When I started on this project, I had seen very little in the way of others' attempts to do the same sort of thing. As I've begun showing the program to others and also as I've gotten access to the Internet, I've finally seen some of these efforts. Some are in the form of published tables while some others are in the form of computer programs (some free).

So what makes this program different? For one thing, most (though not quite all) of the others base performance on a single result. While this has the advantage of requiring little in the way of input, it does not at all address the problem (discussed above) of the different makeup (i.e. speed/endurance) of different runners. Usually the models or charts seem geared heavily towards runners specializing in the longer distances (5 or 10 K and up) and are quite far off when applied to, say, an 800 meter specialist who wants to try the 1500. In addition, some of these charts are really accurate only for elite runners, with fairly inaccurate results for more modest achievers. One attempt to address this can be found in Martin and Coe's book (referenced below). This consists of three sets of formulas - for 10K, 5K, and 1500 m specialists. Other than an obvious typo and some very minor discrepancies, I found these to fit my program's output very closely if I used two points for each formula. Coming from such an authoritative source, this may be seen mostly as a nice validation of my program, but still, it's three separate formulas and one may not know offhand which to use. There are also no provisions for race distances other than the 5 or 6 listed or for runners with other specialties. In short, it's useful but incomplete.

Another approach I have seen really has a different purpose in mind. A number of 'equivalent performance' schemes have been devised (a good example being Gardner and Purdy's reference below). These can work very nicely, but only over a rather limited range surrounding the runner's optimum event. For example, a miler who rates 700 'Purdy points' in that event probably rates quite close to that in the 2 mile and the half mile, but outside this the fit starts to stray significantly. The authors acknowledge this problem and, again, the issue of comparing performances at different distances in GENERAL is quite separate from that of comparing an INDIVIDUAL'S performances at different distances.

To address some specific models, one type I've run across is the power-law fit. An example of this is found on Runner's World's web page. When testing against data I've collected, I find this one to be fairly good only under certain circumstances. First of all, it assumes that an individual's race times are proportional to a certain power (1.07) of the race distance. This gives a rather small drop-off in speed with increasing distance, mainly appropriate for runners specializing in distances of at least 10K and running relatively high mileage. The other problem is that even in general (allowing different power laws for differnt runners), the fit is not the best. Specifically, I believe it gives over-optimistic interpolations and pessimistic extrapolations. Again, RUNPACES uses a model that has a sound physical/physiological basis and therefore fits real data much better than most arbitrary (even if inspired) choices of function are likely to, though even this model contains 'free parameters' that have allowed me to 'bend' the curve to make it even more accurate.

At this point, I need to point out that some of these other approaches DO have a place . . . in this program! For example, a generalized performance curve like Gardner and Purdy's allows a type of objective rating system and, when used in combination with an individual's performance curve, allows one to see which event that individual is 'best at'. I had developed such a performance curve based on world records, both for males and for females. I also adapted this curve to fit U.S. records, state high school records, or any other level. I found later that these curves almost exactly fit equal-Purdy-point curves, though suspect the mathematical form may be fairly different.

As a first attempt to use such curves to rate performances, I simply had the program divide the individual's speed for a race by the generalized speed for that race using the particular level used for comparison. This works well, however, only if the individual is being compared to a curve based on runners of about the same ability. Getting a typical high-schooler's speeds as a percentage of world records, for instance, can be misleading. A 'good' high school sprinter, for example, may run 100m only 10% slower than the world record, while an 'equally good' high school miler might be nearly 20% off world records. To compensate for this effect, I developed a quantity I call 'performance factor' (not surprisingly, I found recently that this term has been used before for a similar type of rating). This quantity equals a percentage of world records at the mile, but is skewed to yield lower values at shorter distances and higher at longer ones so that, for example, the top high school sprinter in a state should get about the same rating for 100 m as the top cross country runner gets for 5K. In this way, performance factor measures essentially the same thing as do Purdy points, and the runner's best event is approximately the one that yields his/her highest p.f.

As for curves based on only one point, there is some merit as well, since a runner may have been running only one event in recent weeks. For this reason, the program does allow single entries, but to make the curve more realistic, age and training data (in the simplified form of total miles per week, which ideally assumes some appropriate-to-the-event balance ofspeed versus endurance work). Generally, higher mileages are assumed to be associated with greater endurance versus speed and aging is assumed to have a similar effect, though small since both endurance and speed show declines past about 30 years. With this information, the single point curve can be nearly as good as the two point one, or even better if one of the two points was a significantly sub-par performance. Some small sex difference is included as well, though male and female runners of similar ability have fairly similar performance curves.

Perhaps the program's most advanced capability is that it can sort through up to five different performances, weed out the bad ones, and try every possible combination of two points to yield the best one (though on very rare occasions with unusual data a point could get missed). It also can find the likely best performance of all and take into consideration the curve suggested by the remainder of points as well as the training and age data to generate a really accurate curve. Both options can be tried alternately on the same data set. If the races span a large range of distance and were allreally good efforts, the 'best two' method may be better; with narrowly spaced results and/or widely varied race conditions or efforts the 'use all data' method is probably better.

Three other outputs generated are the 'fully aerobic training pace', which is actually used by the program, the 'aerobic threshold pace', and the 'VO2max pace'. The first closely represents an appropriate pace for longer training runs or 'easy' days, with heart rate about 70% of maximum, especially for fairly typical distance runners, though sprinters' (who don't often run far anyway) data may yield 'aerobic paces' that may be too slow. The second refers to the pace at which lactic acid begins to build much more rapidly and is appropriate on certain types of 'hard' days. The VO2max pace produces maximum oxgenuptake, though one can sprint faster. This pace is appropriate forinterval training with the goal of increasing this ability to take inoxygen; faster interval training yields little additional benefit in this area and can be too stressful for optimal training.

In summary, I believe many aspects of this program's approach to be truly unique and remarkably accurate over a very wide range of abilities and distance specialties. A number of other options are available in the registered version.