Ever wonder why sports books try really, really hard to get you to place parlay wagers?
It’s because the parlay bet, a bet type where you bet on multiple events, and ALL of them have to happen for you to win, leverages an idea that human beings are notoriously bad at comprehending: compound probability.
When multiple, independent events all have to go right for you to win, the probability of the entire sequence happening is the product of the probabilities of the individual events.
For example, the chance of flipping a fair coin and getting heads is 1/2, while the chance of flipping 4 fair coins, and getting ALL heads is 1/16, eight times less likely.
The Surprising Effects of Compound Probability
Let’s imagine you possess a shot which you know, from your practice, has a 90% success rate – maybe it’s your deep, cross-court forehand. That’s pretty good, right? You’re only missing this shot 1 out of every 10 times you attempt it.
You use this shot out of neutral situations. Sometimes, your opponent drops you a short ball, and you can transition to offense, and other times, they return the ball back cross-court, forcing you to hit this shot again.
If you’re forced to execute this shot:
- 3 times in order to win a rally, your chance of winning the rally is (.9)3, or 73%.
- 7 times in order to win a rally, your chance of winning the rally is (.9)7, or 49%.
Despite the fact that the shot you’re hitting is, by all accounts, very consistent, if your opponent can force you to hit just 7 of these shots, they’re actually favored to win the point (51 to 49).
Most people don’t have a great sense of what happens to the odds of highly likely events (like a shot which succeeds 90% of the time) when they’re and’ed together. Even a probability close to 1, like 0.9, rapidly decreases when multiplied by itself.
“I’m making so many errors.”
Many players end up confused when they encounter the following situations:
- They are used to playing 3 shot rallies, and winning 73% of them. They lose about 27% of their points to errors, and they’re okay with it.
- All of the sudden, they play an opponent who forces them to play 7 shot rallies instead of 3 shot rallies, and now they’re only winning 49% of points, and making errors on 51% of them. They perceive this change, incorrectly, as “making more errors.”
Here’s the thing though – between situation #1 and situation #2, their stroke success rate remains unchanged. It feels to the player like they are playing worse, because their rally success rate has cratered from 73% to 49%, but, in reality, they’re playing how they always play. Their opponent is forcing them to make more balls than usual.
It’s also common for these two situations to occur against the same player, but at different times in the match. Often, an opponent’s consistency will increase as they get used to your ball, especially if you hit an especially novel ball – whether it’s heavier or flatter than is typical at your level, or if you’re a lefty.
Early in the first set, your opponent’s miss rate is higher while they adjust, and they can only force you to play 3 shots. Later, as they get used to your shot, they can force you to play 7 shots instead, and all of the sudden the match is tight.
Again, you feel like it’s you who has changed, because you now lose 51% of the points to an error, rather than 27%, and again, this is incorrect. Your opponent has changed, and you haven’t. Your opponent is now making you play 7 shots instead of 3. You’re being forced to execute more shots in a row without missing in order to win the points.
If you take anything away from this article, let it be this – 90% isn’t that high. For a shot that has to be executed over, and over, and over again throughout a match, missing 1/10 is actually a lot.
If we’re able to train our deep, cross-court forehand up from 90%, to just 95%, the examples we gave at the top become far more appealing:
- 3 shots to win a point: 86% chance to win
- 7 shots to win a point: 70% chance to win
Here’s another way to say this. If you’re hitting your forehand at 90%, that’s 10 misses every 100 balls. If you’re hitting it at 95%, you miss 5 less times. Those 5 points go a long way over the course of a set. If just one or two of them end up costing you a game, all of the sudden, you’re losing the set 6-4 instead of winning it.
It’s not you, it’s them.
Once you’re already in the match, you’re working with whatever success rate you’re working with – you’re hitting at 90%, and now that your opponent has adjusted, 90% isn’t good enough. Instead of lamenting that “you’re making so many more errors now,” you need to correctly identify that your neutral rally balls are no longer good enough to win the match, and adjust. Understand that your opponent has improved, and unless you alter you’re strategy, you’re going to lose.
Whatever non-standard tools you have, the non cross-court grinding parts of the game that you are best at, now’s the time to increase the frequency at which you go to them.
The heavy, cross-court ball is certainly the corner stone of tennis, but there’s a lot more to the game than just that. Every tennis player has their unique strengths, their own tools for breaking out of bad patterns, and matches where your rally ball isn’t good enough are the time to break those tools out.