By William Figary and Miky Wright

Pickleball is growing in popularity. When a team in a doubles game gets to serve first, they seem to be in control of the match and may continue to score until they win. But there are a lot of other things besides serving that affect the chances of winning. The sun and wind have a huge influence on tournaments staged outside. To ensure fair play, there are numerous rules, but here we are interested in whether serving first in pickleball matches increases chances of winning.

We constructed a program and ran a series of simulations with three parameters: serving skill levels, scoring, and the side advantages. Each simulation had a different set of starting characteristics, and we played 10,000 games to determine the winning percentage. Pickleball matches are often played to 11 or 15 points, with a two-point advantage for the winning team. In each scenario, we compare the results if games are played to 11 or 15, and switch sides at 6 or 8, respectively. The outcomes are as follows, with Team 1 serving first.

Case I. In terms of serving ability, all players are roughly equal.

Results: The side that serves first has a slight disadvantage if the game is played to 11, but a minor advantage if it is played to 15.

We wanted to know if the difference of 0.48% is significant when games are played to 11. To examine that we performed a two-sample z-test for the difference between proportions. At α=0.10, with the following null and alternative hypotheses, can we reject the claim that the proportion of Team 1 who serves first has less chance of winning the game?

What about the difference between winning proportions when games are played to 15? Does the team that serves first always have a better chance of winning?

Again, we perform a 2-sample z-test with the null and alternative hypotheses being

This time the P-value is 0.01, less than α. Hence, we can reject the null hypotheses and there is enough evidence to support the claim.

The hypothesis tests indicate that the team serving first has an advantage when games are played to 15, but not so much when games are played to 11.

Case II. Each team has one very proficient server. Both proficient servers serve first for their team.

Results: Serving first has a significant advantage in this instance, regardless of whether the game is played to 11 or 15. However, if the game is played to 11, the side that serves first has a higher chance of winning compared to if the game is played to 15.

Case III. Each team has one proficient server. Proficient server serves first for Team 1, second for Team 2

Results: In this situation, serving first provides a noticeable advantage whether the game is played to 11 or 15.

Case IV. Each team has one proficient server. Both proficient servers serve second for their team.

Results: In this scenario, serving first seems to be disadvantageous. Statistical analysis comparing the results to previous cases suggests that it would not be a good idea to save your better server for later if your side wins the right to serve first.

Case V. Each team has one proficient server. Proficient server serves second for Team 1, first for Team 2.

Results: It's obvious that this strategy is awful if you get to serve first but save your stronger server for last. The results are worse when the game is only played to 11. You could wind up losing the entire game and not having a chance to recover.

Case VI. All players have equal skill levels. One side of the court has a distinct advantage. Team 1 will serve first on the favorable side.

Results: It is deceiving to have the first serve on a favorable side. You would expect them to have a better chance of winning if they had all the advantages at the start of the game, yet this dramatically increases their chances of losing.

Case VII. All players have equal skill levels. One side of the court has a distinct advantage. Team 1 will serve first on the unfavorable side.

Results: The results are like those in Case VI; whichever team plays on the advantageous side until the finish of the game has a far better chance of winning, regardless of whether they serve first or not.

The rules that teams switch sides after 6 or 8 points account for the significant advantages in Cases VI and VII. Imagine a scenario in which one side of the court has a 100% chance of winning. The team that starts on that favorable side will win the first 6 points before switching. From 0 - 6 until the end of the game, the opposing team will thereafter begin to win points. The first team’s score will freeze at 6. The same concept holds true if one side’s advantages give probabilities of winning that are higher than 50% but not 100%. The team that starts on the side with the advantage will win most of the points until they score 6, then the other team will win most of the points until the end of the game. For example, if the score after the first half of the game is 6-3, the teams would switch sides and likely score 3 and 6 points again, respectively, the score would later be 9-9. Then, the team that was on the advantageous side second is more likely to win each additional point, making it more likely they will get to 11 before the first team.

To summarize, there are four major decisions a team can make at the start of a game:

1. Which of these decisions is more important: choosing to serve first or the side you want to start the game on?

If there are obvious disadvantages on one side, our results show that choosing the side of the court is more important.

2. If you are on the team that decides a side of the court to start on, which side of the court should you choose?

You should always choose to start on the side with a disadvantage.

3. If you are on the team that decides which team serves first, should you choose your own team, or the other team?

Assuming you follow the advice in the first question, you should always choose to serve first. The results in Case I don't exactly align with this, but it's such a small difference that it's still good in general.

4. Who on your team should serve first?

Your better server should always serve first, regardless of other factors.

We believe that these statistical results will help you make better judgments. Even yet, there are a lot of other variables that might affect a game's result besides starting on one side or serving first. We sincerely hope that you keep your strength up and have fun in the competition.

William Figary is an engineer from Elizabethtown, KY. He has worked in manufacturing for six years, designing new products and processes, and developing programs to help other engineers.

Miky Wright is a full-time faculty member at Elizabethtown Community and Technical College (ECTC). 2024 is her tenth year teaching mathematics for ECTC. Besides mathematics, she’s passionate about pickleball. She’s the founder of Twin Lakes Pickleball in Leitchfield, Kentucky.