How Much Should Bale Cost Real?

It looks increasingly likely that Gareth Bale will transfer from Tottenham to Real Madrid for a world record transfer fee. Negotiations are ongoing, with both parties keen to get the best deal possible deal with the transfer fee. Reports speculate that this transfer fee will be anywhere in the very wide range of £80m to £120m.

Given the topical nature of this transfer saga, I decided to explore the world record breaking transfer fee data, and see if these data can help predict what the Gareth Bale transfer fee should be. According to this Wikipedia article, there have been 41 record breaking transfers, from Willie Groves going from West Brom to Aston Villa in 1893 for £100, to Cristiano Ronaldo’s £80m 2009 transfer to Real Madrid from Manchester United.

When comparing any historical price data it is very important that we are comparing like with like. Clearly, a fee of £100 in 1893 is not the same as £100 in 2009. Therefore, the world record transfer fees need to be adjusted for inflation. To do this, I used the excellent measuringworth website, and converted all of the transfer fees into 2011 pounds sterling.

bale

The plot above demonstrates a very strong linear relationship between logged real world record transfer fees and time. The R-squared indicates that the year of the transfer fee explains roughly 97% of the variation in price.

So, if Real Madrid are to pay a world transfer fee for Bale, how much does this model predict the fee will be? The above plot demonstrates what happens when the simple log-linear model is extrapolated to predict the world record transfer fee in 2013. The outcome here is 18.37, so around £96m, in 2011 prices. We can update this value to 2013 prices. Assuming a modest inflation rate of 2% we get £96m[exp(0.02*2)]=£99.4m. No small potatoes.

rm(list=ls())

bale = read.csv("bale.csv")
# data from:
# http://en.wikipedia.org/wiki/World_football_transfer_record
# http://www.measuringworth.com/ukcompare/

ols1 = lm(log(real2011)~year, bale)

# price
exp(predict(ols1,data.frame(year=2013)))
# inflate lets say 2% inflation
exp(predict(ols1,data.frame(year=2013)))*exp(0.02*2)

# nice ggplot
library(ggplot2)
bale$lnprice2011 = log(bale$real2011)
addon = data.frame(year=2013,nominal=0,real2011=0,name="Bale?",
                   lnprice2011=predict(ols1,data.frame(year=2013)))

ggplot(bale, aes(x=year, y=lnprice2011, label=name)) + 
  geom_text(hjust=0.4, vjust=0.4) +
  stat_smooth(method = "lm",fullrange = TRUE, level = 0.975) +
  theme_bw(base_size = 12, base_family = "") +
  xlim(1885, 2020) + ylim(8, 20) +
  xlab("Year") + ylab("ln(Price)") +
  ggtitle("World Transfer Records, Real 2011 Prices (£)")+
  geom_point(aes(col="red"),size=4,data=addon) + 
  geom_text(aes(col="red", fontface=3),hjust=-0.1, vjust=0,size=7,data=addon) + 
  theme(legend.position="none")
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8 thoughts on “How Much Should Bale Cost Real?

  1. Great idea here! Is there any way to also take into consideration the perceived value of the player at the time of transfer? For example, if you looked at all transfer fees instead of just world records you would probably see a stronger correlation between player quality and price than date of transfer and price.

    Combining the two, might offer readers the possibility to assess Bale’s value for themselves and then determine on a scale about where he would fit.

      • Thank for your response. It seems like just an exercise in regressions unless you appropriately apply it to your question: What will be the value of Gareth Bale? The current assessment could also be considered as the regression to predict the transfer fee of (insert next world record transfer fee here).

        Here’s another source of data that just shows 50(ish) of the larger transfer fees since 1999. (http://en.wikipedia.org/wiki/Transfer_%28association_football%29)

        Using this data instead might enhance your forecast for several reasons including (1) being more relevant data to modern times, (2) having more data points that are in the expected range of Bale’s in both time and price, (3) includes a more diverse group of players (i.e. not disproportionately mostly English/Scottish players), and (4) could possibly be sorted by quality using rankings of players in any given year (or another method).

        I think you’re doing something cool here, just babbling because it is really awesome!

  2. Pingback: Is Gareth Bale Over Priced?

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