The logic behind tanking a part of a tennis match–deliberately playing with less than maximum effort–is simple. If you have fallen behind early in the first set, you could choose to take it easy for the rest of the set. You probably would’ve lost the set anyway, and having semi-rested for several games, you’ll have more mental and physical energy to draw upon for the rest of the match.
By the end of this post, we’ll have some idea how useful that extra energy must be to make tanking worthwhile. It will take a few steps to get there.
The scenario
Consider some sample numbers to make this more concrete. Take two evenly matched men, each of whom win 70% of their service points. Maybe they are powerful–though not one-dimensional–servers on a reasonably fast surface. Winning seven out of ten service points means that nine out of ten games are holds of serve, so in our hypothetical match, breaks are at a premium.
Imagine that the match opens with one of those rare breaks. Given the 90% hold rate for both players, the man who got his nose in front has improved to an 83% chance of winning the set. In the simplest formulation, the player who has fallen behind faces two options for the balance of the set:
- Continue playing at his usual level despite the low chance of winning, or
- Take it easy, as the set is probably lost.
The tank
In the continue-as-usual scenario, our early front-runner has an 83% chance of winning the set. If both players continue playing at the same level for the duration of a best-of-five-sets match, that translates to a 62% chance of winning the match, leaving our player who decided not to tank with a 38% chance. (I’m using best-of-five because in a longer match, it’s more likely that a player can recover from losing the first set. That makes tanking a more plausible strategy.)
To evaluate the take-it-easy scenario, we need to pile on more assumptions. How much worse does a tanking player play? You will probably disagree with my estimates of the point-level costs and benefits of tanking, which is fine. I don’t have strong opinions about them, and they don’t matter much to the conclusions below. Consider these numbers just one illustration of the model. As soon as the trailing player decides to take it easy, let’s say his numbers fall to the following:
- 20% return points won (instead of 30%)
- 65% serve points won (instead of 70%)
That’s not a very good player–picture an unmotivated Nick Kyrgios. Down a break after the first game and playing a newly lackadaisical brand of tennis, he has a mere 1.3% chance of coming back to win the set. We’re simplifying quite a bit here, in large part because a player could always decide midway through the set to pause the tank, perhaps raising his game if he reaches 15-30 or better on his opponent’s serve. But again, this is just a model, and one I’m trying to keep from getting too complex.
The trade-off
The tanking player has, according to these assumptions, chosen to decrease his chance of winning the first set from 17% to a tick above 1%. If he received no benefit from conserving energy and both players returned to their 90% hold rate at the beginning of the next set, the tanking player’s chances of winning the match have fallen from 38% to 32%.
Clearly that’s not the whole story. A player who chooses to conserve energy at the expense of their immediate fortunes must assume that there are benefits coming later.
To further simplify, let’s assume that the tanking player loses the first set. Here are his chances of winning the match based on a few possible post-tank levels he could sustain:
- 70% serve points won (SPW), 30% return points won (RPW): 31.3% (no benefit from tanking)
- 71% SPW, 32% RPW: 46.3%
- 72% SPW, 34% RPW: 61.9%
- 73% SPW, 36% RPW: 75.8%
- 74% SPW, 38% RPW: 93.3%
Remember that our tanking player has only a 38% chance of winning the match after sustaining the opening-game break, so the second scenario, in which his level improves to 71% SPW and 32% RPW, represents an improvement. That would be hardly noticeable over the course of three or four more sets. If the remainder of the match spanned 200 more points, it would mean winning 103 of them, instead of 100. If conserving energy early on confers even bigger benefits, it starts to look like a no-brainer.
Complications
Of course, it’s never this simple. The leading player might realize that his opponent was tanking and conserve some energy himself. The tanking player could have a hard time resuming his usual level (or better) at the right moment. Some points are more important than others, so the difference between 100 and 103 might not matter. Most matches are best-of-three, and giving up on the opening set in a shorter match is much more dangerous.
Those qualifications shouldn’t stop us from considering what tanking has to offer. While players don’t tank sets as often as they used to, there’s surely some energy-conservation benefit, and extra energy must have some value for the remainder of the match, right? I have no idea whether that value is equivalent to one point per hundred or something much higher or lower, but surely it’s possible that in some situations, it’s worth it.
The illustration I’ve used shows that the value of the extra energy doesn’t have to be that substantial to make tanking a plausible tactic. The small margins that determine the outcome of tennis matches mean that we’ll rarely recognize when a player is taking advantage of a tank, but those margins also mean that a small edge could be enough to make it worthwhile.
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All calculations of game, set, and match probabilities are based on my publicly-available code.