Conclusion: four-player mahjong2.50 and three-player mahjong2.00 are "standard average values"
Average placement is calculated by dividing the total rank for each match by the number of matches. four-player mahjong2.50, if three-player mahjong (three-player mahjong)2.00is the average value. However, this is not a passing line of strength, but only a starting point for analysis. The key is to understand your opponent's level, rules, number of matches, first-place rate, last-place rate, and ranking distribution.
If you are worried about the basic terms of mahjong such as hansho, bureau, parent, etc., please read first.Introduction to mahjong rules for beginnersBy understanding the big picture, you can understand the performance indicators more easily.
How to calculate average placement
Add up the ranking for each match and divide by the number of matches in that period. The smaller the value, the more matches finished in higher ranks.
average placement = total rank ÷ number of matches
four-player mahjong10match example
If there are 1st place 3 times, 2nd place 2 times, 3rd place 3 times, and 4th place twice, the total ranking is "1 x 3 + 2 x 2 + 3 x 3 + 4 x 2 = 24". Since we divide 24 by 10match, the average placement is2.40It is.
Displaying average placement to the second decimal place makes it easier to follow changes. However, increasing the number of displayed digits does not eliminate the chance of a small number of matches.
The same average placement can also be calculated from the ranking rate.
If you know the rank rate of four-player mahjong, it can be calculated by "1 x first-place rate + 2 x 2nd place rate + 3 x 3rd place rate + 4 x last-place rate". Convert percentages to decimals when calculating. If first-place rate is 30%, second-place rate is 25%, third-place rate is 25%, and last-place rate is 20%.1×0.30＋2×0.25＋3×0.25＋4×0.20＝2.35It is.
This formula matches the result calculated from the number of ranks. If they do not match, check the causes, such as the aggregation period is different, incomplete matches are included, or there is an error due to rounding of the percentage display.
four-player mahjong2.5 and three-player mahjong2.0 are the center of mathematics
Assuming that everyone has the same conditions and the probability of being in each position is the same, average placement is the average of the position numbers.
| format | calculation | center value |
|---|---|---|
| four-player mahjong | (1＋2＋3＋4) ÷ 4 | 2.50 |
| three-player mahjong | (1＋2＋3) ÷ 3 | 2.00 |
2.5 and 2.0 are neither target values nor passing scores.
Even for the same person, the distribution of results will vary depending on the composition of the opponent, whether it is an East-only game or a half-sho game, ranking points, early termination conditions, etc. Instead of making a quick judgment like "2.49 is strong" or "2.51 is weak," use it as an entry point to compare records from the same group and the same rules.
When using average placement guidelines found on the Internet, please check that the target service, table/dan rank, three-player mahjong/four-player mahjong, Dongfeng/Southeast, aggregation period, and number of matches match your record. Numerical values that do not explain the population cannot be directly translated into individual goals.
When looking at your own performance, check not only the difference from the center value, but also how the average placement has changed over the past period under the same conditions. The evaluation for the same average placement will also change depending on whether the ranking points are focused on top or last avoidance.
Metrics to look at along with average placement
| indicators | Calculation/Contents | Points to see |
|---|---|---|
| average placement | Total rank ÷ number of matches | Ranking level for the entire period |
| first-place rate | Number of 1st place ÷ Number of matches × 100 | winning percentage |
| last-place rate | Lowest number of matches ÷ number of matches × 100 | Frequency of large ranking losses |
| rank distribution | Number of times and percentage of each rank | Dispersion in offense and defense and results |
| average score | Total score ÷ number of matches | Gains and losses including ranking points |
| profit and loss | Increase/decrease including rate, tip, table fee | Results including costs |
| number of matches | Number of games to be counted | Amount of records that support the numbers |
Score and profit and loss are not the same. Since profit and loss includes rates, chips, table fees, etc., it is saved separately from the score that shows the competition results. For detailed conversionmahjong's profit and loss calculation methodYou can check it here.
It is not possible to understand the cause of the batting style just by ranking index.
Even if the average placement worsens, it cannot be determined from that alone that you are being too aggressive or too defensive. First, we will determine whether the first-place rate has decreased, the last-place rate has increased, or whether the second place has moved to the third place. If you want to find the cause further, compare the match memo with the metrics you can record, such as the Agari rate, deal-in rate, riichi rate, and secondary rate for the same period.
The M League's official scoreboard also lists multiple indicators, including not only average placement, but also the number of finishes, first-place rate, consecutive match rate, last avoidance rate, hit rate, and deal-in rate. However, the values for a particular season in the Pro League are not the standard for regular players. Here, we will refer to it as a "display example of combining indicators."
Same average placement but different contents
Compare two people with an average placement of 2.50 in 20 matches. Both have a total rank of 50, but their rank distributions are very different.
| player | 1st place | 2nd place | 3rd place | 4th place | average placement |
|---|---|---|---|---|---|
| A: The top and bottom are large. | 8 times | twice | twice | 8 times | 2.50 |
| B: Many in the middle | twice | 8 times | 8 times | twice | 2.50 |
A's first-place rate and last-place rate are both 40%, and B's both are 10%. Even though the average placement is the same, A's results fluctuate widely, and B's results are concentrated in 2nd and 3rd place. Which one is preferable depends on the ranking points and purpose, so we leave the distribution in mind when making a decision.
