Dissecting the DUPR Algorithm: A Coach Explains "Modified Elo" and Expectation Formulas

"I want to know more about how DUPR is calculated." For those of you who love numbers, this article will dissect the "inner workings" of DUPR as accurately as possible.

Hi, I'm Coach Yoshi. I've been playing tennis for 15 years and discovered pickleball in 2026. In my previous article, How DUPR Works, I explained it intuitively without formulas. This article is the "formulaic version." It might be a bit niche, but understanding it will significantly deepen your appreciation for the numbers.

*DUPR is a field where systems and numerical values are rapidly revised. This article explains the system as it was at the time of writing, based on official information. Please check the official dupr.com for the latest accurate specifications.

Based on "Modified Elo"

DUPR is based on "Modified Elo," an improved version of the Elo rating used in chess and many other competitions, adapted for pickleball.

The basic idea of Elo is as follows:

1. Before a match, calculate the "probability of winning (expected value)" from the ratings of both players.
2. After the match, increase or decrease the rating according to the difference between the actual result and the expected value.
3. If the result is better than expected, the rating goes up; if worse, it goes down.

DUPR incorporates pickleball-specific elements (point differential, type of match, newness, etc.) into this.

"Expected Score" and Logic of Increase/Decrease

DUPR calculates an "expected score" (approximately what the point difference should be) from the ratings of both players. This is then compared to the actual score.

• Actual > Expected → Rating increases
• Actual < Expected → Rating decreases

The following factors primarily influence this:

• Win/Loss: Whether you won or lost
• Point differential (points scored): What was the point difference?
• Opponent's rating: Was the opponent higher or lower rated?

Therefore, "losing to a higher-rated player after a good fight" can increase your rating, while "barely winning against a lower-rated player" can decrease it. This is the essence of the expected value approach (for specific examples, see How DUPR Works).

In doubles, the team's rating is treated as the average of the two players' DUPR ratings, and the expected score is calculated from that.

Only Considers "Recent Matches" (Match Window)

DUPR does not equally consider all past matches. It primarily evaluates recent matches.

• Singles: Approximately the most recent 30 matches
• Doubles: Approximately the most recent 60 matches

This "window" ensures that "current ability" is reflected, rather than past form. The mechanism of "half-life," where the influence of older matches diminishes over time, is explained in detail in DUPR Reliability and Half-Life.

"Match Type" Has Different Weighting

Not all matches are weighted equally. Matches with higher reliability are weighted more heavily.

According to official explanations, self-posted matches have a smaller impact on ratings, while results entered by clubs or tournaments are weighted more heavily. Specific multipliers are not disclosed, but it's sufficient to understand that "the more reliably recorded a match is, the more impact it has." Therefore, the more records you have from reliable sources, the more stable and accurate your rating will be.

💡 Coach Yoshi's Tip "Properly recording matches in official settings" directly leads to the accuracy of your numbers. Self-reporting alone can be inconsistent. Utilize records from tournaments and clubs.

Differences in Design Philosophy from Elo / Glicko

The base Elo of DUPR represents skill with "a single rating value." In contrast, the Glicko system (a later improved version) features not only a rating but also "the certainty (uncertainty) of that rating."

DUPR's unique approach is to incorporate this concept of "certainty" as a separate metric called "Reliability." This allows for distinguishing between the rating itself (skill) and its reliability (how certain it is). The differences from other ratings based on Glicko-2 (such as WPR) are compared in DUPR vs UTR-P・UTPR・WPR.

Summary

• DUPR is based on Modified Elo. Ratings increase or decrease based on the difference between expected and actual scores.
• Key factors are win/loss, point differential, and opponent's rating. Doubles ratings are calculated using the average of two players.
• It considers the most recent 30 matches (singles) / 60 matches (doubles) = current ability.
• Match types have different weights (official/club > self-reported).
• Distinguishing between skill (rating) and certainty (reliability) is DUPR's style.

Once you understand the mechanics, the movement of the numbers makes sense. Next, we'll delve into DUPR Reliability and Half-Life, which determines certainty. Don't be swayed by the numbers; use them as a tool for improvement. If you have any questions, feel free to ask on LINE.

Related Products

Related Articles

• How DUPR Works — Intuitive version without formulas
• DUPR Reliability and Half-Life — The mechanism of certainty
• What is DUPR? — The hub of the series
• DUPR vs UTR-P・UTPR・WPR — Design differences with other ratings
• How to Improve Your DUPR — Practical ways to raise your rating

References

1. DUPR Help — How is the DUPR rating calculated
2. DUPR — How It Works