Description
Comprehensive mathematical and statistical analysis of the 6th round of the Primera Division – Clausura in Costa Rica, season 2025-2026
The Costa Rican football ecosystem, governed by the Union of First Division Football Clubs (UNAFUT), is one of the most dynamic and competitive environments in the CONCACAF region. The current 2025-2026 season is entering a critical phase with the arrival of the sixth round of the Clausura tournament, where statistical trends are beginning to crystallize into predictable patterns. A deep understanding of this championship requires not only knowledge of the current form of the teams, but also the application of rigorous mathematical protocols that isolate emotional biases and focus on the objective data provided by Soccerway. In this context, this report applies the “Mathematical Computation Protocol” to define a Harmony Index (HI) for each match, providing professional analysts with a robust framework for assessing risk and predictability.
Structural framework of the mathematical model and methodology
The analysis process is based on an eight-step computational protocol that starts with the extraction of raw statistical data and ends with the generation of a harmony index reflecting the internal stability of the prediction. The first step involves collecting the percentages of wins (W%), draws (D%) and losses (L%), along with the average number of goals scored (GF) and goals conceded (GA) for each team since the start of the current Clausura season. The use of “overall” statistics is essential as it provides a broader context for team performance compared to home or away statistics alone, especially in the early stages of the championship.
The mathematical core of the model consists of calculating “Attacking Power” ($A$) and “Defensive Power” ($D$) for each team. Attacking power is defined as the sum of the win percentage, the loss percentage and the average number of goals scored, while defensive power is calculated as the reciprocal of the win-loss balance adjusted by the average number of goals conceded. These two indicators are used to derive the expected goals (xG) for each match, which in turn serve as input data for the Poisson distribution. This distribution allows us to determine the probabilities of the three main outcomes of the match – home win (1), draw (X) and away win (2).
The next phase of the analysis introduces the concepts of stability ($K$) and evenness index ($L$). Stability is measured by the standard deviation of the Poisson probabilities, normalized to their mean and adjusted by a factor of 1.67, with its maximum value limited to 0.99. The evenness index, on the other hand, measures the absolute difference between the balance of attack and defense of the two rivals. The ultimate goal of these calculations is the Harmony Index (HI), which synthesizes stability and evenness into a single security indicator. Matches with an HI above 100 are classified as “Platinum Selection”, while those below 7.50 are considered high-risk.
| Step | Parameter | Mathematical formula / Source |
| 1 | Input data | W%, D%, L%, GF, GA (Soccerway) |
| 2 | Attack power (A) | $A = W\% + L\% + GF$ |
| 3 | Defensive power (D) | $D = 1 / (W\% – L\% + GA)$ |
| 4 | Expected goals (xG) | $(A_{Home} + D_{Away}) / 2$ and $(A_{Away} + D_{Home}) / 2$ |
| 5 | Probabilities (Poisson) | Poisson distribution for 1, X, 2 |
| 6 | Stability (K) | $(STDEV.P(1, X, 2) / AVERAGE(1, X, 2)) \times 1.67$ |
| 7 | Equality Index (L) | $ABS(ABS(A_H – A_A) – ABS(D_H – D_A))$ |
| 8 | Harmony Index (HI) | $(2 / K) + (1 / (1 – L))$ |
Analysis of the current state of the Primera Division – Clausura 2025-2026
Before the start of the sixth round, the Costa Rican standings show a significant dominance of several teams, while others struggle with serious defensive deficits. Herediano leads the table with 12 points, demonstrating a high offensive efficiency with 10 goals scored in 5 matches. In contrast, the Puntarenas FC team occupies the last position with only two points, having yet to record a victory in this tournament. This data is fundamental to our model, as large differences in performance often lead to higher statistical stability in the predictions.
