In this first article we pay homage to the late great Jonah Lomu by attempting to use Artificial Intelligence (AI) to answer the question of how good a rugby team where Jonah Lomu played every position would be.
The most successfully used AI technique for making decisions in games are Monte Carlo algorithms. These have been applied to achieve human level performance in games such as Go and Chess.
We’ll begin here with a brief explanation of how a Monte Carlo algorithm can be applied in the context of replicating player decision making in sport. In future articles we will layer in further details on how these and other AI and mathematical techniques work, and how they can be used to assist in making decisions in sporting operations.
To utilise a Monte Carlo algorithm in a full match rugby simulation we must first build a model of the sport which describes the physical environment and the rules of play. Armed with this, we need to allow players within the environment to make decisions, for better or worse. Consider a virtual rugby player standing in such an environment carrying the ball and faced with the decision to run left, right, straight, or pass to the player next to him. Depending on the player we might allow him to consider many more decisions such as other passing options, fending off a defender, or a chip kick over the defence. In a Monte Carlo algorithm we allow the player to effectively simulate each of his options, perhaps many times each. The player is effectively thinking through his options and considering their outcomes. He then chooses the option to take based on the outcome or average outcome of these simulations relative to his objectives and what he perceives to be important.
Combining the model of the physical environment, rules of play and decision making process we effectively end up with what could be termed an AI engine capable of modelling a sport. We’ve spent the past few years developing such an engine for the sport of rugby, and we will be using it here and in coming articles to answer many questions about the sport of rugby, but the results and approach will often be generally applicable to many sports.
Once we have an engine/model, we can use it to answer a question by performing Monte Carlo simulations of entire matches or parts of them (as differentiated from the Monte Carlo decision making algorithm discussed above). A simple way to understand Monte Carlo simulation of a match is to imagine rolling a six sided die 10,000 times and recording the result of each roll. If you did this you would be able to get a reasonably accurate estimation of the probability of a 6 being rolled which would be close to the true value of 1/6. What say you then weighted one of the sides? You could then re-run the experiment rolling the die another 10,000 times and determine what effect this weight had on the probability of rolling a 6, something that might be very difficult to determine otherwise.
This is the exact same approach we will use here, except in our case the AI engine is the die and the outcome is the result of the match and all the data that comes along with it (e.g. points scored, tackles made etc.). We’ll perform many simulations with standard players and then many simulations when each of the players are progressively replaced by someone with the key attributes of Jonah Lomu. From the difference we will be able to answer our question of how good a team of Jonah Lomu’s would be.
In our case, our standard players have attributes (speed, acceleration, handling error probability, tackle success probability etc.) taken from various sources which describe typical rugby players (with positional specificity where available) at about the level of a current professional club player. Using these players as our input, the AI engine and the assumptions it are based on have been adjusted until the output matches that of the Super Rugby competition. This process of modelling and model validation is very important and something we will detail further in future articles. For now, we will just accept that we are satisfied with the results of this process, so that our next task is to ask what should the input attributes of Jonah Lomu be?
To make things simpler we will consider the attributes which perhaps contributed most to Jonah’s ability to terrorise his opposition: height, weight, speed, acceleration, and of course, his ability to break tackles. In all other attributes we will consider him the equal of the typical player in each position. For example, we’ll assume the front row version of Jonah can scrummage and the flyhalf version is adept at kicking for touch.
With that in mind, Jonah was about 120 $latex kg &s=0$ and 1.96 $latex m &s=0$ tall. He was exceptionally fast for a man of his size and able to run the 100 $latex m &s=0$ sprint in 10.8 $latex s &s=0$ in his prime. If we assume his acceleration was about that of a typical rugby back at 6.31 $latex m.s^{-2} &s=0$ then his maximum speed can be calculated as 9.99 $latex m.s^{-1} &s=0$. Imagine that, the big man storming toward you covering around 10 meters every second. Not an easy prospect for a defender.
