The power law model applied to the marathon world record

Andrés Bernardo Fernández-Revelles, Eduardo García Mármol

Abstract

In September 2013 the world record in the marathon men's race was broken. The aim of this study is to apply to the 2013 Berlin Marathon a mathematical model based on the power law that analyses the marks distribution and checks its connection. The results show that the correlations obtained in all the different categories have been very significant, with a result of (r ≥ 0.978; p < 0.000) and a linear determination coefficient of (R2 ≥ 0.969). As a conclusion it could be said that the power law application to the 2013 Berlin Marathon Men's race has been an useful and feasible study, and the connection between the data and the mathematical model has been so accurate.


Keywords

Ranking; Power law; Marathon; World record; Space-Time distribution

References

Alvarez-Martinez, R., Martinez-Mekler, G., y Cocho, G. (2011). Order-disorder transition in conflicting dynamics leading to rank-frequency generalized beta distributions. Physica a-Statistical Mechanics and Its Applications, 390(1), 120-130. https://doi.org/10.1016/j.physa.2010.07.037

Amaral, L. A. N., Scala, A., Barthelemy, M., y Stanley, H. E. (2000).Classes of small-world networks.Proceedings of the National Academy of Sciences of the United States of America, 97(21), 11149-11152. https://doi.org/10.1073/pnas.200327197

Campanario, J. M. (2010a). Distribution of changes in impact factors over time.Scientometrics, 84(1), 35-42. https://doi.org/10.1007/s11192-009-0094-y

Campanario, J. M. (2010b). Distribution of ranks of {beta}-decay half-lives [physics.gen-ph].arXiv:1011.5390v1.

Campanario, J. M. (2010c). Distribution of Ranks of Articles and Citations in Journals.Journal of the American Society for Information Science and Technology, 61(2), 419-423. https://doi.org/10.1002/asi.21238

Campanario, J. M. (2010d). Self-Citations That Contribute to the Journal Impact Factor: An Investment-Benefit-Yield Analysis. Journal of the American Society for Information Science and Technology, 61(12), 2575-2580. https://doi.org/10.1002/asi.21439

Campanario, J. M. (2011a). Empirical study of journal impact factors obtained using the classical two-year citation window versus a five-year citation window. Scientometrics, 87(1), 189-204. https://doi.org/10.1007/s11192-010-0334-1

Campanario, J. M. (2011b). Large Increases and Decreases in Journal Impact Factors in Only One Year: The Effect of Journal Self-Citations. Journal of the American Society for Information Science and Technology, 62(2), 230-235. https://doi.org/10.1002/asi.21457

Carbone, V., y Savaglio, S. (2001). Scaling laws and forecasting in athletic world records. Journal of Sports Sciences, 19(7), 477-484. https://doi.org/10.1080/026404101750238935

Coile, R. C. (1977). Lotkafrequency-distribution of scientific productivity. Journal of the American Society for Information Science, 28(6), 366-370. https://doi.org/10.1002/asi.4630280610

del Rio, M. B., Cocho, G., y Naumis, G. G. (2008). Universality in the tail of musical note rank distribution.Physica a-Statistical Mechanics and Its Applications, 387(22), 5552-5560. https://doi.org/10.1016/j.physa.2008.05.031

Edwards, R., y Collins, L. (2011). Lexical Frequency Profiles and Zipf's Law. Language Learning, 61(1), 1-30. https://doi.org/10.1111/j.1467-9922.2010.00616.x

Egghe, L. (2009a). Mathematical derivation of the impact factor distribution.Journal of Informetrics, 3(4), 290-295. https://doi.org/10.1016/j.joi.2009.01.004

Egghe, L. (2009b). A Rationale for the Hirsch-Index Rank-Order Distribution and a Comparison With the Impact Factor Rank-Order Distribution.Journal of the American Society for Information Science and Technology, 60(10), 2142-2144. https://doi.org/10.1002/asi.21121

Egghe, L. (2010a). The distribution of the uncitedness factor and its functional relation with the impact factor.Scientometrics, 83(3), 689-695. https://doi.org/10.1007/s11192-009-0130-y

Egghe, L. (2010b). A New Short Proof of Naranan's Theorem, Explaining Lotka's Law and Zipf's Law.Journal of the American Society for Information Science and Technology, 61(12), 2581-2583. https://doi.org/10.1002/asi.21431

