Participants

The participants of this study were male artistic gymnasts who competed in the six apparatus finals events, namely floor exercise, pommel horse, still rings, vault, parallel bars, and horizontal bar, across three Olympic Games and nine World Championships held between 2013 and 2024 (a total of 12 competitions). Qualification for each apparatus final was granted to the top eight athletes in the respective qualification rounds, with a maximum of two gymnasts per country permitted to advance. In instances where the gymnast ranked ninth in the qualification round had the same D-score, E-score, and final score as the eighth-ranked gymnast, both were allowed to progress to the final. Consequently, some apparatus finals included a ninth competitor. In total, data were collected from 580 finalist appearances. All participants were senior male elite gymnasts who qualified for apparatus finals according to FIG regulations. Because the study relied on publicly available competition records, individual demographic variables such as exact age, educational background, and socioeconomic status were not accessible. Additional demographic and competition characteristics of the study sample are presented in S1 Table.

Data collection

Data were obtained from the apparatus finals of three Olympic Games, namely Rio 2016, Tokyo 2020, and Paris 2024, and nine World Championships in men’s artistic gymnastics. The years and locations of the World Championships are as follows: Antwerp (2013); Nanning (2014); Glasgow (2015); Montreal (2017); Doha (2018); Stuttgart (2019); Kitakyushu (2021); Liverpool (2022); and Antwerp (2023). Performance records for all apparatus finals were obtained from publicly accessible official competition records published on the FIG/World Gymnastics official results platform. The FIG Event IDs and direct URLs for all competitions included in this study are provided in S2 Table. On each official event page, the official result files can be accessed by clicking “Show Files” under “Event Files” and selecting the relevant official result files, such as results books, start lists, qualification results, final results, and related competition records.

Data processing

The official competition results from the 2016, 2020, and 2024 Olympic Games and the 2013–2023 World Championships included the start order, nationality, and final ranking of male gymnasts in each apparatus final. These data were directly used in the compilation and statistical analyses for this study. The data compilation procedure is as follows:

1. (1). The data entry sequence began with the three Olympic Games (2016 Rio, 2020 Tokyo, and 2024 Paris), followed by the World Championships in chronological order: 2013 (Antwerp), 2014 (Nanning), 2015 (Glasgow), 2017 (Montreal), 2018 (Doha), 2019 (Stuttgart), 2021 (Kitakyushu), 2022 (Liverpool), and 2023 (Antwerp).
2. (2). Data for the apparatus events were recorded in the following order: floor exercise, pommel horse, still rings, vault, parallel bars, and horizontal bar.
3. (3). The following information was recorded for each apparatus final: start order, country represented, final ranking, D-score, E-score, and total score. Data for each final were compiled beginning with the first-place gymnast, followed sequentially through to the last-ranked finalist. All data were entered into Microsoft Excel 2016 (Microsoft Corp., Redmond, WA, USA).
4. (4). After entry, each gymnast’s data, including start order, country, final ranking, D-score, E-score, and total score, were cross-checked against the information published on the official website to ensure accuracy before proceeding to enter the data of the next gymnast. In the vault final, each gymnast performed two different vaults, each receiving its own D-score, E-score, and final score. The D-scores and E-scores from the two vaults were averaged separately, and the final score was defined as the average of the two vault scores.
5. (5). Upon verifying the accuracy of all gymnast data for a given apparatus and competition, the same cross-checking procedure was repeated for the next apparatus. This process was applied consistently across all events and competitions.
6. (6). Once all data were recorded, gymnasts were grouped in accordance with start order: athletes who performed in orders 1–4 were categorized as the “first-half group,” and those in orders 5–8 (or 5–9 when applicable) comprised the “second-half group.” Examining the distribution of finalists’ national affiliations (Table 1) revealed that athletes from European countries constituted the largest proportion (n = 281), followed by Asia (n = 195), the Americas (n = 100), Oceania (n = 4), and Africa (n = 0). Accordingly, the dataset was divided into two geographic groups, namely the European and non-European groups, with all European nations classified as the former and all Asian, American, Oceanian, and African countries classified as the latter.

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Table 1. Distribution of finalists’ national affiliations by apparatus.

https://doi.org/10.1371/journal.pone.0351760.t001

Data analyses

After data collection and processing were completed, statistical analyses were conducted using SPSS Statistics 24.0 for Windows (IBM Corp., Armonk, NY, USA). To comprehensively examine the effect of start order, both ordinal-based analyses and grouping-based analyses were performed.

