Grand Prix motorcycle racing

0.1 The 2019 FIM motoGP world championship

Here I analyse a series of Grand Prix motorcycling race results using the hyper2 package which implements the Plackett-Luce likelihood function. Consider the following dataset, taken from Wikipedia:

moto_table <- read.table("motoGP_2019.txt")
head(moto_table)

##            QAT ARG AME SPA FRA ITA CAT NED GER CZE AUT GBR RSM ARA THA JPN AUS MAL VAL points
## Marquez      2   1 Ret   1   1   2   1   2   1   1   2   2   1   1   1   1   1   2   1    420
## Dovizioso    1   3   4   4   2   3 Ret   4   5   2   1 Ret   6   2   4   3   7   3   4    269
## Vinales      7 Ret  11   3 Ret   6 Ret   1   2  10   5   3   3   4   3   4 Ret   1   6    211
## Rins         4   5   1   2  10   4   4 Ret Ret   4   6   1 Ret   9   5   7   9   5   5    205
## Quartararo  16   8   7 Ret   8  10   2   3 Ret   7   3 Ret   2   5   2   2 Ret   7   2    192
## Petrucci     6   6   6   5   3   1   3   6   4   8   9   7  10  12   9   9 Ret   9 Ret    176

Each row is a driver (rider?) and each column (after the first) a venue. Taking the first row we see that Marquez came second in Qatar (QAT), first in Argentina, retired in Austin, and so on. In the first column, we see the result from Qatar (QAT) in which Marquez came second, Dovizioso first, Vinales third, and so on. Notation used also includes six different classes of no-score such as “Ret” for retired, “WD” for withdrawn, and so on. I now use package function ordertable2supp(), that translates data of this type into a log-likelihood. In the package, object moto is the corresponding Plackett-Luce likelihood function; we drop the final column which is the points scored by each rider.

moto <- ordertable2supp(moto_table[,-ncol(moto_table)])
head(moto)

## Warning in print.hyper2(x): powers have nonzero sum

## log(A_Espargaro^14 * (A_Espargaro + Abraham + Bagnaia + Bradl + Crutchlow + Dovizioso + Guintoli + Iannone
## + Kallio + Lecuona + Lorenzo + Marquez + Miller + Mir + Morbidelli + Nakagami + Oliveira + P_Espargaro +
## Petrucci + Pirro + Quartararo + Rabat + Rins + Rossi + Smith + Syahrin + Vinales + Zarco)^-19 *
## (A_Espargaro + Abraham + Bagnaia + Bradl + Crutchlow + Dovizioso + Guintoli + Iannone + Kallio + Lecuona +
## Lorenzo + Marquez + Miller + Mir + Morbidelli + Nakagami + Oliveira + P_Espargaro + Petrucci + Pirro +
## Quartararo + Rabat + Rins + Rossi + Smith + Syahrin + Zarco)^-2 * (A_Espargaro + Abraham + Bagnaia + Bradl
## + Crutchlow + Dovizioso + Guintoli + Iannone + Kallio + Lecuona + Lorenzo + Marquez + Miller + Mir +
## Morbidelli + Nakagami + Oliveira + P_Espargaro + Petrucci + Pirro + Quartararo + Rabat + Rossi + Smith +
## Syahrin + Vinales + Zarco)^-2 * (A_Espargaro + Abraham + Bagnaia + Bradl + Crutchlow + Dovizioso + Guintoli
## + Iannone + Kallio + Lecuona + Lorenzo + Marquez + Miller + Mir + Morbidelli + Nakagami + Oliveira +
## P_Espargaro + Petrucci + Pirro + Quartararo + Rabat + Smith + Syahrin + Vinales + Zarco)^-1 * (A_Espargaro
## + Abraham + Bagnaia + Bradl + Crutchlow + Dovizioso + Guintoli + Iannone + Kallio + Lecuona + Lorenzo +
## Marquez + Miller + Mir + Morbidelli + Nakagami + Oliveira + P_Espargaro + Pirro + Quartararo + Rabat + Rins
## + Rossi + Smith + Syahrin + Vinales + Zarco)^-1)

Above, we see a small part of the Placket-Luce likelihood function for the 2019 results. We can find the maximum likelihood estimator by using the maxp() function:

moto_maxp <- maxp(moto)
moto_maxp

## A_Espargaro     Abraham     Bagnaia       Bradl   Crutchlow   Dovizioso    Guintoli     Iannone      Kallio     Lecuona 
##  2.0089e-02  1.6014e-02  1.5682e-02  3.8040e-03  2.8787e-02  1.1266e-01  3.4048e-03  1.5649e-02  3.7095e-03  1.0119e-06 
##     Lorenzo     Marquez      Miller         Mir  Morbidelli    Nakagami    Oliveira P_Espargaro    Petrucci       Pirro 
##  1.4637e-02  3.3127e-01  3.3520e-02  2.3260e-02  2.3510e-02  2.2356e-02  1.8844e-02  3.1716e-02  5.7184e-02  8.6998e-04 
##  Quartararo       Rabat        Rins       Rossi       Smith     Syahrin     Vinales       Zarco 
##  3.9398e-02  1.3085e-02  5.0789e-02  4.0858e-02  1.7252e-03  1.3677e-02  5.1917e-02  1.1591e-02

dotchart(moto_maxp,pch=16)

Figure 1: Dot chart of riders’ strengths

pie(moto_maxp)

Figure 2: Pie chart of riders’ strengths

In figures 1 and 2, note the dominance of Marquez. It is sometimes preferable to plot the estimated strengths on a log scale:

dotchart(log10(moto_maxp),pch=16)

Figure 3: Dot chart of riders’ strengths, log scale

(in figure @ref(fig:dotchartlogmoto ) observe that the bottom-ranked player, Lecuona, has a ML strength of zero but the estimate is slightly positive for numerical reasons).

Package dataset

Following lines create moto.rda, residing in the data/ directory of the package.

save(moto,moto_table,moto_maxp,file="moto.rda")