Traditional giants Alajuelense and Saprissa are in the middle of the table, with Saprissa showing an unusually high number of draws – three out of five games. This tendency towards draws is a key factor in calculating the $L$ index, as it reflects teams that are difficult to beat but also have difficulty realizing their full offensive potential. The average number of goals in the championship so far is around 2.25 per game, which is an important benchmark in determining the attacking strength compared to the league average.
| Team | M | P (W) | P (D) | H (L) | GF | General Directorate (GA) | W% | L% | GF (average) | GA (average) |
| Herediano | 5 | 4 | 0 | 1 | 10 | 2 | 0.80 | 0.20 | 2.00 | 0.40 |
| Carthage | 5 | 3 | 1 | 1 | 5 | 3 | 0.60 | 0.20 | 1.00 | 0.60 |
| San Carlos | 5 | 3 | 0 | 2 | 6 | 4 | 0.60 | 0.40 | 1.20 | 0.80 |
| Alajuelense | 5 | 2 | 2 | 1 | 7 | 5 | 0.40 | 0.20 | 1.40 | 1.00 |
| Zeledon | 5 | 1 | 4 | 0 | 8 | 6 | 0.20 | 0.00 | 1.60 | 1.20 |
| Saprissa | 5 | 1 | 3 | 1 | 6 | 7 | 0.20 | 0.20 | 1.20 | 1.40 |
| Liberia | 5 | 1 | 2 | 2 | 5 | 6 | 0.20 | 0.40 | 1.00 | 1.20 |
| Sporting FC | 5 | 1 | 1 | 3 | 2 | 6 | 0.20 | 0.60 | 0.40 | 1.20 |
| Guadalupe | 5 | 1 | 1 | 3 | 4 | 10 | 0.20 | 0.60 | 0.80 | 2.00 |
| Puntarenas FC | 5 | 0 | 2 | 3 | 3 | 7 | 0.00 | 0.60 | 0.60 | 1.40 |
Detailed analysis of the matches from the 6th round
Match 1: AD Municipal Liberia vs. Puntarenas FC
The match between Liberia and Puntarenas FC pits two teams from the bottom half of the table against each other. Liberia is in seventh place, with their recent form having been inconsistent – a loss to San Carlos and a win over Herediano earlier in the season. Puntarenas FC, on the other hand, are on a tough losing streak, with their latest defeat coming at the hands of Herediano with a score of 1:2. The odds for this match are set at 2.07 for a home win, 3.11 for a draw and 3.46 for an away win [Screenshot].
Applying the protocol, we calculate the attacking power for Liberia: $A_h = 0.20 (W) + 0.40 (L) + 1.00 (GF) = 1.60$. The defensive power is: $D_h = 1 / (0.20 – 0.40 + 1.20) = 1 / 1.0 = 1.0$. For Puntarenas FC, the attacking power is: $A_a = 0.00 (W) + 0.60 (L) + 0.60 (GF) = 1.20$, and the defensive power is: $D_a = 1 / (0.00 – 0.60 + 1.40) = 1 / 0.8 = 1.25$. These values lead to expected goals (xG) of 1.425 for the home team and 1.10 for the away team.
The Poisson distribution generates probabilities of 44% for Liberia, 27% for a draw and 29% for Puntarenas. The stability of the model ($K$) is calculated to be 0.38, which is a relatively low value indicating some volatility. The draw index ($L$) is 0.15. The final Harmony Index (HI) for this match is 6.44. This result classifies the match in the “High Risk” zone, as the value is below 7.50. The V3 verdict is $0.44 – 0.29 = 0.15$, which according to the algorithm corresponds to a prediction of “1” (Home win).
Match 2: LD Alajuelense vs CS Herediano
This is the derby of the round, pitting two of the most successful clubs in Costa Rican history against each other. Alajuelense, playing at their “Alejandro Morera Soto” stadium, has a capacity of nearly 19,000 spectators and is traditionally a strong home team. However, they come into the match after two consecutive draws, while Herediano is on a winning streak, interrupted only by one occasional loss. The odds reflect the home advantage: 1.96 against 3.85 for the away team [Screenshot].