1. (1). Spearman’s rank-order correlation and Kendall’s tau-b correlation analyses were conducted to examine the relationships between start order (positions 1–8 or 1–9 in the case of ties) and final rankings across apparatus finals.
2. (2). Binary logistic regression analyses were performed to examine the association between start order and medal outcomes (medaled vs. nonmedaled) for each apparatus. Odds ratios (Exp(B)) and their corresponding 95% confidence intervals were reported.
3. (3). The Mann–Whitney U test (nonparametric) was used to compare the final ranking distribution between the two start-order groups for each apparatus each year, namely floor exercise, pommel horse, still rings, vault, parallel bars, and horizontal bar. The rank-biserial correlation (r_rb) was used to indicate effect size, which ranged from −1–1; larger values indicate greater effect sizes.
4. (4). Chi-square tests were used to examine the association between start-order grouping and medal outcomes (medaled vs. nonmedaled) for athletes in each apparatus final. Cramér’s V was used to indicate effect size.
5. (5). Independent-samples t tests were conducted to compare D-scores, E-scores, and total scores in the two start-order groups for each apparatus. Cohen’s d was used to indicate effect size.
6. (6). Chi-square tests were also used to compare the association between start-order grouping and medal outcomes among European and non-European athletes across all six apparatus events. Cramér’s V was used to indicate effect size. In addition to testing for statistical significance, this study also reported effect sizes to assess the magnitude of practical effects. The level of statistical significance was set at α = 0.05.

Ethical considerations

This study was based exclusively on publicly available official competition results published on the FIG/World Gymnastics official results platform. The data included only competition-related variables, such as start order, final ranking, D-score, E-score, final score, apparatus, competition year, nationality, and medal outcome. No private, confidential, nonpublic, or personally sensitive information was collected or analyzed. Therefore, institutional ethical approval and informed consent were not required.

Associations between start order and final rankings and medal outcomes across apparatus finals

As shown in Table 2, no significant associations were observed between start order and either final rankings or medal outcomes across all apparatus. Kendall’s tau-b and Spearman’s rho indicated no ordinal relationships (all p > 0.05). However, in the parallel bars event, although the association did not reach statistical significance, the results approached the threshold of significance (Spearman’s ρ = 0.194, p = 0.057), suggesting a potential trend. Logistic regression analyses further indicated that start order was not significantly associated with medal attainment (all p > 0.05).

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Table 2. Associations between start order and final rankings and medal outcomes.

https://doi.org/10.1371/journal.pone.0351760.t002

Effects of start-order grouping on final rankings across apparatuses

No significant differences in rankings were observed between the two start-order groups in any of the six apparatus finals (Fig 1); p values were 0.400 for floor exercise, 0.081 for pommel horse, 0.184 for still rings, 0.929 for vault, 0.075 for parallel bars, and 0.122 for horizontal bar. Accordingly, the final rankings of gymnasts in apparatus finals of the 12 competitions were generally not affected by start-order grouping. As shown in Fig 1, no significant differences were observed between start-order groups and ranking performance in floor exercise (p = 0.398, r_rb = 0.09), pommel horse (p = 0.081, r_rb = 0.21), still rings (p = 0.184, r_rb = 0.16), vault (p = 0.929, r_rb = 0.01), parallel bars (p = 0.075, r_rb = 0.20), and horizontal bar (p = 0.122, r_rb = 0.18). The median rankings and interquartile ranges for each apparatus are presented in Fig 1. Overall, effect sizes ranged from 0.01 to 0.21 across apparatuses (i.e., from negligible to small effects). These findings indicate that final rankings across the 12 apparatus finals included in this study were minimally influenced by start-order grouping.

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Fig 1. Comparison of final ranking distributions between start-order groups across six apparatus finals.

