McNair Scholars Journal Volume 19 | Issue 1 Article 9 2015 Modeling the Development of World Records in Track and Field Marie Griffith Grand Valley State University Follow this and additional works at: http://scholarworks.gvsu.edu/mcnair Recommended Citation Griffith,a M rie (2015) "Modeling the Development of World Records in Track and Field," McNair Scholars Journal: Vol. 19 : Iss. 1 , Article 9. Available at: http://scholarworks.gvsu.edu/mcnair/vol19/iss1/9 Copyright © 2015 by the authors. McNair Scholars Journal is reproduced electronically by ScholarWorks@GVSU. http://scholarworks.gvsu.edu/ mcnair?utm_source=scholarworks.gvsu.edu%2Fmcnair%2Fvol19%2Fiss1%2F9&utm_medium=PDF&utm_campaign=PDFCoverPages Modeling the Development of World Records in Track and Field I. INTRODUCTION II. LITERATURE REVIEW Previous researchers have used various To comprehend the changes in speed of analytical techniques to develop a model athletes based off of various distances with of world records in track and field events. respect to time, “Models for Comparing This can be a difficult task considering that Athletic Performances” was reviewed for there is not a set time frame in which world modeling that is fitted to 1996 world re- records are broken. Some records have cords for various distances (Grubb, 1998). been broken several times within one year, A developed three parameter model in- while others have taken multiple years only cluding speed at long distances, the maxi- to move very slightly (as in one-hundredth mum speed over distance obtained, and of a second or one-fourth of an inch). It is decrease in speed with respect to distance assumed that there is a limit in human per- was used to compare performances by the formance for track and field events since same athlete at different distances to de- it seems unreasonable that a runner can termine an athlete’s strengths and train- run a race in zero seconds or that a high ing effects (Grubb, 1998). This model was jumper reaches 100 feet. The purpose of constructed given that every athlete is built Marie Griffith this study is to assess the trends of world differently, has different strengths, and dif- McNair Scholar records in track and field events over time ferent endurance levels. After data was and to discover the possible threshold in collected, the composed model showed which world records start to approach for the decrease in world records over several the events of the 100 m, 200 m, 400 m, years and predicted lower bounds on these long jump, and shot put. records using various parametric forms. World records are those that have Given the fact that it is believed that there been officially ratified by the Interna- is a threshold for every track and field tional Association of Athletics Federations world record and that there will be asymp- (IAAF). If the ratified world record is totic convergence above these thresholds, wind-aided over an altitude of 1,000 me- this was alluring information. ters in an event where air has a positive Since it is favorable to develop a mod- effect, the unofficial best time or measure- el that displays asymptotic convergence, an ment is sub-listed (World Records-Men, article titled “Are there limits to running 2015). Specific criteria of submitted world records?” was examined in which qualifying marks must be satisfied for world record breaking for men and wom- ratification such as the dimensions of the en was assessed for modeling techniques track and equipment used must conform (Nevill and Whyte, 2005). Instead of us- Paul Stephenson to IAAF standards, events must be ac- ing a linear model, it was decided to use Faculty Mentor curately measured by a certified measurer, the “S-shaped” logistic curve to provide a and running events up to 800 meters in better fit for world record data overtime. distance are required to have a photo fin- In this study, it was identified that there ish fully automatic timing. It is of interest was a “slow rise” in world record speeds to the researchers to explore the patterns, at the beginning of the century. This was differences, and influential factors of followed by an acceleration period, which records in numerous events over time. It showed a major increase in speeds and de- is assumed that there will be a significant crease in times due to the enhancement of improvement in the world records from the sport and new technology. At the end the starting years of the sport to the most of the century, there appeared to be a re- current years. The eventual goal of our duction in record breaking performances research is to find the limit values that due to the challenges of beating previous these times and measurements appear times now that the sport is more advanced to be approaching and witness if there (Nevill and Whyte, 2005). Their model seems to be asymptotic convergence along also hinted towards men’s world records these thresholds. reaching an asymptotic limit and that it is 28 GVSU McNair Scholars Journal highly unlikely that women’s world records mented world record to the most current events previously mentioned (100 m 200 will reach those achieved by men. on the following events: 100 m 200 m, 400 m, and 400 m, long jump and shot put). After reviewing the two previous m, long jump, and shot put. The data col- The Gompertz curve growth model is sources, the idea of asymptotic conver- lected included the following variables: given by: gence and curve fitting techniques seemed Name, Time or Measurement, Record appealing. In another literature source, Year, and T. Record Year represents the The lower asymptote (slowest time “Modelling the Development of World year in which a world record was broken or measurement) is represented by a. The Records in Running,” the authors dem- and T represents the current year (that in- upper asymptote (fastest time or measure- onstrated the progression of world records cludes every consecutive year from the first ment) is represented by b. The growth rate for metric running events from the 100 documented world record for that event of the times and measurements is denoted meter dash to the marathon for men and until the year 2014). The data was then by c. The point of inflection of the pro- women using time-series curves (Kuper imported into JMP for analysis. duced curve is represented by d. The last and Sterken, 2008). Multiple curve fittings Next, various curves were reviewed component T represents the current year. were examined including the linear mod- based off of previous literature sources in The implied limit values are com- el, exponential curve, logistic curve, and an effort to identify the most appropriate puted as such: the Gompertz curve to identify the “best way to model the development of world fit” for modeling world record data. The records in track and field. While a linear Gompertz-curve was ultimately chosen for model was first examined, it was evident modeling. This curve was used for sixteen that the data did not follow a linear form events and implied limit values were com- because the world records were not con- puted for each event. After thresholds were stantly being broken at a steady rate. Be- determined, a log-log model was used and cause of this, the linear trend was declared determined that if the distance increased as not a good fit for this type of modeling. by 10%, the limit value increased by 11%, The exponential curve was the next model not necessarily taking gender into account explored for fitting the data. This curve Graphical output of the Gompertz (Kuper and Sterken, 2008). Based off of was also problematic because the events curve and implied limit values were pro- this modeling, the researchers chose the did not produce a trend that is constantly duced for the selected events and reviewed Gompertz curve for analysis due to valida- decreasing or increasing until it reaches an to ascertain the reasonableness of the fit. 2 tion of the curve choice and the high R asymptote. Produced R2 values were used to assess values that were produced from their com- The next type of curve that was re- how much variation is explained by the puted threshold limits. This study influ- viewed was the logistic curve. The shape of model and whether the limit values were enced the researchers to develop a model this curve was appealing to this particular reasonable estimates. that compares using similar methodology type of modeling because it has the poten- to see the differences in limit value predic- tial to form an “S” pattern when graphed. IV. RESULTS tions. This shape is favorable for world record The Gompertz curve was used to com- data because there appeared to be a slow pute limit values for the following events: III. RESEARCH DESIGN AND change in times/measurements in the be- 100 m 200 m, 400 m, long jump, and shot METHODS ginning stages of the sport, followed by a put. The computed thresholds and their The purpose of this research is to model more rapid change during its development associated R2 values for each event tested the development of world records in stages as the sport progressed, and leveling are listed in Table 1. track and field using statistical analysis. off of records in the later years once the Throughout this process, raw data was sport started getting perfected. Although obtained by records listed on the official the logistic curve seemed reasonable for websites of the Olympic Movement and modeling, it was identified that the Gom- IAAF organizations (iaaf.org and Olym- pertz curve was the model of “best fit” for pic.org).