Biomechanics and Medicine in Swimming XI

was calculated for each year and averaged within each event. This number
was used to estimate the standard deviation of the predicted time for
each event using the formula 1.25*(mean percent difference)*(predicted
value)/100. This standard deviation was used to establish the 95% confidence
interval for that event (predicted time ± 2 standard deviations).
The mean time of the finalists of the 2008 Olympics were compared to
this 95% confidence interval and actual times that fall outside the interval
were concluded to be significantly faster or slower than predicted.
To examine each Olympic year as a whole, a count was made of the
number of events for which the actual time was above or below the corresponding
prediction curve. A binomial test of statistical significance
was used to test whether or not the likelihood of the number of events
being either faster or slower than our predictions was different than
50%. This table of event counts was tested to determine whether or not a
particular year was faster or slower, in general, than predicted.
To test the repeatability of this prediction method, the same calculations
were performed to compare actual versus predicted performances of
the 2004 Games using data from 1972 through 2000 only. These procedures
were repeated for all Olympic Games 1988-2000 (using data since 1972).
results
Prediction Analysis: For the 2008 Olympic Games, 10/13 (77%) men’s
and 7/13 (54%) women’s events recorded mean times for the eight finalists
that were significantly faster than the predicted outcome values.
Only 34% of the events in the 2008 Games were successfully predicted.
Between 1988 and 2004, 10/61 (16%) men’s events were significantly
faster and 1 (2%) event was significantly slower than predicted. For the
women, 1/61 (2%) events was significantly faster and 9 (15%) events
were significantly slower than predicted. That is, 87% of all events were
successfully predicted. These data are presented in Table 1 and Figure 2.
Table 1. Comparisons between predicted and actual Olympic final performance
for all men’s events from 2000, 2004, and 2008. Predictions were
based on the mean of top 8 performances for each event beginning in 1972
up to the Olympics prior. For example, to predict the 100 Free in 2000, top
8 means from 1972, ’76, ’80, ’84, ’88, ’92, and ’96 were plotted and regressed
using a power function. † denotes significantly faster than predicted.
2000 2004 2008
Men's Predicted Actual ƀ
Act-Pred Predicted Actual ƀ
Act-Pred Predicted Actual ƀ
Act-Pred
Event Mean (s) Mean (s) (S.D.) Mean (s) Mean (s) (S.D.) Mean (s) Mean (s) (S.D.)
50 Free 22.28 22.19 0.85 22.10 22.11 -0.12 22.00 21.57 5.46†
100 Free 49.28 48.95 1.17 49.00 48.80 0.74 48.79 47.77 3.36†
200 Free 107.58 107.43 0.19 107.13 106.49 0.96 106.61 105.81 1.23
400 Free 227.10 226.21 0.59 225.90 225.92 -0.01 225.09 223.72 1.13
1500 Free 899.22 901.67 -0.26 896.68 898.05 -0.16 894.18 888.61 0.63
100 Back 55.03 54.85 0.39 54.76 54.52 0.57 54.50 53.28 3.04†
200 Back 119.79 118.43 1.75 118.97 117.98 1.17 118.31 115.54 3.44†
100 Breast 61.47 61.25 0.66 61.14 61.15 -0.02 60.91 59.64 4.45†
200 Breast 132.86 132.85 0.02 132.21 131.14 1.32 131.34 129.44 2.06†
100 Fly 53.16 52.53 2.16† 52.77 51.98 2.41† 52.38 51.23 3.29†
200 Fly 117.54 116.69 1.37 116.92 115.89 1.51 116.33 113.86 3.87†
200 IM 121.26 121.13 0.42 120.74 119.71 3.55† 120.02 117.88 5.46†
400 IM 255.79 256.74 -1.49 255.00 254.71 0.42 253.99 250.54 5.45†
% of Total Events
Predictive Success Rate of All Olympic Events (1988-2008)
100
90
80
70
Men
60
Women
50
Combined M & W
40
30
20
1988 1992 1996 2000 2004 2008
Figure 2. Percent of total events successfully predicted (within 95% C.I.)
for each Olympic Games (1988-2008) for men, women, and combined
men and women categories.
chaPter4.trainingandPerformance
When all events are “pooled,” the 2008 Games deviated from our predictions
significantly more than any previous Games, with the average
event offset being faster than statistical models by nearly 3 standard deviations
(Figure 3). From 1988 until 2004, only one other Games was
significantly different from other Games. In that case (1996), however,
the swimmers were slower than predicted, not faster. Additionally, unlike
2008, the events of the 1996 Games were, on average, not statistically
different than predicted outcomes (within 1.96 standard deviations).
Standard deviations
3
2
1
0
-1
1988 1992 1996 2000 2004 2008
*
-2
Figure 3. Average difference, in standard deviations, between actual and
predicted performances of Olympic swimming events (1988-2008). A
positive value denotes the average of actual event means were faster than
the predicted event means. * denotes significant difference compared to
all other groups.
Binomial Analysis: Finally, the results of binomial tests of statistical significance
are presented in Table 2. At the 2008 Games, all 26 events
(13 men and 13 women) were faster than our predictions. That is, all
events lay below the prediction curve, but were not necessarily significantly
faster than predicted. As a result, the binomial test of statistical
significance revealed that the 2008 Olympic swimming event was, as a
whole, significantly faster than expected (p < 0.05). For prior Olympics
(1988-2004), the performances of the women were significantly slower
than expected (p < 0.05) in 1992 and 1996. During the Olympic Games
in 1988, 2000 and 2004, however, women swimmers performed as expected.
Meanwhile, performances of the men were significantly faster
than expected in 2000 (p < 0.05). However, the Games in 1988, 1992,
1996 and 2004 were as expected. The men and women combined swam
significantly slower than expected (p < 0.05) in 1996, significantly faster
than expected in 2000 (p < 0.05), and as expected in 1988, 1992 and
2004.
Table 2. Count of events that were faster or slower than our predictions
(above or below the regression line) for men, women, and combined
men and women categories for each Olympic Games (1988-2008). The
results of the binomial test of statistical significance shows the probability
that this many events will be slower (†) or faster (*) than predicted is
less than 5% (p < 0.05).
Men Women Total
Slower Faster Slower Faster Slower Faster
1988 2 9 4 7 6 16
1992 4 8 10† 2 14 10
1996 8 4 12† 0 20† 4
2000 2 11* 4 9 6 20*
2004 4 9 7 6 11 15
2008 0 13* 0 13* 0 26*
*
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