The mathematical analysis for Alajuelense shows $A_h = 0.40 + 0.20 + 1.40 = 2.00$ and $D_h = 1 / (0.40 – 0.20 + 1.00) = 0.833$. For the leader Herediano the values are impressive: $A_a = 0.80 + 0.20 + 2.00 = 3.00$ and $D_a = 1 / (0.80 – 0.20 + 0.40) = 1.0$. Herediano’s high attacking power leads to an expected goal score of 1.917 for them as guests, while Alajuelense is expected to score 1.50 goals.
The Poisson probabilities are 28% for Alajuelense to win, 22% for a draw and 50% for Herediano. Here we see a significant discrepancy between the market odds and the mathematical model that favors the away team. The stability $K$ is 0.60 and the draw index $L$ is 0.833. The Harmony Index reaches 9.32. This places the match in the “Medium Risk” zone. The V3 verdict is $-0.22$, which strongly points to a win for the away team (“2”). This prediction is of high value, considering the odds of 3.85 for Herediano [Screenshot].
Match 3: CS Cartagines vs Municipal Perez Zeledon
Cartagines is enjoying a solid season, occupying second position, while Zeledon is the team that is the most difficult to beat, thanks to their four draws in five matches. Zeledon’s statistics are paradoxical – they have zero losses, but are in fifth place. Cartagines relies on a strong defense (only 3 goals conceded) and the home factor at the “José Rafael Fello Meza” stadium.
The calculations for Cartagines: $A_h = 0.60 + 0.20 + 1.00 = 1.80$ and $D_h = 1 / (0.60 – 0.20 + 0.60) = 1.0$. For Zeledon: $A_a = 0.20 + 0.00 + 1.60 = 1.80$ and $D_a = 1 / (0.20 – 0.00 + 1.20) = 0.714$. Here we notice a complete equality in the attacking power of the two teams, which is a strong indicator of a contested match. The expected goals are 1.257 for the home team and 1.40 for the away team.
The Poisson probabilities are almost evenly distributed: 33% for 1, 28% for X, and 39% for 2. The stability index $K$ is 0.23, and $L$ is 0.286. The Harmony Index is calculated to be 10.10, which is again “Medium risk”. Since the difference in probabilities $V3$ is only $-0.06$, the model predicts equality (“X”), falling within the range $[-0.08, 0.06]$ . The odds ratio for this outcome is 3.41 [Screenshot].
Match 4: Deportivo Saprissa vs AD San Carlos
Saprissa is Costa Rica’s most successful club, but their form at the start of the Clausura has been far from optimal. They have only one win and three draws, while San Carlos is in third place with three wins. However, the market continues to favor Saprissa with odds of 1.41, the lowest of the entire round [Screenshot]. This is often a trap for analysts if the mathematical filter is not applied.
The analysis for Saprissa: $A_h = 0.20 + 0.20 + 1.20 = 1.60$ and $D_h = 1 / (0.20 – 0.20 + 1.40) = 0.714$. For San Carlos: $A_a = 0.60 + 0.40 + 1.20 = 2.20$ and $D_a = 1 / (0.60 – 0.40 + 0.80) = 1.0$. San Carlos demonstrates higher attacking power, resulting in an xG of 1.457 versus 1.30 for the home team.
The Poisson probabilities are 33% (1), 27% (X) and 40% (2). The value of $V3$ is $-0.07$, which according to the formula again points to a draw (“X”). The stability $K$ is 0.27 and $L$ is 0.314, which generates a Harmony Index of 8.87. This match is classified as “Medium Risk”. The prediction of a draw at a market coefficient of 4.13 represents a serious opportunity for value analysis.
Match 5: Sporting FC vs. Guadalupe FC
This is a match between two teams at the bottom of the table, with Guadalupe FC having the worst defense in the league so far, conceding 10 goals in 5 matches. Sporting FC are not in much better shape, having scored only 2 goals since the start of the tournament. The odds for a home win are 1.56, which seems low considering their form [Screenshot].
