PhD A.V. Ermakov ^{1, 2}
P.E. Myakinchenko^1
1Federal Scientific Center of Physical Culture and Sports VNIIFK, Moscow
²Russian State University of Physical Education, Sports, Youth and Tourism (SCOLIPE), Moscow

Keywords: mathematical modeling, moving average, forecast, winter sports.

Background. Competitive performance and progress forecasts are indispensable for the modern long-term sports training systems, sports team formation, sports progress trends analyzing and many other purposes; and this is the reason why the competitive progress forecasts are critical for professional expertise and decision-making in modern physical education and sports [2, 3].

Forecasting methods and issues have long been among the priorities for many disciplines including statistics, economics, natural sciences, etc. [1, 4, 6]. One of the forecast methods is geared to analyze and profile the historical relative success rate – which may be defined as the ranking in specific sports discipline (hereinafter referred to as the ranking). One of the analytical tools used for this purpose is an array of functions known as moving average [5, 6], with a point value ​​of every function depending on its past values for certain period. Moving average may be applied for time series to smooth the short-term fluctuations and highlight the major cycles/ trends. Therefore, an individual sports career may be profiled by dated competitive successes to identify the key progress trend and thereby forecast further competitive progress path when designing and scheduling the long-term sports training and competitive systems.

Objective of the study was to forecast an individual relative competitive progress by the mathematical modeling method, with winter sports taken for the case study.

Methods and structure of the study. Our hypothesis assumes that an individual competitive progress may be approximated by an alternately increasing and decreasing time series, with a polynomial moving average trend method used as the key one to forecast the competitive progress. Note that the most generalized individual competitive progress model assumes a gradual competitive progress growth till the individual best under the given conditions followed by a natural competitive progress fall thereafter. Therefore, the polynomial degree will be assumed to equal two in the case. In case of a competitive progress model with two peaks, the polynomial degree will equal three. We sampled for the competitive progress modeling study 83 elite winter sports competitors of different ages and both genders.

Results and discussion. We used for the competitive progress analysis the World Cup rankings (as of the year end) of the following sample: male freestylers (ski acrobats) (n=31); female speed skaters (n=22) and male cross-country skiers (n=31). A prior check of the sample found that the required degree of reliability/ approximation (R² ≥8) is achievable only for 34 athletes (40.5% of the sample). Despite the fact that the negative check results may be explained by the input data shortages or inaccuracies, they still show the method having some limitations that need to be removed by further improvements. Athletes who were screened out by the second-degree polynomial were retested for compliance with the third-degree trend, and thereby we arrived to the following two possible competitive progress models: see Table 1 hereunder.

Table 1. Relative competitive progress forecast using the moving average method

Figure 1. Trend forecast model with the second-degree polynomial: individual competitive progress forecast (first stage)

Let's consider an individual case of the relative competitive progress forecast. Given on Figure 1 is the individual relative competitive progress forecast based on the rankings of 2009 through 2017 (save for 2010). The individual competitive progress was forecast in the case to sag in 2018 to 21-31 ranking. Having matched the forecast data with the actual ones (see Figure 2 that covers 2018 as well), we found the actual performance exactly matching with the forecast not only in the competitive progress trend but also in the actual ranking – as the athlete was ranked 27th in fact.

Figure 2. Trend forecast model with the second-degree polynomial: individual competitive progress forecast (first stage)

Figure 2 shows the forecast ranking of 31-41, whilst actually the athlete was ranked 40 in 2019. It should be stated, however, that we are still unprepared to fully rely on the high accuracy of the forecast method since discrepancies may be more significant. We would recommend the moving-average-based relative competitive progress forecast model as fairly accurate at this juncture albeit still having certain limitations for application. More sophisticated and inclusive competitive progress forecast models need to be developed to cover a wider variety of the factors of influence on the competitive progress in sports.

Conclusion. The study data and analyses give reasons to conclude that the moving-average-based relative competitive progress forecast model is recommendable as fairly accurate at this juncture albeit still having certain limitations for application. We found the model producing fairly accurate competitive progress forecasts in 40% of individual cases, with sufficiently high degree of reliability/ approximation (R² ≥8). We tested two competitive progress models with the second- and third-degree polynomials and, hence, the study cannot be considered complete. More sophisticated and inclusive competitive progress forecast models need to be developed to cover a wider variety of the factors of influence on the competitive progress in sports.

References

1. Greshilov A.A., Stakun V.A., Stakun A.A. Mathematical methods for building forecasts. M.: Radio i svyaz publ,, 1997. 112 p.
2. Ermakov A.V. Methods to form private security guards' self-defense skills in cold weapon attacks. PhD diss.. Volgograd, 2005. 194 p.
3. Skarzhinskaya E.N., Sarafanova E.V. Updating integrated assessment of qualifications of physical education and sports sector experts. Teoriya i praktika fiz. kultury. 2019. no. 11. pp. 104-104.
4. Booth E., Mount J., Viers J. H. Hydrologic variability of the Cosumnes River floodplain. San Francisco Estuary and Watershed Science. 2006. v. 4. no. 2. National Institute of Standards and Technology (États-Unis). NIST/SEMATECH e-handbook of statistical methods. – National Institute of Standards and Technology, 2000.
5. Kenney J.F., Keeping E.S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, p. 223, 1962.
6. Kenney J.F., D. Van Nostrand Mathematics of statistics. p. 259 1939, 1947, 1952.

Corresponding author: fizkult@teoriya.ru

Abstract

Objective of the study was to forecast an individual relative competitive progress by mathematical modeling method, with winter sports taken for the case study.

Methods and structure of the study. We sampled for the competitive progress modeling study the following elite winter sports competitors of different ages and both genders: men freestylers (ski acrobats) (n=31); women speed skaters (n=22) and men cross-country skiers (n=31). The individual relative competitive progress forecasts were made using the moving average functions to find the key relative competitive progress trends with smoothed short-term fluctuations.

Results and discussion. We qualified a part of the sample by prior checks for the relative competitive progress forecasting method with a high degree of approximation using model 1 with the second-degree polynomial and model 2 with the third-degree polynomial, and selected model 1 as the key one for the case study, albeit model 3 with the third-degree polynomial is also applicable in certain cases. We found the moving-average-based relative competitive progress forecast model fairly accurate at this juncture albeit still having certain limitations for application. More sophisticated and inclusive competitive progress forecast models need to be developed to cover a wider variety of the factors of influence on the competitive progress in elite winter sports.