Which Stroke is Truly the Decider in the Individual Medley? (Long Course Edition; Stats Included)

Individual Medley - Lochte and Phelps

Which Stroke is Truly the Decider in the Individual Medley? (Long Course Edition; Stats Included)

The individual medley races can be some of the most exciting races, due to the variety of strategies employed by different swimmers. This can lead to significant changes in the race in just one 50 or one 100. But which stroke is it where we see the most variability?

In a previous analysis, we looked at such results in short-course yards, and found that, in agreement with prevailing wisdom, breaststroke is the stroke where we see the largest spread between swimmers. This was especially true in the 400 IMs, where breaststroke clearly had the higher variability. In this latest analysis, we will take a look at long course, and see if these trends hold up.


Splits were taken from the 2016 Olympics and the 2017 and 2019 World Championships. For both the 200 IM and 400 IM, the top 16 finishers from prelims were included, along with all results from semifinals and finals. This meant that the 400 IM had significantly less data points, since it does not have a semifinal round.

In order to determine which splits had the greatest variation, we will look at the spread, standard deviation, and coefficient of variation. This will give a good idea of where there is the most average difference between swimmers.


The first thing I looked at was the general spread of the data. The first table shows the difference between the slowest and fastest splits, and the second shows the range of the middle 50% of the data.

Total Range

W 200 IM M 200 IM W 400 IM M 400 IM
Fly 2.64 2.02 4.29 4.92
Back 3.49 2.99 7.03 5.69
Breast 4.96 3.40 7.92 7.82
Free 4.67 3.09 7.72 5.30


Middle 50% Range

W 200 IM M 200 IM W 400 IM M 400 IM
Fly 0.68 0.47 1.20 1.54
Back 0.88 0.93 1.87 1.70
Breast 1.11 0.98 2.71 2.15
Free 0.92 0.73 2.53 1.60


In terms of the ranges, breaststroke still looks like it is the most variable across all four events. For the men’s events, backstroke is the second most variable, while for women, it is freestyle. Notably, freestyle looks more variable when we look at the total range than the middle 50% range. This indicates that more swimmers are fading at the ends of their races, driving up the overall range while leaving the middle 50% relatively unaffected. Butterfly has the smallest range in all four events, by both measures, indicating that it has the least variability. A possible explanation for this is that butterfly is the first stroke, so the best butterflyers prefer to stay controlled instead of going all out.

Standard Deviation

Unfortunately, measuring the range does not really get at the average variation, which is what we are looking for. The standard deviation gives a better idea of the average difference from the mean, making it a much more focused measure than the range. The standard deviations are listed below.

W 200 IM M 200 IM W 400 IM M 400 IM
Fly 0.49 0.33 0.89 1.12
Back 0.72 0.64 1.42 1.26
Breast 0.86 0.65 1.85 1.70
Free 0.75 0.56 1.63 1.13


The results still seem to favor breaststroke, but the difference is not quite as pronounced as in the short-course results. For example, the men’s 200 IM only has a 0.01 difference between backstroke and breaststroke. The second most variable is backstroke for men and freestyle for women, which is consistent with the spread results. Butterfly remains the least variable, which is also consistent with the spread.

Coefficient of Variation

However, another important consideration is that the breaststroke splits are simply slower than the other splits. Because of this, it makes sense that there would be more deviation on average. In order to control for this, I looked at the coefficient of variation, which is the standard deviation divided by the mean. Results are in the table below

W 200 IM M 200 IM W 400 IM M 400 IM
Fly 0.0174 0.0130 0.0142 0.0195
Back 0.0215 0.0215 0.0200 0.0194
Breast 0.0227 0.0192 0.0232 0.0236
Free 0.0240 0.0195 0.0255 0.0189


The results here are significantly murkier. Interestingly, only the men’s 400 individual medley maintains the trend of breaststroke having the most variability. On the women’s side, freestyle takes over as the most variable stroke for both the 200 and 400 distances. Meanwhile, the men’s 200 IM has backstroke as the most variable stroke. The results do not seem to tell any clear story here.

Analysis and Comparison to Short Course

As we have seen, breaststroke has the most variation among the four strokes in terms of overall time. However, this makes sense, because more time is spent swimming breaststroke than any of the other strokes. When adjusting for that fact, the only trend that remains is that the women’s events have the most variation in freestyle.

The results differ quite a bit from the short-course results. In short course, breaststroke was the most variable for the 400 IM events for both men and women, while backstroke was the most variable for the 200 IM events. The most striking difference is the increase in variability among freestyle splits (except for men’s 400 IM). A potential explanation for this is that since the races take more time in long course, swimmers who might have gotten away with fatiguing in short course are suffering the consequences here.

Another interesting thing to note was the difference between men and women. Women’s races tended to have much more variability in the freestyle. This could be attributed, once again, to the women’s race taking more time and thus causing more fatigue. It could also simply indicate a difference in the way the race is swum between the genders.

The main limitation of this study was the number of years included. This came up specifically in the men’s 200 IM, where the standard deviation of backstroke in 2016 was 0.77, which shot the overall standard deviation up to 0.64, right up with breaststroke for the highest value. Notably, this was the only year in the data set to include individual medley stalwarts Michael Phelps, Ryan Lochte, and Thiago Pereira, all of whom were outstanding backstrokers (>1 second faster than the mean). Their inclusion in prior years could further cement backstroke as the most variable in the 200 IM.

Ultimately, these results demonstrate that there is not one clear stroke where all the lead changes happen. While it is true that breaststroke takes up more time than the other strokes, the average deviation is very close when we adjust for this. The individual medley events are meant to create a race where all four strokes are equally valued, and from the data, it appears that this is true.

All commentaries are the opinion of the author and do not necessarily reflect the views of Swimming World Magazine nor its staff.

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3 years ago

Well done Hunter. I see they teach Statistics at Columbia. Bottom line is that 400 IMers know how to suffer!

Matthew Shirley
Matthew Shirley
2 years ago

I question your decision to factor out breaststroke being the slowest leg. That’s not a flaw; that’s exactly the point. This is true from two different angles. First, if a you can gain a 1% improvement in one stroke, 1% of your breaststroke time is more than 1% of another stroke because (duh) the breaststroke split is larger. Two, as your raw stats demonstrated, the difference between the fastest and slowest breaststroke splits is greater than any other stroke, as is the difference between faster and slower breaststrokers. Real world example, when Amanda Beard won the 200 breast at Athens, she was the world record holder in that event, but unlikely to make the U.S. team in another individual stroke. Yet, she was so awesome at that one stroke, she won silver in the 200 IM. As always, Michael Phelps is the exception.
Now, if it were a 2 or 4 minute IM (equal time for each stroke, whoever gets farthest wins) instead of 200 or 400 meters, the situation would be reversed.

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