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  • Writer's pictureSimon Chi

RUGBY ANALYTICS 101: Pythagorean Expectation – Part 2

In the previous post, the concept of the Pythagorean Expectation within the context of rugby was introduced. The equation can be optimized so that a team’s win percentage can be predicted by its points scored and points conceded.

I know what you’re thinking.

Well, you aspiring general managers/coaches may recall in Michael Lewis’ Moneyball that Paul DePodesta (Assistant to General Manager Billy Beane) calculated that the Oakland As needed to win 95 games in order to make the playoffs. He further extrapolated that they would need to score 135 more runs than they conceded in order to achieve the 95-win threshold. These targets can be calculated using the Pythagorean Expectation. In retrospect, we know that these calculations were accurate – can the same thing be done for rugby?

Let’s look at the 2018-2019 Guinness Pro 14 (GP14) competition and select a team that finished out of the playoffs (Table 1). For the purpose of this analysis let's look at the Cheetahs who finished far enough out of the playoffs that you couldn't target bad luck as a reason they fell short, but did well enough that they might have a realistic shot of making the playoffs the next season. A quick survey of historical performances indicates that a team will need to win ~12 games to make the playoffs. As you can see, the Cheetahs finished the 2018-2019 season with 8.5 wins (8 wins, 1 draw). Thus, simple math would dictate that the Cheetahs would need to win 3.5 more games to make the playoffs.

TABLE 1: 2018-2019 Guinness Pro 14 regular season standing (Conference A)

By taking the Pythagorean Expectation equation specific for GP14 and manipulating the variables, it can be determined that the value of a “win” is 37 points. To be clear this doesn’t mean that if you score 37 points that you are guaranteed to win a game, but rather, over the course of a season, if you can increase your total points scored by 37 points, you should win one more game (assuming everything else is constant). As a corollary, using the same calculation, a decrease in points conceded of 34 points is also equivalent to a win. Thus, if the Cheetahs want to make the playoffs, they could look to the following possible strategies:

  1. They can increase their total points scored by 131 points (37 x 3.5 = 131.3)

  2. They can decrease their total points conceded by 119 points (34 x 3.5 = 119)

  3. Or they could do a combination of the above 2 strategies such as increasing their points scored by 92.5 AND decreasing their points conceded by 34.

One of the interesting insights highlighted by this type of analysis is that a “win” is slightly easier to achieve by reducing points conceded compared to increasing points scored. The fact that the difference between the two values is a converted penalty is likely just a coincidence but it does provide a useful reference. If you are a coach looking for margins to improve your team’s performance in the GP14, a focus on defense might be the better strategy?

In the 2018-2019 season, the Cheetahs had a potent attack (ranked 4th overall in points scored) but struggled in defense (ranked 9th overall in points conceded). So, a realistic goal for the Cheetahs could be to increase their points scored by 37 and decrease their points conceded by 85 (34 x 2.5) which would result in a predicted Pythagorean Expectation win percentage of 0.560. This would be enough for the Cheetahs to sneak in just ahead of the Ospreys (0.556) for the final playoff spot in Conference A.


TABLE 2: Guinness Pro 14 Conference A table with anticipated finish should the Cheetahs meet their Points For/Points Conceded goals as determined by the Pythagorean Expectation.

Many of you are likely wondering how the Cheetahs actually performed in the 2019-2020 season compared to our playoff target. Due to the global pandemic the season was not completed but we can take the season total after 13 rounds and prorate them to anticipated totals after 21 rounds.

TABLE 3: Comparison of Cheetahs playoff target to prorated performance for the 2019-2020 Guinness Pro 14 competition


As you can see, the points for totals are comparable. However, when comparing the points conceded the Cheetahs actually exceeded their target and were on track to reduce their points conceded by 152 points compared to the previous season. This results in a projected win percentage of 0.614 which – lo and behold – would have been sufficient to secure a playoff spot for the Cheetahs. It is important to note that the calculation does not take into account bonus points, so it is possible that a team could perform well enough to make playoffs based on Pythagorean Expectation but could fall short due to another team accumulating more bonus points.

The Pythagorean Expectation is a useful tool because it allows teams to set goals and allocate resources to attack and defense based on team performance from the previous season. While teams can identify performance targets, the hard part is actually hitting those targets. In future posts we will look at how teams can use advanced analytics to identify ways to increase points scored and decrease points conceded.

What are your team’s performance goals for the upcoming season?

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