Egghe, L. (2011a). The impact factor rank-order distribution revisited. Scientometrics, 87(3), 683-685. https://doi.org/10.1007/s11192-011-0338-5

Egghe, L. (2011b). Mathematical relations of the h-index with other impact measures in a Lotkaian framework. Mathematical and Computer Modelling, 53(5-6), 610-616. https://doi.org/10.1016/j.mcm.2010.09.012

Egghe, L. (2012). Study of rank- and size-frequency functions and their relations in a generalized Naranan framework.Mathematical and Computer Modelling, 55(7-8), 1898-1903. https://doi.org/10.1016/j.mcm.2011.11.047

Egghe, L. (2013). Study of the rank- and size-frequency functions in the case of power law growth of sources and items and proof of Heaps' law. Information Processing y Management, 49(1), 99-107. https://doi.org/10.1016/j.ipm.2012.02.004

Fernández-Revelles, A. B. (2013).Modelomatemático de ley de potenciasaplicado al maratón.RevistaHabilidadMotriz, 41.

Garfield, E. (1980).Bradford law and related statistical patterns.Current Contents(19), 5-12.

Hong, H. S., Ha, M., y Park, H. (2007). Finite-size scaling in complex networks. Physical Review Letters, 98(25). https://doi.org/10.1103/PhysRevLett.98.258701

Joyner, M. J., Ruiz, J. R., y Lucia, A. (2011). Last Word on Viewpoint: The two-hour marathon: Who and when? [Letter]. Journal of Applied Physiology, 110(1), 294-294. https://doi.org/10.1152/japplphysiol.01265.2010

Katz, J. S., y Katz, L. (1999). Power laws and athletic performance.Journal of Sports Sciences, 17(6), 467-476. https://doi.org/10.1080/026404199365777

Laherrere, J., y Sornette, D. (1998). Stretched exponential distributions in nature and economy: "fat tails" with characteristic scales. European Physical Journal B, 2(4), 525-539. https://doi.org/10.1007/s100510050276

Lavalette, D. (1996). Facteurd'impact: impartialitéou impuissance? Report, INSERM U350.Orsay, France: Institut Curie-Recherche, Bât, 112, Centre Universitaire, 91405.

Mansilla, R., Koppen, E., Cocho, G., y Miramontes, P. (2007).On the behavior of journal impact factor rank-order distribution.Journal of Informetrics, 1(2), 155-160. https://doi.org/10.1016/j.joi.2007.01.001

Naumis, G. G., y Cocho, G. (2007). The tails of rank-size distributions due to multiplicative processes: from power laws to stretched exponentials and beta-like functions. New Journal of Physics, 9. https://doi.org/10.1088/1367-2630/9/8/286

Naumis, G. G., y Cocho, G. (2008). Tail universalities in rank distributions as an algebraic problem: The beta-like function. Physica a-Statistical Mechanics and Its Applications, 387(1), 84-96. https://doi.org/10.1016/j.physa.2007.08.002

Newman, M. E. J. (2005).Power laws, Pareto distributions and Zipf's law. [Review]. Contemporary Physics, 46(5), 323-351. https://doi.org/10.1080/00107510500052444

Phillips, J. R. (2010, 19-01-2011). ZunZun.com Online Curve Fitting and Surface Fitting Web Site Retrieved 30-09-2013, 2013, from http://www.zunzun.com/

Popescu, I. (2003). On a Zipfs Law extension to impact factors. Glottometrics, 6(83-93).

Savaglio, S., y Carbone, V. (2000). Human performance - Scaling in athletic world records. Nature, 404(6775), 244-244. https://doi.org/10.1038/35005165

SCC-Events. (2013, 30-09-2013). BMW 40 Berlin Marathon Retrieved 30 Septiembre, 2013, from http://results.scc-events.com/2013/

Waltman, L., y van Eck, N. J. (2009). Some comments on Egghe's derivation of the impact factor distribution. Journal of Informetrics, 3(4), 363-366. https://doi.org/10.1016/j.joi.2009.05.004




DOI: https://doi.org/10.14198/jhse.2019.141.02





License URL: http://creativecommons.org/licenses/by-nc-nd/4.0/