Note. Box-and-whisker plots illustrate the distribution of final rankings for the first-half and second-half groups across six apparatus finals: (A) floor exercise, (B) pommel horse, (C) still rings, (D) vault, (E) parallel bars, and (F) horizontal bar. Boxes represent the interquartile range (Q1–Q3), the horizontal line within each box indicates the median, and whiskers denote the minimum and maximum values. No significant differences were observed between the two groups across all apparatus (p > 0.05).

https://doi.org/10.1371/journal.pone.0351760.g001

Medal outcomes by start-order grouping across apparatuses

As shown in Table 3, Chi-square tests were conducted to examine the association between start-order grouping and medal attainment across the six apparatus events (i.e., floor exercise, pommel horse, still rings, vault, parallel bars, and horizontal bar). A significant association was observed only in the pommel horse event (χ²(1) = 4.096, p = 0.043, Cramér’s V = 0.205). Specifically, in the pommel horse final, athletes in the first-half group recorded 13 medal-winning performances and 35 nonmedaled performances, whereas those in the second-half group recorded 23 medal-winning performances and 26 nonmedaled performances, showing a higher proportion of medal attainment among athletes competing in the second-half. However, the effect size (Cramér’s V = 0.205) did not reach the threshold for a medium effect, suggesting that although the association was significant, its practical magnitude was limited. No significant associations were found for floor exercise (χ²(1) = 0.024, p = 0.878, Cramér’s V = 0.016), still rings (χ²(1) = 2.844, p = 0.092, Cramér’s V = 0.208), vault (χ²(1) = 0.178, p = 0.673, Cramér’s V = 0.043), parallel bars (χ²(1) = 0.248, p = 0.618, Cramér’s V = 0.051), or horizontal bar (χ²(1) =1.099, p = 0.294, Cramér’s V = 0.107). The corresponding effect sizes were predominantly negligible to small, indicating a generally weak association between start-order grouping and medal outcomes.

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Table 3. Association between start-order grouping and medal outcomes in men’s apparatus finals.

https://doi.org/10.1371/journal.pone.0351760.t003

As shown in Table 4, among the men’s apparatus finals, a significant difference in E-score was observed only in the pommel horse event. Specifically, the mean E-score was significantly higher in the second-half group (8.41 ± 0.59) than in the first-half group (8.07 ± 0.79; p = 0.017). However, the effect size (Cohen’s d ≈ 0.49) did not reach the threshold for a large effect, indicating that although the difference was significant, its practical magnitude was limited. By contrast, no significant differences were found in D-scores (first-half: 6.50 ± 0.42 vs. second-half: 6.49 ± 0.36, p = 0.918) or total scores (first-half: 14.57 ± 1.07 vs. second-half: 14.90 ± 0.81, p = 0.089). These results indicate that athletes in the two start-order groups exhibited similar performance in terms of D-scores and total scores in the pommel horse final. Although the difference in total scores did not reach significance, the p value was close to the significance threshold (p = 0.089).

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Table 4. D-scores, E-scores, and total scores stratified by start-order group for each apparatus event.

https://doi.org/10.1371/journal.pone.0351760.t004

In the remaining five apparatus finals, namely floor exercise, still rings, vault, parallel bars, and horizontal bar, no significant differences were observed between the first-half and second-half groups in D-score, E-score, or total score. For floor exercise, the D-scores were 6.41 ± 0.36 for the first-half group and 6.42 ± 0.43 for the second-half group (p = 0.966); the E-scores were 8.29 ± 0.49 and 8.28 ± 0.49, respectively (p = 0.956); and the total scores were 14.70 ± 0.65 and 14.70 ± 0.70, respectively (p = 0.988). For still rings, the D-scores were 6.45 ± 0.32 for the first-half group and 6.40 ± 0.31 for the second-half group (p = 0.477); the E-scores were 8.59 ± 0.40 and 8.65 ± 0.24, respectively (p = 0.371); and the total scores were 15.04 ± 0.55 and 15.05 ± 0.42, respectively (p = 0.890). For vault, the D-scores were 5.75 ± 0.31 for the first-half group and 5.71 ± 0.29 for the second-half group (p = 0.492); the E-scores were 9.02 ± 0.37 and 9.02 ± 0.35, respectively (p = 0.995); and the total scores were 14.77 ± 0.40 and 14.71 ± 0.51, respectively (p = 0.574). In the parallel bars event, the D-scores were 6.61 ± 0.32 for the first-half group and 6.48 ± 0.37 for the second-half group (p = 0.067); the E-scores were 8.53 ± 0.60 and 8.50 ± 0.59, respectively (p = 0.755); and the total scores were 15.14 ± 0.73 and 14.97 ± 0.84, respectively (p = 0.299). For horizontal bar, the D-scores were 6.45 ± 0.53 for the first-half group and 6.32 ± 0.58 for the second-half group (p = 0.259); the E-scores were 7.96 ± 0.66 and 7.85 ± 0.78, respectively (p = 0.490); and the total scores were 14.41 ± 0.95 and 14.18 ± 1.17, respectively (p = 0.289). These results revealed that start-order grouping had limited effects on the performance outcomes in these apparatus events.