Calculations for Sporting FC: $A_h = 1.20$ and $D_h = 1.25$. For Guadalupe FC: $A_a = 1.60$ and $D_a = 0.625$. Guadalupe’s extremely low defensive strength ($0.625$) is the key factor here. Expected goals are 0.913 for Sporting and 1.425 for Guadalupe.
The Poisson probabilities are 24% for 1, 27% for X and 49% for 2. The stability $K$ is 0.55 and $L$ is 0.225. The Harmony Index is 4.93, which is the lowest value for the entire round, placing the match in the “High Risk” category. The V3 verdict is $-0.25$, which is a strong signal for the away win (“2”). The market coefficient for Guadalupe is 5.46, which reflects the huge risk, but also the mathematical discrepancy in the bookmakers’ estimates [Screenshot].
Synthesis of results and strategic conclusions
The analysis of the 6th round of the Clausura in Costa Rica reveals several critical insights into the predictability of sports in this region. First, we notice the absence of “Platinum Selection” (HI > 100), which is explainable for the fifth-sixth round of the championship, where statistical accumulation has not yet reached the critical point of complete stability. Compared to examples from the English Premier League, where teams such as Manchester City often reach HIs above 100, in Costa Rica parity levels are significantly higher, which increases the overall risk.
Second, the mathematical model often contradicts the market odds, especially in the cases of Alajuelense and Saprissa. While the market relies on the historical reputation of these clubs, the statistics of the current form (GF, GA, W%) show deficits that the Poisson distribution immediately captures. This makes the matches of the “grandes” extremely volatile and places them in the zone of medium risk, despite the seemingly safe odds.
Third, the Harmony Index serves as an extremely valuable noise-filtering tool. Matches like Sporting FC vs. Guadalupe, which at first glance appear to be routine home wins, are revealed as high-risk statistical anomalies with a low HI (4.93). This protects analysts from “traps” where low odds are not supported by real defensive or offensive dominance.
Final Statistical Report and Verdict V3
The table below summarizes all calculations and provides the final prediction according to the requirements of the analysis protocol for Round 6. Each match is categorized according to the new risk zones based on the Harmony Index.
| Meeting (Home – Away) | Predicted goals (xG H – xG A) | Predicted outcome | Verdict V3 | Match Category (Risk) | Odds (Verdict) |
| Liberia – Puntarenas FC | 1.43 – 1.10 | 1 | 0.15 | High risk (HI: 6.44) | 2.07 |
| Alajuelense – Herediano | 1.50 – 1.92 | 2 | -0.22 | Medium risk (HI: 9.32) | 3.85 |
| Cartagines – Zeledon | 1.26 – 1.40 | X | -0.06 | Medium risk (HI: 10.10) | 3.41 |
| Saprissa – San Carlos | 1.30 – 1.46 | X | -0.07 | Medium risk (HI: 8.87) | 4.13 |
| Sporting FC – Guadalupe | 0.91 – 1.43 | 2 | -0.25 | High risk (HI: 4.93) | 5.46 |
This analysis highlights the importance of adhering to mathematical discipline. In a league like Costa Rica, where factors such as home advantage and climate are often exaggerated, statistical modeling using Poisson and Harmony Index provides the necessary objectivity. For the sixth round of the 2025-2026 Clausura, the strategy should be aimed at identifying value in medium-risk matches, such as the derby between Alajuelense and Herediano, where the model shows a significant advantage for the away team, inconsistent with the odds offered.
In the long term, regular application of this protocol will allow users to better understand the dynamics of model stability and focus on “Platinum Selections” as they emerge in the later stages of the season, when the data becomes even richer and more accurate. This report serves as a fundamental basis for informed decision-making based on pure mathematics and statistical rigor.
