AUTO MANUFACTURERS are careful to qualify their gas mileage claims with the phrase, “Your mileage may vary.” And so it is with distance running. What works for one person may or may not work for another. There are varying degrees of correlation between one runner’s training regimen and his or her results when compared to those of other runners.

One of the problems in determining how best to train for and run marathons is that opinions are so varied about what works and what doesn’t. Every coach and writer has a biased view about what you ought to do to maximize your training and realize your potential. Unfortunately, much of their advice is not backed up by hard evidence. In many cases, the data required for adequate analysis simply does not exist.

Over the years, I’ve been collecting an extensive amount of data about my own training and racing. Although this data applies only to myself, and your mileage may vary, some analysis will still be useful to others. At best, you may be able to apply some of the deductions to your own training. And at the very least, you’ll be able to find out what has worked or not worked for this one individual.

The analysis of the data shows the correlation between the following factors and marathon performance (see pages 90-91 for the data):

• Overall training factors such as total mileage, overall pace, and mile repeat pace.
• Various long run factors, such as long run pace and distance.
• Various other miscellaneous factors, such as weight and age.

These factors were chosen for two reasons: first, they may actually provide useful information, and second, I actually have data relating to them.

THE DATA

To determine which training factors have the most influence on a given race, I first select the marathons and then analyze the related training data. Here are the criteria for selecting which of my 50+ marathons to include in the analysis:

• There must be data available relating to all of the factors.
• The marathon itself must have been a serious effort, not just a “long training run.”
• I must have not become injured or sick just before or during the race.
• I must not have “hit the wall” badly during the race. This is because these efforts are generally precipitated by starting out too fast, and then finishing with a much slower time than I would have had I simply run a steady but slower pace.

I was interested in the races where I would and should expect a certain result, based as much as possible on the training itself. I came up with 30 marathons that fit the criteria (see pages 90-91).

It so happens that for many of these marathons, the expected result was a time in the neighborhood of 3 hours. [For more on the subject of how to break 3 hours, see “Six Fifty-Two” in the November/December 1999 issue of M&B.] Some of these efforts were successful and some not. For the purposes of this study, however, that objective shouldn’t matter. The correlation between the various training elements and the marathon performance ought to apply regardless of the time goal.

Several environmental factors, such as weather conditions and what I ate the night before the race, may cause variations in marathon performances. Using larger quantities of data help to mitigate these factors in such a way that they begin to lose significance, however. They will not be taken into account for this study.

Most marathon training programs span a time period of 12 to 18 weeks. Although a longer build-up period is generally preferable, the first several weeks are often devoted to base-building. The factors analyzed assume that I already have a solid base, so the period chosen for the data is generally 1 of 12 weeks before the marathon.

INFORMATION, CORRELATION, AND CAUSATION

Although I’ve collected all of this data, I haven’t always done so great a job of processing it into useful information. Sure, I do look back once in a while to determine some of the training that led to a successful race effort. But these looks back are not very qualitative or quantitative. Sharing a detailed analysis of the data is the goal of this article. The transformation of the available data into useful information involves correlating the training data with the marathon performance data by use of statistical models.

Probability and statistics were not among my strongest courses back in my college days. Those days, in turn, happen to be a long time ago in a galaxy far, far away. I am fortunate, however, to have two daughters in college who were able to help out their ole Dad with his homework. You won’t need to be a statistician to understand the basic principles here, however.

To show correlation, each set of training data is plotted against the marathon performance data. In addition, a correlation coefficient, R, is computed. R is a number that describes the relationship between two sets of data. I’m sure there’s a reason why it’s called R, but please don’t ask me what that reason is. To make the correlations more meaningful, R is squared and then multiplied by 100 to arrive at the percentage of variation in one factor explained by the other factor.

To put it more concisely, for each set of training data versus the marathon performance data, a scatter diagram will be created, and the percentage of variation will be calculated; the larger the percentage, the stronger the correlation. The actual formula for R, as well as that for any other method of measuring correlation, is left as an exercise for the reader. For my part, I used Microsoft Excel.

There is one other thing. Each daughter independently informed me that “correlation does not imply causation.” Causation, I said, is the whole idea of training. On the other hand, it is conceivable that a strong correlation between, say, mile repeat pace and marathon pace may simply be due to being in shape (or young, or not being injured, etc.), and not due to one thing causing the other. More on this later.

