Hello,
The main critique, I think, is that we assume a certain type of model
where the times can decrease until zero. And that they can do so
linearly. I believe that records can allways be beaten but 40-50 years
ago times were measured in tenths of a second, now we see a gain in the
hundreths as extraordinary. So the assumption doesn't seem to be
completely reasonable.
As for your assumption that little variation in the responses results in
little variation in the predictions, I would add that that is true but
given a model only. The predictions can and do vary from model to model
(obvious). See the logistic model in the same Gesmann work or Michael's
ARIMA in a response to my post. Three different predicted values with
variations from model to model in the tenths of a second. The values
are, resp., 19.61 (Gesmann) and 19.67 and 19.56 (Weylandt).
Maybe the linear model performs well because, like you say, the
sprinters post times very close to each other and a straight line is
not far from what a more complex model would do. I'm not betting on the
marathon times.
Rui Barradas
Em 10-08-2012 05:31, Mark Leeds escreveu:
Hi Rui: I hate to sound like a pessimist/cynic and also I should state that
I didn't look
at any of the analysis by you or the other person. But, my question, ( for
anyone who wants to chime in ) is: given that all these olympic 100-200
meter runners post times that are generally within 0.1-0.3 seconds of each
other or even less, doesn't it stand to reason that a model, given the
historical times, is going to predict well. I don't know what the
statistical term is for this but intuitively, if there's extremely little
variation in the responses, then there's going to be extremely little
variation in the predictions and the result is that you won't be too far
off ever as long as your predictors are not too strange. !!!!! ( weight,
past performances, height, whatever )
Anyone can feel free to chime in and tell me I'm wrong but , if you're
going to
do that, I'd appreciate statistical reasoning, even though I don't have
any. thanks.
mark
On Thu, Aug 9, 2012 at 4:23 PM, Rui Barradas <ruipbarra...@sapo.pt> wrote:
Hello,
Have you seen the log-linear prediction of the 100m winning time in R
mailed to the list yesterday by David Smith, subject Revolutions Blog:
July roundup?
"A log-linear regression in R predicted the gold-winning Olympic 100m
sprint time to be 9.68 seconds (it was actually 9.63 seconds):
http://bit.ly/QfChUh";
The original by Markus Gesmann can be found at
http://lamages.blogspot.pt/**2012/07/london-olympics-and-**
prediction-for-100m.html<http://lamages.blogspot.pt/2012/07/london-olympics-and-prediction-for-100m.html>
I've made the same, just changing the address to the 200m historical data,
and the predicted time was 19.27. Usain Bolt has just made 19.32. If you
want to check it, the address and the 'which' argument are:
url <- "http://www.databasesports.**com/olympics/sport/sportevent.**
htm?sp=ATH&enum=120<http://www.databasesports.com/olympics/sport/sportevent.htm?sp=ATH&enum=120>
"
Plus a change in the graphic functions' y axis arguments to allow for
times around the double to be ploted and seen.
#
# Original by Markus Gesmann:
# http://lamages.blogspot.pt/**2012/07/london-olympics-and-**
prediction-for-100m.html<http://lamages.blogspot.pt/2012/07/london-olympics-and-prediction-for-100m.html>
library(XML)
library(drc)
url <- "http://www.databasesports.**com/olympics/sport/sportevent.**
htm?sp=ATH&enum=120<http://www.databasesports.com/olympics/sport/sportevent.htm?sp=ATH&enum=120>
"
data <- readHTMLTable(readLines(url), which=3, header=TRUE)
golddata <- subset(data, Medal %in% "GOLD")
golddata$Year <- as.numeric(as.character(**golddata$Year))
golddata$Result <- as.numeric(as.character(**golddata$Result))
tail(golddata,10)
logistic <- drm(Result~Year, data=subset(golddata, Year>=1900), fct =
L.4())
log.linear <- lm(log(Result)~Year, data=subset(golddata, Year>=1900))
years <- seq(1896,2012, 4)
predictions <- exp(predict(log.linear, newdata=data.frame(Year=years)**))
plot(logistic, xlim=c(1896,2012),
ylim=range(golddata$Result) + c(-0.5, 0.5),
xlab="Year", main="Olympic 100 metre",
ylab="Winning time for the 100m men's final (s)")
points(golddata$Year, golddata$Result)
lines(years, predictions, col="red")
points(2012, predictions[length(years)], pch=19, col="red")
text(2012 - 0.5, predictions[length(years)] - 0.5,
round(predictions[length(**years)],2))
Rui Barradas
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