Association between start-order grouping and medal outcomes among European and non-European athletes

As shown in Table 5, Chi-square tests were conducted to examine the association between start-order grouping and medal attainment among European and non-European male gymnasts in apparatus finals. The results indicated no significant differences in floor exercise (χ²(1) = 2.857, p = 0.091, Cramér’s V = 0.282), pommel horse (χ²(1) = 1.541, p = 0.214, Cramér’s V = 0.207), still rings (χ²(1) = 0.286, p = 0.593, Cramér’s V = 0.089), vault (χ²(1) = 0.111, p = 0.738, Cramér’s V = 0.056), parallel bars (χ²(1) = 0.003, p = 0.955, Cramér’s V = 0.009), and horizontal bar (χ²(1) = 0.711, p = 0.399, Cramér’s V = 0.139), with all p values exceeding 0.05. In terms of effect size, Cramér’s V ranged from 0.009 to 0.282 across apparatuses, signifying small-to-moderate effects. These findings suggest that start-order grouping did not clearly influence medaling outcomes for either European or non-European athletes.

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Table 5. Association between start-order grouping and medal outcomes among European and Non-European athletes.

https://doi.org/10.1371/journal.pone.0351760.t005

Effects of start-order on final rankings

As shown in Table 2, correlation analyses indicated that start order was not significantly associated with final rankings across any apparatus, suggesting that start order did not exert a clear influence on gymnasts’ final placements in apparatus finals. Further analyses examining the relationship between different start-order groups and final rankings demonstrated that the nonparametric tests revealed no significant differences in final rankings between start-order groups across all six apparatus finals (Fig 1). In addition, the effect sizes (r_rb) across apparatuses ranged from −0.010 to 0.208 (i.e., from negligible to small). This indicated that start-order differences exerted limited influence on final rankings in men’s artistic gymnastics apparatus finals. Rotthoff [6] reported that in women’s artistic gymnastics apparatus finals, athletes performing later in the start order achieved significantly higher E-scores; specifically, each subsequent start position was associated with an average increase of approximately 0.01 to 0.03 points in E-score. This finding suggests that scores are positively correlated with start order. Pizzera [9] noted that in aesthetic sports, scoring decisions may be influenced by the cognitive biases of judges and the performances of preceding athletes, such that evaluations are not based entirely on objective criteria. Suominen [10] further stated that in high-level artistic gymnastics competitions, even minimal score differences may alter final rankings. Overall, the research suggests that start order indirectly affects final rankings by influencing scoring outcomes. However, the present study found no significant association between start order and final rankings in men’s artistic gymnastics. Joustra et al. [11] obtained similar findings, reporting no overall order effects in men’s events. Rotthoff [12] remarked that substantial differences exist between men’s and women’s artistic gymnastics in terms of scoring systems, particularly with respect to artistic evaluation. In addition to technical elements, women’s artistic gymnastics includes artistic components such as rhythm, musical interpretation, and choreography, rendering the scoring process more subjective. Men’s artistic gymnastics places greater emphasis on technical difficulty and execution quality [2,13]. Given differences in scoring criteria and the random assignment of start order by draw in apparatus finals, the influence of start order on final rankings in men’s artistic gymnastics is likely to be relatively limited.

