## There is No Such Thing as Logarithmic Progression

Edit: The intitial version of the article contained the equations describing the increase of only the clean and jerk. The graphs have been revised to include the total as described in the article. Furthermore, the dataset will be available to those who whish to proof or expand this analysis (subject to a few conditions). Email data@olystats.com for more information.

Have you heard of linear progression? Read Starting Strength? Maybe you have seen the chart in The Science and Practice of Strength Training or read elsewhere that long term strength gains over time are logarithmic. Today, thanks to the massive Oly Stats database, we have a model for weightlifting performance over time….and it is not logarithmic. The analysis laid out in this blog post will provide two equations, one for each sex, that describe performance over time. For you stats nerds out there, this is an initial study to provide a descriptive model, not a predictive one. Further studies will dive more deeply into the data.

This model was created from the competition results of 14,503 men and 5,060 women between 1998 and 2013. In total 100,443 meet entries (the results for one lifter in one competition) were analyzed. For each lifter, progress was determined by calculating how each of their totals changed in comparison to their first competition. The length of time it took to achieve this change, in weeks, was also calculated. Then, the average total change for each week of improvement was calculated; separating men and women.

Once these calculations were completed the data was ready for analysis. The first step was looking at the data as a whole. At the broadest level of analysis, weightlifting performance is best described as a parabolic curve. For those who may not remember, a parabolic curve looks like an umbrella: it increases, peaks, and then decreases. This result is actually quite logical and expected. At first an athlete gets strong until they reach their greatest point and then some factor (usually age) kicks in and performance steadily decreases. Although quite interesting, the parabolic curve is less predictive of performance at any given time in an athlete’s life and therefore I have excluded the equation from this blog post.

The second step in the analysis was to calculate how an athlete’s performance increases over time. To do this, only the first 5 years of training performance were analyzed. At first, a logarithmic model was used to attempt to model the data; however it turns out that a polynomial function is much more accurate at predicting performance. The results are displayed in the graphs below. For men the equation is y = -0.0192x2 + 2.1567x, R² = 0.9698. For women, y = -0.0144x2 + 1.5633x, R² = 0.965.

Now to the fun part, what does this mean? Well, it does not mean that for every week you call yourself a weightlifter you get a little bit stronger. However, it does present a means of analyzing how effective your program is or where you need to be in the future. Most weightlifters will improve or get worse consistent with the equations presented here. Therefore they can be used for goal setting and long term evaluation of training. Unfortunately this model does not describe what factors contributed to the increase in performance. It only describes the average increases likely to happen over time.

The reason a polynomial model works better than a logarithmic one is that adaptation to training occurs in stages and therefore a single line (linear or logarithmic) cannot accurately describe the changes. A polynomial equation allows for a model that can better predict changes for each stage of adaptation. For those unfamiliar with the R² measure of accuracy, these models are about 96% accurate for men and women. The models may lose descriptive power after the 5 year training period; however they will accurately describe how the average athlete will progress over time.

The models of performance presented here are accurate, or else I would not post them. However I would like to point out several sources of error. Only the US was analyzed, it lumps together all levels of athlete from youth to internationally competitive lifters, using weightlifting competitions may exclude individuals who are not drawn to weightlifting, competitions may not be representative of training due to odd conditions, and there may be errors in the results analyzed. I’ll handle these in order.

Yes, the results are from the US, but the large amount of individuals involved in the analysis should make it accurate for the average athlete anywhere. Furthermore, Oly Stats will be adding the local meets of other countries to the results database. Expect periodic blog posts comparing countries and refining the models.

Although many levels of athlete are lumped together, this is what makes the equations so powerful. We know how humans respond on average. With more data, the equations can be refined for different stages of athletic development to increase their predictive power for specific sub-populations.

The models presented here apply specifically to weightlifting and therefore the use of weightlifters who have decided to compete is acceptable. Although I believe they can be generalized to overall strength gains we cannot know for certain without a broader dataset.

The conditions of a weightlifting meet a certainly different from everyday training, but I believe they enhance the accuracy of these models. Using competitions allows for the comparison of data collected in standardized conditions and where athletes are at similar points in the training cycle. The standard for judging and timekeeping might be more relaxed at a local meet, but overall we are comparing data collected in very similar circumstances with similar judging criteria.

Finally, there may be errors in the results data. I think it is very likely that some of the meet result data are incorrectly. Although Oly Stats is constantly combing the database to remove inaccuracies, it should be assumed that some errors have worked their way into the data analyzed. Due to the large number of athletes in the analysis, there would need to be a huge amount of errors in order to cause the equations to be inaccurate.

In conclusion, the equations presented here are accurate models of how weightlifting performance increases over time for men and women. These equations can be used to evaluate performance for goal setting or to measure the effectiveness of a training program. In further blog posts I will elaborate on more ways coaches and athletes can use this data to evaluate performance and present more refined.