We have all seen it. A player controls a tennis match, seemingly on his way to victory, then – seemingly out of nowhere – his opponent gets an unexpected hold or break. Doubts begin to set in. Before you know it, you’re looking at a final set decider.
These defining moments are often limited to break points or important service catches, but the reality is that there are equally important points leading up to these scenarios. In this article, we introduce two new Stats Perform metrics – leverage and momentum – which allow us to highlight important points in WTA tennis matches beyond the generic points mentioned above. The Stats Perform AI group presented the concepts at the MIT Sloan Sports Analytics Conference 2022.
What are leverage and momentum?
To cut to the chase, leverage measures how important a single point is to the end result of a tennis match by quantifying how much a player’s probability of winning the match changes. Imagine, for example, that an underdog has a break point opportunity in the first game of a match. Of course, it’s always good to take a break point; however, with such a big part of the first set to go, it wouldn’t be surprising if the stronger player showed his superior quality and got the break. Now imagine it’s a break point opportunity to win the first set. The strongest player does not have time to come back into the set – lose that point and you lose the set. The second scenario is clearly a bigger point, and it would result in a higher leverage value. To be self-explanatory, leverage measures how the player’s match winning probability changes depending on the outcome of the next point – but more on that shortly.
The power of leverage comes from the ability to quickly and easily highlight important points, as well as quantify the importance of the point. One can go beyond the typical restrictive break/set/match points. For example, those crucial “setup” points (as coined by former player and coach Brad Gilbert in his book “Winning Ugly”) when a player is two points away from winning a game.
Momentum aims to describe which player is in control at any point in the match – who currently earns the most points? And who wins the big (high leverage) points? It is defined as “an exponentially weighted moving average of leverage acquired by a player”. At each point in a match, there will be a single momentum value favoring a player. This allows us to better quantify periods of dominance beyond the standard “Player A won X of the last there points”, while easily highlighting specific points in a match that constitute real momentum swings.
How are leverage and momentum calculated?
As mentioned above, leverage is the amount of change in a player’s probability of winning a match given the outcome of the next point. For example, let’s say that a player’s probability of winning the match will be to augment 15% (0.15) if they win the next point. But, if they lose this point, their probability of winning the match will be to diminish by 5% (-0.05). The difference between these probabilities of winning a game is 20 percentage points (0.15 – (-0.05) = 0.20). So we say that this point has a leverage of 0.20.
Of course, this depends on whether we have predictions for each player’s match-winning probability. The underlying leverage is a chain of models designed to predict all the possibilities of a tennis match, which take into account the following characteristics:
- Type of land
- Current match status (i.e. game in progress and score set)
- In-game statistics (e.g. difference in points/games/sets won, serve/return percentage, etc.)
- Pre-match odds
We first predict the probability that a player will win the next point. This is then passed on to the next part of the chain – predicting the winner of the game, then predicting the winner of the set, and finally, predicting the winner of the match. In total, the model is built from 1.5 million points played on the WTA Tour between 2012 and 2020. This chain shows how the outcome of a single point changes the probability that each player wins the match.
Momentum is built from leverage and, as mentioned above, is defined as “an exponentially weighted moving average of leverage earned by a player”. The result of this is a momentum value at each point which is determined by each player’s performance in the previous points. The more recent a point, the more influence it has. The more important a point is (high leverage), the more influence it has. A “swing” in momentum is defined as momentum passing from one player to another by an magnitude of 3% or more.
Apply leverage and momentum in the real world
Let’s see how these two new metrics are used in a real game. Bad Homburg Open, June 25, 2021. Petra Kvitová and Angelique Kerber battle it out for a place in the final – a victory on grass here would be the perfect preparation for Wimbledon. With an initial win probability of 55.7%, Kerber is the favorite, albeit a very narrow one.
The match ended in a 6-3 4-6 6-7 (3-7) tiebreaker victory for Kerber. But along the way, a number of crucial points determined how the match unfolded. The graph below shows how each player’s probability of winning changed as the match progressed.
Leverage immediately alerts us to a number of key match points:
1. At 4-2 40-A in the first set, Kvitová is already out, but now Kerber has the chance to get him back. Earning this point would increase Kerber’s chance of winning the match by 16.0% – a chance she ultimately doesn’t take.
2. Kerber found himself 3-1 30-15 on his own serve in the second set. His task is starting to look daunting as his odds of winning the match bottom out at just 4.0%.
3. Still, she manages to hold the serve and this is marked as a potential boost in her favor.
4. Kerber finds himself at 4-5 15-30 on Kvitová’s serve. Taking this “setup” point would grant him two set points and improve his probability of winning by 18.0%.
5. The most important point of the match. With Kvitová serving at 4-5 30-30 in the final set, winning that point for Kerber would mean match point – a whopping 26.3% increase in his probability of winning the match.
Each point has a leverage value. As well as allowing us to quickly highlight and quantify important points in a match, it also means that we can consider points beyond the traditional boundaries of break/breakpoints – just as we did with (4) and (5) above. In combination with momentum, we have two powerful metrics that allow us to easily describe the flow of a match and highlight the most important moments.
But that’s not all. Beyond that, leverage opens up the exciting possibility of exploring how players perform in those high-pressure moments – look for another explainer on our Clutch metric.
Banner design by Ruben Dias.
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