As a side note, it’s implicit in the above that we are assuming rugby players can be adequately described as accelerating constantly to maximum speed. This is an example of one of the many simplifying assumptions made in our AI engine which help to ensure our Monte Carlo approach remains computationally feasible in a reasonable amount of time. We’ll detail other assumptions as they arise in future articles. Given adequate data, we can often demonstrate the validity of such simplifying assumptions by showing that they have negligible impact on the output we are interested in.
Finally, in the absence of any hard data we will assume the probability that Jonah would break a tackle was twice that of a typical player. It’s probably a fair estimate. Just ask the English fullback Mike Catt who was trampled by Jonah on his way to score a try in the 1995 Rugby World Cup quarter final between New Zealand and England.
Having estimated our input data for Jonah Lomu, we are now ready to carry out our simulations. Rather than just replace the entire team at once, we’ll replace them one by one in the following order by jersey number 11, 14, 15, 13, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. For those not familiar with rugby this amounts to replacing the outside backs (11, 14, 15) followed by the remaining backs (13, 12, 10, 9) and finally the forwards. Backs are generally faster and more agile players who look to exploit space and finish scoring opportunities. Forwards are generally bigger and stronger and are crucial to controlling and maintaining possession of the ball on attack.
Jonah was a winger and wore jersey 11, so we are replacing his position first. The graph below shows the effect of sequential replacement of each player on the team by Jonah on the winning percentage of the team. Each data point represents 2000 match simulations.
When zero players are replaced (our control) the win percentage is around 50%, representing a match between two identically matched sides. The winning percentage is actually slightly lower than 50% as a result of draws. It turns out that draws account for around 3% of all results when teams are perfectly evenly matched. This number reduces to much less than 1% as teams become increasingly mismatched.
Replacing just one player in Jonah’s 11 jersey results in only a small increase in winning percentage. This obviously shows that one man can’t make a team, especially in a 15 aside game like rugby union. But it is perhaps also a tribute to Jonah and the impact he had on the sport of rugby. Before Jonah came along rugby union wingers were generally smaller. In the modern game there are plenty of big wingers, and that change is at least partly attributable to Jonah Lomu demonstrating how devastating a big fast man on the wing can be. So because our baseline player attributes are that of a modern winger, replacing them with Jonah has a small but not drastic effect. Smaller than it would have been back when Jonah burst onto the world rugby stage in the mid 90’s.
However, as we progress through the rest of the backline replacing each player with Jonah Lomu like players as we go, the effect of winning percentage starts to increase drastically, reaching about 85% once the entire backline has been replaced. It is clear that an entire backline with all their position specific skills in tact, and yet still sporting the size and mobility of Jonah would be fairly unstoppable, and certainly not something the modern game has ever seen. Though, with player sizes seeming to continue to trend upward, it is something we might see in the future!
As we continue through the forwards the winning percentage continues to climb, before leveling out as it reaches more than 99% by the time the locks have been replaced. We barely even need to bother replacing the final three players in the front row of the forward pack, as the damage is already done. Although modern forwards are of similar size to Jonah Lomu, once they are endowed with his speed and acceleration as they have been here, they become virtually unstoppable.
When all is said and done the final winning percentage once all 15 players have been replaced is 99.8%. So, we have answered our initial question. A team where every player possesses the physical characteristics of Jonah Lomu, whilst retaining the skills specific to their position would be almost impossible to beat.
As an interesting side note, the classic video game ‘Jonah Lomu Rugby’ released in 1997 featured an unlockable ‘Team Lomu’ which had Jonah in every position. Just as we predicted here, they were pretty unstoppable!
Although the subject of this article has considered a hypothetical scenario, it points to more practically useful applications of AI in sports. Things like determining what we should train players in, and who we should recruit.
In essence, all applications boil down to potentially allowing us to determine what is important to winning. We will explore such applications in the future and try to answer questions like,
What makes the All Blacks so good?
How important are offloads in the modern game of rugby?
What are the most important physical attributes and skills to train?
Would recruiting Usain Bolt be a good idea for a rugby team?
What is the effect of a bad refereeing call?
In the next article we will determine how important the bounce of the ball is in determining the result of a rugby match.