フットボール統計学 デュエルを評価するための新指標(前編)

The Liverpool defender and legendary hard man Tommy Smith is supposed to have said: "The ball may pass, the man may pass but never the two together." Football has become less bloodthirsty since Smith last played for Liverpool in 1978, but performance in 1v1 contests remains a key element of the game.


Opta recognizes several types of 1v1 event, collectively known as duels. Aerial duels occur when two players contest a ball in the air; this is a symmetrical event because neither player starts with possession. Ground duels are asymmetrical events, because one player has possession and the other is trying to regain it. Frequently it is the attacker that has possession, rather than the defender; however, in this article I want to rank attackers and defenders on the same scale, so I will not distinguish between the two sides of the duel, the only variable of interest is who wins it. Opta also includes fouls within the duel category, and accordingly I include them as well.

Optaは、いくつかの種類の1対1イベントを認識し、これらはまとめて「デュエル」と呼ばれる。空中戦は、2人の選手が空中でボールに争うときに発生する。どちらの選手もポゼッションを始めないため、これは対称的なイベントである。地上のデュエルは非対称的な出来事であり、なぜなら1人の選手がポゼッションを持ち、もう1人がボールを回復しようとしているからである。しばしば守備側ではなく、ポゼッションしているのは攻撃側であることが多い。しかし、この記事では、同じスケールで攻撃者と守備側をランク付けしたいので、私(Garry Gelade氏)はデュエルの両面を区別しない。興味のある変数は勝者のみである。Optaには、デュエル部門内のファウルも含まれているので、同様にそれらも含める。

In this post I discuss the evaluation of player 1v1 abilities within this framework. I will keep ground and aerial duels separate; these are statistically two different kinds of skill, and a player who ranks highly on does not necessarily rank highly on the other.


1v1 abilities are traditionally assessed on a simple percentage basis; a player’s duel success rate is:
Duel success rate = Number of duels won / total number of duels



This is reasonable, but it does not take opponents’ abilities into account. For large numbers of encounters between randomly selected opponents, opponent ability averages out. But we cannot assume that players are randomly paired in practice. For one thing, managers often assign their best defenders to mark the most dangerous attackers, so that dangerous attackers face stronger opposition than their less dangerous counterparts. Percentage success rates will therefore underestimate the ability of the dangerous attackers and overestimate the ability of the less dangerous ones. The same thing applies to defenders.


Here I use the ’Bradley-Terry‘ model to explicitly model opponent ability. A key question is how the Bradley-Terry ratings compare with the duel success rate, and we shall see there are some surprising differences in how certain players are evaluated.


But first, let’s look at some general features of duels and how they fit into the wider picture.


The importance of duel supremacy


Duel supremacy (winning more duels than the opposition) is a correlate of success; teams who win duels win matches.

デュエルの覇権(相手よりも多くのデュエルで勝利すること)は成功の相関関係である。 デュエルを勝ち取ったチームが試合に勝つ。

Figure 1 shows for instance that the team winning on aerial duels has a 39.2% chance of winning the match while the team losing on aerial duels has only a 32.6% chance of winning. Similarly, the team winning on ground duels has a 40.7% chance of winning the match while the team losing on ground duels has only a 32.1% chance of winning.


Figure 1: Duel supremacy and match results


Of course, most duels do not directly influence the scoreline. But in recent Premier League seasons, 29% of goals were scored within 10 seconds of winning a fair duel. If we add goals attributable to 1v1 fouls (i.e. scored within 10 seconds of the resulting free kick, or from the direct free kick or penalty) the number jumps to 39%.


The effect of pitch location


Figure 2 shows the probability of winning a duel at various distances from goal.


Figure 2: Duel supremacy and pitch location




フットボール統計学 デュエルを評価するための新指標(前編)




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