A New Metric for Evaluating 1v1 Ability

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 recognises 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.

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.

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

We see a general rule that the closer to goal a player is, the more likely he is to prevail in the duel; the advantage is with the defending team. This makes sense because duels close to goal are usually between an attacker and a defender. The defender has one job here, which is to dispossess the attacker and break down the attack, and he specialises in it. In contrast, the attacker’s true specialisation is shooting, and although he may have good 1v1 abilities, he needs to be creative to beat the defender; simply pressuring the defender is unlikely to work.

Evaluating 1v1 abilities

Duel events were drawn from the 2015/16 and 2016/17 seasons and the 2017/18 season to date. In all there were 114,063 duels, of which 50% were fair ground duels, 31% were fair aerial duels and the remaining 19.9% were 1v1 fouls. To analyse the encounters I used the Bradley-Terry paired comparison model. For a 1v1 contest between two players i and j, this model can be expressed as follows:

Given the results of multiple encounters, the analytical problem is to estimate the ability λ_i for each player i. I used a Bayesian model, and aerial and ground duels (both fair and foul) were analysed separately. For aerial duels, I computed Bradley-Terry (BT) abilities for the 234 players with over 100 duels; for ground duels I computed abilities for the 286 players who had over 200 duels.

(On a technical note, I used three Markov chains. The player with the median duel success rate was selected as the reference player, with an ability fixed at zero. Abilities of the remaining players were allotted vague Gaussian priors with zero mean and constrained in the range -15 to 15. Estimation was preceded by 5,000 burn-in steps, and 10,000 samples were drawn from the posterior distribution, and diagnostics showed the estimates had converged satisfactorily.)

Comparison of Bradley-Terry abilities with duel success rates

As suggested above, a key question is whether the Bradley-Terry ability estimates differ from the duel success rates. In fact there is a strong relationship between the two; for aerial duels the correlation is .94 and for ground duels it is .86. So why bother with all this complexity when we can just divide the number of duels won by the total and have done with it?

Despite the strong correlations, individual players with the same success rate can have markedly different Bradley-Terry abilities, as shown in Figure 3.

Figure 3: Bradley-Terry abilities and duel success rate.

We can see what this means in practice by looking at Tables 1 and 2. These show the top 20 players for Aerial and Ground duels respectively, sorted according to their BT abilities.

Top 20 Aerial Players

The results show that the top three aerial players, Kompany, Zouma and van Dijk have the three highest duel success rates.  However, some players rank quite differently on the two measures; Crouch, ranked 15^th on percent of duels won ranks 4^th on BT ability, while Andy Carroll, who only ranks 44^th on duels won ranks 11^th on BT ability.

Conversely, Phil Jones who is 6^th on duels won, is down in 20^th spot on BT ability. Other well-known players whose aerial rankings are quite different under the two estimation methods include Giroud (Success Rate rank = 96, BT rank = 42) and Ibrahimovic (success rate rank = 107, BT rank =  54).

Top 20 Ground Players

Eden Hazard tops the BT rankings for ground duels, with Traore taking the 3^rd spot. Both players are ranked higher than they are on duel success rate. Wilshere, Loftus-Cheek, Dembele and Kyle Walker also perform considerably better under the BT model than they do on duel success rate. Other well-known players whose duel success rates underestimate their abilities include Sadio Mane (success rate rank = 155, BT rank = 63) and Wilfried Zaha (success rate rank= 147, BT rank = 59).

The take-away

One advantage of the BT model is that it takes opponent’s abilities into account; this can substantially affect the estimated abilities of players in 1v1 situations. This has obvious implications for recruiting, because the duel success rate can sometimes substantially over- or under-estimate 1v1 ability.

A second advantage of the BT model, which I don’t have space to describe here, is that we can use the raw BT scores to estimate the outcome of a contest between two specific players – whether or not they have actually met. For example, a club could predict the frequency of a particular attacker beating a particular defender. This type of information could be used in match planning and to inform team selection.

BT abilities could also be used in more detailed match planning, for example to assign marking responsibilities to neutralize opposition attackers, or to exploit 1v1 weaknesses in the opposition defence. BT abilities could also be used to position players so as to increase the chances of winning the ball at corners, or in other set-piece situations involving 1v1s.