Two routes to improve average placement
Average placement improves both "increasing the top" and "decreasing the bottom." In 20 matches, if you move from 4th place to 3rd place by 2 times, your total ranking will decrease by 2 and your average placement will improve by 0.10. Similarly, if 2nd place moves to 1st twice, it is an improvement of 0.10. Even though the amount of change in numbers is the same, the former is a change in avoiding the last one, and the latter is a change in getting to the top.
Therefore, by placing "previous month difference in first-place rate" and "previous month difference in last-place rate" next to average placement in the monthly report, you can briefly explain the direction of change. For months where the number of matches is different, compare by percentage rather than the number of matches, and be sure to include the number of matches in the denominator.
Four conditions to meet when comparing grades
1. three-player mahjong and four-player mahjong
Since the rank range and center value are different, be sure to tabulate them separately.
2. East-only game and Hanshuang
The length and number of games per game vary. Even if the average placement is the same, it will be easier to read the changes if you align them for comparison.
3. Rules and competition group
Notes will be made in the records on days when red fives, midway finishes, ranking points, member composition, etc. change.
4. Period and number of matches
Short-term numbers include random ups and downs. Don't just decide that ``how many matches will tell you how good you are.'' Please write down the monthly and total numbers, and check the number of matches for each.
With a small number of matches, the influence of one game is large.
If 4th place changes to 1st place once in four-player mahjong10match, the total ranking will decrease by 3 and the average placement will move by 0.30. For 100 matches, the difference in one match is 0.03. Even if it is displayed to the second decimal place, it is not possible to conclude that the difference between 2.40 and 2.50 in 10match is a long-term difference in ability.
Research on mahjong ability estimation also addresses the issue of the fact that estimation based only on average placement can have large variance. In this article, instead of setting a groundless fixed line such as "minimum number of races," we line up the short-term and total numbers and observe whether the trend remains even when we increase the number of aggregations.
List this month/last 30 matches/total
For beginners, it is sufficient to list three items: "This month," "Last 30 matches," and "Total." You can see the amount of activity this month, recent changes in the last 30 matches, and long trends in the total. If it's only good in the recent past, it may be a sign of improvement, but check to see if the opponent or rules have changed.
Order of reviewing grades
- Align the aggregation conditions such as three-player mahjong, four-player mahjong, Dongfeng, Hanzhuang, etc.
- Check the target period and number of matches
- Sorting average placement and rank distribution
- Check whether first-place rate or last-place rate has changed
- Check average score and profit and loss separately
- Looking back at match content and rule changes during a period of significant change
If you haven't decided how to record yet,How to choose a mahjong profit and loss management appPlease also refer to
How to write a monthly review
Write down the conditions, denominator, three main indicators, and reservations in one set, such as "four-player mahjongEast-South game・24match. average placement 2.38 (previous month 2.55), first-place rate 29.2%, last-place rate 16.7%. Last-place rate has decreased, but the number of matches is small, so check the total value and next month as well."
After the numbers, leave an event that can be confirmed, not an impression. If you have a memo like ``2 reversals on Nanba Oya's turn'' or ``3 deal-ins on the station that received riichi and pressed musuji'', you can connect it to the next learning theme. However, MemoJong does not automatically evaluate push-fold or dangerous tiles. Judging the situation is based on your own judgment.
Frequently asked questions about mahjong's average placement
What is the best average placement for mahjong?
Four-player mahjong2.5 and three-player mahjong2.0 are central values assuming that each ranking has the same probability, but it is not an absolute standard for good or bad. Compare your past results with the same format, rules, group, and time period, and check the first-place rate, last-place rate, and number of matches.
Can average placement be compared between three-player mahjong and four-player mahjong?
Not directly comparable. Because the ranking range and mathematical center value are different, we will divide them into three-player mahjongs and four-player mahjongs. East-only games and East-South games are also tabulated separately depending on the purpose.
How many matches do I need to trust average placement?
It varies depending on the match conditions and desired accuracy, so we cannot provide a fixed number of matches common to everyone. In a small number of matches, the order of finishing once has a big influence, so specify the period and number of matches, and check the trends by arranging short-term, recent, and total matches.
Scope of reference materials and figures
- M-League Organization General Incorporated Association “Chimu Scorecard” — Example of official statistics including average placement, number of finishes, first-place rate, last avoidance rate, etc.
- Takuya Ogami et al. “Estimation of ability in mahjong using variance reduction method” — Research dealing with ability estimation and variance from average placement
- Totsugeki Tohoku, Takeshi Ito “Analysis of mahjong by analyzing tiles” — How to statistically analyze match records
The displayed values for the M League are statistics for a specific population and period for the 2025-26 season. This article does not use those numbers as target values for general players. Based on our research, we do not create a fixed "strong line" or a minimum number of matches, but limit ourselves to readings that specify conditions and denominators. Document confirmation date: July 25, 2026.
Summary
Average placement is useful as a starting point for grades, but it alone does not reveal the bias between the top and last, the point difference, and the breakdown of profit and loss. Let's understand the meaning of the central values of four-player mahjong2.5 and three-player mahjong2.0, and look back at the combination of first-place rate, last-place rate, rank distribution, score, profit and loss, and number of matches under the same conditions.