OVERALL TRAINING ELEMENTS

Is there a correlation between marathon pace and overall mileage? A nonrunning acquaintance overheard a friend and I discussing his most recent marathon. The acquaintance said, “Wow, a marathon! How did you train for it?” My friend, who didn’t want to be bothered explaining the intricacies of his training to someone who wouldn’t understand (or even ultimately care), replied, “I ran a lot.”

I liked his answer. It really sums things up, doesn’t it? If you want to run a marathon, you’ve got to run a lot. If you want to run a fast marathon, you should probably run even more. But how close is the correlation between number of training miles and the resulting marathon pace?

In comparing the total number of miles run during the 12 weeks before a marathon to the actual marathon pace, there is a fairly strong negative correlation, and a percentage of variation of 11.47 percent. This means that for me, more miles do relate to a faster marathon pace.

How about the correlation between marathon pace and overall pace? There’s no doubt that training is specific. To run fast during a race, you must run fast during your training. The question is, how specific is it? How close is the correlation between the overall training pace over the previous 12-week period and the resulting marathon pace?

The correlation analysis yields a percentage of variation of 0.42 percent. This number is so small that it’s almost insignificant. Could it be that it doesn’t matter how fast I train? Clearly, for me, overall training pace is not as important as I had thought.

It occurs to me that perhaps for my more successful efforts I had more variation in my training pace. That is, I may have done my fast runs faster, although my slow runs may have been slower. I may also have done more fast training. The best way I have to measure this sort of thing is to examine the number of races during the marathon build-up period and my mile repeat pace. The assumption is that I would be doing these runs much faster than my normal training pace. In addition, the number of races gives us some idea of quantity of fast training efforts. See below for analysis.

Correlation Between Marathon Pace and the Number of Previous Races Run During the Marathon Build-Up

Does it help to run other races as part of the marathon training? I often try to fit some shorter races into my schedule. For the data, I examined the total number of races run during the prior 12 weeks. Marathons or other races done as “training runs” are not included, but marathons that were run as races are counted as races. Of course, for a serious attempt at a fast marathon, you generally should not be running another serious marathon within the previous 3 months, but there are always exceptions. Your marathons may vary.

With the exception of those few longer ones, the majority of the races were in the 10K range. It would have been nice to analyze these race paces versus the marathon pace, but the distances do still vary; it may be anything from 5Ks to other marathons. Pace calculators, used to compute one distance’s anticipated pace based on a race pace of a different distance, are available elsewhere.

Comparing the total number of prior races run to the marathon pace itself yields a percentage of variation of 15.20 percent. This means that, for me, it appears that it does help to run other races prior to the marathon, and the more, the better. Contrast this with the philosophy of making the marathon one’s first road race of any kind!

Correlation Between Marathon Pace and Average Mile Repeat Pace

For all 30 of the marathons in this analysis, my preparation included several sessions of 1-mile repeats. These interval sessions are generally done in the form of 1600-meter repeats, with a 400-meter rest in between. Of course they also include warm-up and cool-down periods. I usually do one session of six to nine of these each week during the 12 weeks leading up to the race. The exceptions come when I substituted other speed work, say 1200-meter repeats or a race or tempo run. I also usually avoid or curtail these sessions during the final 2 weeks. Due to all these variables, I was not able to analyze the number or frequency of repeats— only their pace.

The pace for the repeats is important, however. I usually try to run them at close to my current 10K pace. How closely correlated is this pace with the resulting marathon pace? The percentage of variation is 34.81 percent. This indicates a strong correlation: a faster average mile repeat pace definitely does relate to a faster marathon pace.

LONG RUNS

There is general agreement that the long run is the cornerstone of any marathon training program. Opinions vary widely, however, on how long the long runs should be and on the optimum pace for these runs.

Correlation Between Marathon Pace and the Distance of Long Runs

There has been much controversy over the years regarding how long long runs ought to be. Some say that they should not exceed 20 miles, so that you’re able to resume mid-week training sooner. Others have opined that to prepare for the rigors of the last 10K of the marathon itself, much longer training runs, say 27 to 29 miles, are necessary.

A more recent, and I think more sensible, notion has come along that you should run long runs of the same amount of time that you expect to run the marathon. This may indicate a maximum of about 22 miles, depending on the difference between marathon and long run pace.

I calculated the average distance for all runs 18 miles and longer during the 12 weeks before the marathon. These runs have generally been done on a weekly basis. The comparison to marathon pace yielded a slight surprise: the percentage of variation is only 0.02 percent, so there’s no significant correlation. This means that I haven’t necessarily run faster marathons when my long runs have been longer; the distance of those runs doesn’t appear to matter. Perhaps I’ve been overdoing it a bit, however. It may be better to save my legs for my other training.

