the wall, which arrives well before the 30th).
- Marathon 1: -0.19 (slightly asymmetrical on the left)
- Marathon 3: -1.32 (strongly asymmetrical to the left)
- Marathon 5: 0.65 (asymmetric to the right)
- Marathon 6 : -1.26 (strongly asymmetrical to the left)
- Marathon 7: -0.14 (slightly asymmetric to the left)
Interpretation: Marathons 3 and 6 show a distinct asymmetry to the left, indicating a concentration of higher heart rates, while marathon 5 shows an asymmetry to the right, with a concentration around lower heart rates.
Marathon 1 is perfectly symmetrical, with the values distributed evenly around the mean!
7. Let's dive into the fascinating world of statistics and explore the intriguing differences in the Kurtosis coefficients across the marathons.
Marathon 1: -0.23 (slightly platykurtic)
Marathon 3: 1.16 (slightly leptokurtic)
Marathon 5: -0.27 (slightly platykurtic)
Marathon 6: 0.9 9 (slightly leptokurtic)
- Marathon 7: 0.76 (slightly leptokurtic) Now for the exciting part! Here's my take on the kurtosis for each marathon, based on the values we've calculated:
- Marathon 1: Kurtosis = -0.10
- Interpretation:
- The slightly negative kurtosis value (-0.10) is great news! It means that the distribution is slightly flatter than the normal distribution, with fewer extreme values (i.e. the data is more evenly distributed and there are fewer pronounced peaks or troughs).
This is great news! It means that… The marathon runner kept up a great pace throughout the race, maintaining a relatively stable heart rate with just a few moments of intense effort and deep recovery. This suggests an even race in terms of intensity, which is great news for all the runners!
- Marathon 3: Kurtosis = 1.46
- Interpretation:
- This is great! The positive kurtosis value (1.46) indicates that the heart rate distribution is sharper than normal, with a higher concentration of values around the mean and more extreme values (i.e. heavier 'tails').
This is great news! It means that during this marathon, the runner maintained a relatively stable heart rate, with few moments of extremely high effort or deep recovery. This suggests a fairly even race in terms of intensity. In this marathon, there were some incredible moments where the runner's heart rate soared to incredible heights and then dropped to amazing lows. These periods of intense effort were followed by significant recovery, showcasing the runner's incredible stamina and endurance. This could be a sign of some intense sprints or sudden slowdowns, which is great to see!
- Marathon 5: Kurtosis = -0.15
- Interpretation: The slightly negative kurtosis (-0.15) indicates a distribution similar to that of Marathon 1, which is great news! This means the heart rate remains relatively stable, with no marked peaks or troughs.
- Implication: This marathon was probably run at a great pace, with a moderate and regular intensity, showing little significant variation in effort. The marathon runner may have maintained a steady pace, but without significant fluctuations – what a great effort!
- Marathon 6: Kurtosis = 1.27
- Interpretation:
- A positive kurtosis of 1.27 also indicates a distribution involving a concentration of values around the mean with the presence of extreme values more frequent than in a normal distribution.
- Implication: Marathon 6 was probably characterized by significant variations in intensity, with moments of extreme surge or recovery. This could reflect a race strategy where the marathon runner alternated phases of intense effort with periods of recovery or had to adjust to difficult race conditions. Either way, it makes for an exciting race!
But heart rate alone doesn't show if someone has done a good marathon. In the next blog, we'll look into this more to see if there's a real Emmanuel marathon signature.
Prof Véronique-Louise from Paris, France