International Human Powered Vehicle Association (IHPVA) with different acceptance in the bicycle type used for the record [6,11,12]. The Streif (Kitzbu¨ hel, Austria) down-hill ski is 3312 m long with an 27% average gradient, held since 1930 and part of the ski world cup since 1967 [6,13]. The Hawaiian Ironman is the first modern long-distance triathlon (3.86 km swimming, 180.2 km cycling and 42.2 km running). Starting in 1978, each year it is considered to be the World championship in long-distance triathlon [6,14]. The channel crossing swim is usually challenged between Shakespeare beach (Dover, England) to ‘‘Cap gris nez’’ (France) over 33.8 km; firstly held in 1875 it has been regulated since 1927 [6,15]. For all events, best performances (BP) only (equivalent to the race record) are accounted for into the analysis [5–15]. Function description and prediction We performed BP modelisation as previously reported [1]: performance series for each event are fitted by the following function: yj (t) = DBP exp(2aj.t9)+b; where DBP = BPi,j2BPf,j is an event indicator for the studied j period; BPi,j and BPf,j are the initial and final BP values respectively; aj is the positive curvature factor given by non linear regression; b is the asymptotic limit. Coefficients a, b and estimated predictions (years, asymptotic values) are obtained through an iterative algorithm. The ratios b (progression range since the beginning of the event) and b9 (present progression range) were calculated to describe the improvement over the final time frame in each event by using the following equation: b = (BPi/b)6100 and b9 = (BPf/b)6100. For each event, this piecewise exponential decaying model provides successive periods. A period refers to a time slot defined by a group of consecutive BP, following a rupture of incline. A procedure based on the best adjusted r2 was used to split BP series into periods. The algorithm was initiated by the first three BP values. The series was iteratively fitted by adding the next BP point using the presented above equation equation. For each fit, we obtained the adjusted r2; local maxima provide the changes of incline corresponding to the beginning of a new period. The minimum period duration is 6 years and the minimal BP number is three per period. Sport Performance Evolution During the period j, parameters aj and bj were estimated using the Levenberg-Marquardt algorithm (LMA) [16] in a non linear least-squares regression to fit the model to BP. Coefficients of the prediction equation were calculated for the last period of each event through LMA with credibility interval [17]. The result was used to estimate the year t when the 99.95% (1/2000) limit is reached. Data are expressed as mean6standard deviation. Results The collected data provided a mean of 17.667.1 BP per event. Events had large differences in their initial progression range (b = 46.27613.5%). Present mean achievement of the asymptotic performance, b9, was 94.667.%2 with seven events over 97%. Events with the lowest b and b9 coefficients were: sailing transatlantic records, Streif and speed ski record and IHPVA hour cycling record (gathered in group 1: b1 = 37.569.5%; b91 = 90.468.8%) whereas group 2 sport events: Oxford-Cam- bridge, Vasaloppet, Elfstedentocht, Ironman, Channel crossing and ICU Hour cycling record had higher values (b2 = 53.5612.1%; b92 = 98.063.2%). The model fits progression periods, depending on the events’ longevity, with high accuracy (r2 = 0.9560.07). A first progression period (XIXth and beginning of XXth century) was modeled for the older events (Oxford-Cambridge, Vasaloppet, speed ski record, ICU cycling: r2 = 0.9760.03, a = 1.9360.96 and b9 = 57.668.9%; Figure 1). A second progression period starts in the early XXth century for seven events (the four previous ones plus Channel crossing, Elfstedentocht (Figure 2) and IHPVA cycling: r2 = 0.9560.03, a = 0.9760.45, b9 = 73.15616.8%). Mod- eled curves for the last period of all 10 events start in the middle of the XXth century (r2 = 0.9560.04, a = 1.2860.51, b9 = 94.567.2%). The progression of the transatlantic records, the Hawaii Ironman and Streif down-hill are modeled by a mono- exponential curve (Figure 3). The curves for the hour cycling record progression according to the specific associations’ rules (ICU and IHPVA) are compared in Figure 4. The year when mean BP will be established at 99.95% of their asymptotic value is predicted to be 2049632.1 years (Table 2). PLoS ONE | www.plosone.org November 2008 | Volume 3 | Issue 11 | e3653 Table 1. Event parameters: longevity, occurrence and available performance number. Event Oxford-Cambridge Transatlantic record Transatlantic record Channel crossing Ironman Hawaii Hour cycling record UCI Hour cycling record IHPVA Elfstedentocht Vasaloppet Speed ski record Streif down-hill Sport Rowing Crew sailing Solo sailing Swimming Triathlon Cycling Cycling Speed ice skating Cross-country ski Down-hill ski Down-hill ski *performance is only registered when the best performance is improved. doi:10.1371/journal.pone.0003653.t001 1829 1980 1960 1875 1978 1876 1933 1909 1922 1930 1930 2 Dates Frequency Performance number total best performance Every four years Annually Free Free Annually Free Free Annually Annually Free Annually 153 11* 13 772 30 29* 20* 16 86 32* 74 19 11 9 16 12 29 20 9 17 32 20