Another philosophy that I’ve adopted in recent years is to alternate between very long and semi-long runs. One week I may do a 25-miler, followed by a 20-miler, and so on. I still like this idea, but even so, perhaps I should cut back on those distances a bit.

Correlation Between Marathon Pace and Long Run Pace

Yet another source of controversy over the years is the pace of long runs. Is it better to run them at or near race pace, or should they be run at a much more leisurely, conversational pace? The arguments go way back.

Over the years, my long run pace has varied quite a bit, as I’ve oscillated between the differing philosophies. Generally, however, it has been about 1 to 1.5 minutes per mile slower than the resulting marathon pace.

In comparing the average pace for all of the long runs during the 12 weeks before the marathon versus the actual marathon pace, we see that the percentage of variation is 1.03 percent. This is not a strong correlation, but it appears that, in general, the faster I’ve run my long runs, the faster I’ve run my marathons.

It may be advantageous to vary the pace of long runs. Begin the long runs at a pace of 2 minutes per mile slower than your planned marathon pace, pick up the pace a bit during the middle miles, and then run the final few miles at marathon pace.

OTHER FACTORS

Some factors have nothing directly to do with training but may have a strong effect on a marathon performance. Some of these, such as ancestry and predilection to train hard, can’t be measured, but others can. Two that I’m particularly concerned about are my weight and my age. Both appear to be headed in an upward direction, and although I may be able to do something about one of them, I wonder how well they relate to my marathons.

Marathon Performance and Training Factors

Date	Marathon	Marathon pace	Overall mileage	Overall training pace	Number previous races	Average mile repeat pace	Average long run distance	Average long run pace	Average weight	Age
3/19/89	Sy Mah	7.25	664.5	8.31	0	6.38	25.57	8.40	159.50	35
5/21/89	Revco Cleveland	6.83	685.4	7.95	3	6.23	23.96	7.99	153.33	36
10/15/89	Detroit Free Press	6.91	627	8.23	4	6.22	22.46	8.71	155.50	36
5/19/91	Revco Cleveland	7.48	573	8.47	3	6.72	21.80	8.97	161.50	38
10/20/91	Detroit Free Press	7.06	657	8.15	3	6.44	24.00	7.92	158.73	38
5/17/92	Revco Cleveland	7.75	493.2	8.23	1	6.71	22.89	8.43	161.50	39
9/5/92	Scotty Hanton	6.83	705	8.13	2	6.50	24.06	8.48	157.00	39
10/18/92	Detroit Free Press	6.98	701.4	8.46	5	6.39	26.65	9.18	155.44	39
9/4/93	Scotty Hanton	6.91	680.2	8.34	4	6.32	22.80	8.52	157.55	40
10/17/93	Detroit Free Press	6.91	692	8.47	4	6.32	24.36	8.21	153.54	40
7/10/94	Ohio/Michigan	6.79	07	7.95	5	6.42	22.14	8.07	157.78	41
4/17/95	Boston	7.02	689	7.92	2	6.58	21.86	8.53	158.24	41
9/3/95	Scotty Hanton	6.83	688.7	7.80	9	6.40	20.86	8.13	155.00	42
10/15/95	Detroit Free Press	6.83	640.5	7.66	7	6.38	23.20	7.86	155.35	42
4/15/96	Boston	7.48	682	7.90	3	6.70	22.40	8.46	158.65	42
7/14/96	Ohio/Michigan	6.79	694	7.66	6	6.43	21.80	8.08	158.84	43
10/14/96	Toe to Tow	6.83	659	7.59	6	6.30	21.74	7.92	157.30	43
4/21/97	Boston	7.06	688	7.71	4	6.47	22.30	7.95	157.22	43
7/13/97	Ohio/Michigan	7.06	681	7.63	6	6.38	22.60	7.84	158.00	44
10/19/97	Detroit Free Press	7.18	587	8.07	2	6.77	22.91	8.10	158.32	44
9/6/98	Scotty Hanton	7.02	684	7.61	3	6.37	22.50	7.87	157.45	45
10/11/98	Chicago	7.06	654	7.52	5	6.32	23.03	7.72	158.32	45
12/13/98	Honolulu	7.40	652	7.58	6	6.48	23.05	7.79	156.00	45
4/19/99	Boston	7.48	645	7.76	6	6.45	23.21	7.96	156.32	45
5/29/99	Bayshore	7.10	630	7.58	6	6.45	23.53	7.75	156.08	46
9/5/99	Scotty Hanton	7.29	688	7.48	7	6.45	23.50	7.75	157.36	46
4/30/00	CVS Cleveland	7.14	701	7.74	2	6.47	23.54	7.86	161.08	47
10/15/00	Towpath	7.10	799	7.87	6	6.22	23.46	8.34	160.00	47
3/31/01	Martian	7.75	736	7.93	1	6.49	22.30	8.22	161.32	47
4/29/01	CVS Cleveland	7.21	734	7.81	3	6.45	22.58	8.17	161.23	47
*Correlation Coefficient, R”			-0.34	0.06	-0.39	0.59	-0.02	0.10	0.58	0.23
Percent of Variation			11.47	0.42	15.20	34.81	0.02	1.03	33.49	5.44

