---
title: "EUfootball"
#output: rmarkdown::html_vignette
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{EUfootball}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(EUfootball)
head(Matches)
```


+ **Elo** rating of each team. Calculated and gathered from \url{http://clubelo.com/} 
(July 2021; Schiefler 2015). It ranges from 1223 (FC Dordrecht in 2014) to 2106 (Barcelona in 2012)
and can be interpreted via the differences in rating, denoted by $d = \text{Elo}_\text{home} - \text{Elo}_\text{away}$. 
The probability for the home team to win is then defined as $\pi = P(\text{HomeWin}) = 1 / \left((10^{\left(\frac{-d}{400}\right)}+1\right)$ 
with ties being counted as a half win (Schiefler 2015. Equal Elo ratings will lead to a probability of 0.5. \\
After each match, the team's Elo scores are adjusted by $\Delta\text{Elo} = (R - \pi) \cdot 20$ with $R$ 
corresponding to the results from each team's point of view (1 for a win, 0.5 for a tie and 0 for a loss). 
The factor of 20 is a weight index chosen by Schiefler (2015). With this scheme, unlikely results like an 
underdog's win will result in bigger Elo changes. \\
These (or similar) types of Elo rankings are commonly used in competitive sports. It was originally 
proposed by Arpad Emmerich Elo (1961) to rank the ability of chess players.

+ **Market Value** (MV) of a team. Determined and gathered from \url{transfermarkt.com} (July 2021). 
Given in million euro and ranges from 2.8 (FC Dordrecht in 2014) to 1,300 (Manchester City in 2019/20). The 
market values of \url{transfermarkt.com} are a community project, where each player's market value is discussed 
and determined by (known or rumoured) transfer fees and the player's standing in his team. The team's value 
is the simple sum of its current players. The values are updated twice a month to timely include transferred players. 
The earliest available data is from 2010-11-01, so missing values occur for the first matchdays of the season 2010/11. 
As the market values are growing over time, we are transforming the raw values to shares of the league's market 
value (MVHomeT, MVGuestT), using each matchday's sum as a total market value. Missing values are imputed as averages. With this approach, 
the dominance of single teams can be modelled over the years without a bias by inflation.

+ **Bookmaker Odds** averaged from multiple bookmaker companies. Collected from \url{oddsportal.com} 
(July 2021) and averaged over six different bookmakers in 2010 up to 
12 bookmakers in 2019. The odds can be transformed to probabilities by inverting them to 
$p_j = \frac{1}{\text{odds}_{j}}, j\in\{1,X,2\}$. As these do not sum up to 1 (due to bookmakers' margins), 
we adjust these by $\tilde{p}_j = \frac{p_j}{p_{1}+p_{X}+p_{2}}$ with $p_1$ and $p_2$ corresponding to 
wins of the first or second named team and $p_{X}$ to a tie. With this, we implicitly assume an evenly 
distributed margin across these outcomes.

+ **Promoted** status of a team. Indicates for each team, whether it has been promoted to 
the division immediately before the current season. This is used to include the ``rookie status''.

+ **Titleholder** from last season. Indicates for each team whether it is the league's current titleholder.

+ **CupTitleholder** from last season. Indicates for each team whether it is the titleholder 
of the national cup (DFB-Pokal in Germany, FA CUP in England, Copa del Rey in Spain, Coppa Italia, 
Coupe de France, KNVB Cup in the Netherlands, Turkish Cup). 

+ **FormGoals3** is the number of goals scored by the corresponding team in its last three 
matches. Easily calculated for matchdays 4 and later. For earlier matchdays the last seasons average 
of all teams $\bar{g}$ is used.

+ + matchday 1: FormGoals3 = $\bar{g}$
+ + matchday 2: FormGoals3 = $\frac{1}{3} g_{\text{matchday1}} + \frac{2}{3} \bar{g}$
+ + matchday 3: FormGoals3 = $\frac{1}{3} g_{\text{matchday1}} + \frac{1}{3} g_{\text{matchday2}} + \frac{1}{3} \bar{g}$
In rare cases, when a result is missing in the last 3 matches, the average of the remaining 2 matches is used.


References:

Schiefler, L. (2015). Football Club Elo Ratings. \url{http://clubelo.com/} [Accessed: July 2021]

Elo, A.\ E. (1961). New uscf rating system. Chess Life 16, 160-161.