Marathon pace is the average pace per mile for the marathon. Overall mileage is the total training miles run during the 12 weeks leading up to the marathon. Overall training pace is the average pace per mile for all overall mileage. Number previous races is the total number of races run in the 12 weeks prior to the marathon. Average mile repeat pace is the average pace for each 1600-meter repeat run during the 12 weeks prior to the marathon. Average long run distance is the average distance for all runs over 18 miles during the 12 weeks prior to the marathon. Average long run pace is the average pace for the long runs. Average weight is the average weight for all weigh-ins taken during the 5 weeks prior to marathon race day. Age is the age on marathon race day.

Correlation Between Marathon Pace and Average Weight

I wasn’t so sure I was going to like this one. A positive correlation would mean that keeping my weight low correlates with faster marathon times. And, like many people, I have some amount of difficulty keeping those pounds off. The average measurement for all weigh-ins over the 5 weeks before the marathon was compared with marathon pace. We’ll have to assume that the scale is consistent. The analysis for the correlation between marathon pace and average weight yields a percentage of variation of 33.49 percent. This is a significant correlation.

And it is just as I had feared. I need to keep working at fighting that battle of the bulge.

Correlation Between Marathon Pace and Age

I was sure I wasn’t going to like this one. A positive correlation here would mean that my race paces are getting slower as my age has increased. And since my marathon times appear to be getting larger over time, and since I have not been able to manage a sub-3-hour marathon since 1996, I thought the analysis would show a strong correlation.

This time the result, a variation of 5.44 percent, was a mildly pleasant surprise. Although the correlation is positive as expected, it isn’t too far from zero, so it is fairly weak. Maybe there still is some hope for me. (Nah!)

CONCLUSIONS

Some of us like to believe in cause and effect: that if we follow a good training schedule, if we just work hard enough, we’ll see a successful conclusion to our quest of running a great marathon. However, it ain’t necessarily so. Sometimes we can do everything right, and the race itself comes out wrong. Sometimes we don’t seem to train as hard as other times, and we still manage to turn out a good race. For me this happens at least once per blue moon . . . but only during leap year. Part of this is because of environmental factors, and part is due to individual differences.

One of my friends chides me about training so hard. He doesn’t appear to work very hard at his own training, and yet he achieves excellent race results. I believe this is evidence of the YMMV thing at work.

On a related subject, there’s something else I noticed in my own data: diminishing returns. It appears that I don’t need to work very hard to run a 3:15 marathon. But to run 3:10 or better, I need to train much harder than you’d expect for a 5 or so minute gain. This may be strictly a perception on my part, but it sure seems real.

Compiling the raw data into the table turned out to be more work than I anticipated. But it was also more enjoyable than I expected. I was able to relive all those long training runs and speed sessions.

Based on the analysis, I’ve learned that my training has actually been remarkably, and surprisingly, consistent over the years. Some training elements, however, appear not to matter as much as expected. I had thought that overall training pace, long run distance, and long run pace would show stronger correlations than they did. I had expected that there was a strong relationship between mile repeat pace and marathon pace, so that result was not a major surprise.

In addition, it appears that running higher overall mileage and doing several prior races relate fairly strongly to marathon performance. As does weight.

This brings us back to causation. Perhaps the strong correlations between marathon pace and weight, or between marathon pace and mile repeat pace, are actually due to being in similar shape for both sets of data. The mile repeats do, however, still represent an important training element. It’s just that they’re not the only one. Indeed, it may be beneficial to study some combinations of training elements.

I’m going to carry on with those 1-mile repeats, continue to include races in my schedule, and try to keep that weight under control anyway. Your mileage may vary.

I would like to thank my daughters Veronica and Valerie as well as my friend David Couper for their assistance with this article.