Relationship between start-order and medal outcomes

As shown in Table 2, logistic regression analyses indicated that start order was not significantly associated with medal outcomes across any apparatus, suggesting that start order did not exert a significant influence on medal attainment. Further analyses comparing medal outcomes between different start-order groups revealed that gymnasts competing in the second-half group won significantly more medals than those in the first-half group did in the pommel horse final (Table 3). Furthermore, the average E-score of gymnasts in the second-half group was significantly higher than that of their first-half counterparts (Table 4). These results may reflect a relative advantage for athletes in the second-half group in terms of execution performance. However, because the effect size did not reach the threshold for a large effect, the magnitude of this influence appears to be limited. Prassas et al. [14] informed that pommel horse requires athletes to maintain balance under dynamic conditions while executing skills, making the apparatus one of the most technically demanding in men’s artistic gymnastics. During pommel horse routines, gymnasts are required to perform continuous circular movements (with legs together or straddled) on the apparatus. These movements involve rotation of the body’s center of mass around the support point and rotation about both the vertical and longitudinal axes. Consequently, even minor deviations in movement can lead to a loss of balance or a fall [15]. In accordance with the Code of Points, point deductions are required for hitting the apparatus, pausing during a routine, or falling [2]. A single major fault, such as a prolonged pause, fall, or strong collision with the apparatus, can eliminate a gymnast’s chance of medaling. Kalinski et al. [16] noted that when athletes have similar D-scores, the E-score becomes the deciding factor affecting the final score. Therefore, athletes in the second-half group may demonstrate greater routine stability and higher success rates, resulting in superior E-scores that may be associated with a higher frequency of medal attainment. However, because the effect size did not reach a moderate level, the practical significance of this association remains limited. Taken together, these findings suggest that although a clear association between start-order grouping and medal outcomes exists in the pommel horse event, start-order grouping does not exert a substantial influence on rankings or score composition in the floor exercise, still rings, vault, parallel bars, or horizontal bar events. Cervin [17] argued that the 2006 revision of the International Code of Points, which separated the D-score and E-score, increased the competitive advantage of athletes performing higher-difficulty routines. Increasing the D-score is a key strategy for athletes to improve their final scores in each apparatus, and the overall score is closely associated with medal attainment [18]. Chen et al. [19] investigated whether increasing the D-score in apparatus finals improves an athlete’s chance of earning a medal, finding that this approach was particularly effective in the pommel horse and horizontal bar events. Overall, the findings from relevant studies may inform the development of routine composition strategies and the strategic use of start order across different apparatus events to improve medaling outcomes.

Furthermore, different statistical approaches may vary in their sensitivity to detecting start-order effects. Analyses that preserve the ordinal nature of start order are more suitable for capturing overall trends, whereas grouping approaches may better reflect structural differences under specific competition formats. Therefore, future studies are encouraged to consider both original start-order positions and grouping strategies to provide a more comprehensive understanding of start-order effects on performance outcomes.

Relationship between start-order grouping and medal outcomes among European and Non-European athletes

As shown in Table 5, no significant differences were observed in medal outcomes between European and non-European athletes across start-order groups in the apparatus finals for floor exercise, pommel horse, still rings, vault, parallel bars, or horizontal bar. These findings indicate that medal attainment did not differ meaningfully between European and non-European finalists across different start-order groupings. Another study highlighted that judges may assign higher scores to athletes from their own country [7]. In addition, research has shown that the extent of national bias may vary among judges from different countries, indicating that scoring may be influenced by national or regional factors. However, across the 12 competitions analyzed in this study, no significant differences were observed in medal outcomes between European and non-European athletes across start-order groups. Sandberg [20] reported that judging decisions may be influenced by multiple sources of bias, including national bias. Other studies have maintained that the magnitude of such biases is generally limited and can be mitigated through the design of scoring systems and the implementation of judge monitoring mechanisms [21]. The scoring rules for men’s artistic gymnastics are revised following each Olympic cycle [2]. Notably, several judging controversies during the 2004 Athens Olympic Games prompted the FIG to implement substantial reforms to the scoring system, including the abolition of the traditional “perfect 10” system in 2006, with the aim of enhancing fairness and transparency [22]. Furthermore, adjustments to the composition of judging panels—such as excluding judges of the same nationality as the competing athlete or ensuring balanced national representation—may help reduce direct scoring bias [8]. With advances in technology, the FIG has also introduced the Computerised Gymnastics Judging Support System, which incorporates artificial intelligence and motion analysis techniques to assist judges in evaluating performance, thereby improving the objectivity and consistency of scoring [23]. Accordingly, revisions to scoring regulations, adjustments to judging panel composition, and the integration of technological support systems may collectively contribute to reducing bias among judges and enhancing overall scoring consistency.

Limitations

This study has several limitations. First, according to FIG regulations, only eight athletes are permitted to advance to each apparatus final. Therefore, the sample size available for analyses within each individual competition was inherently limited. Although the present study included all available data from men’s artistic gymnastics apparatus finals at the Gymnastics World Championships and Olympic Games between 2013 and 2024, the overall sample size remained restricted by the design of finalist participation. Second, this study primarily analyzed final rankings, medal outcomes, and score performance. The study did not incorporate individual judges’ scoring data. As a result, directly examining judging bias at the individual judge level was not feasible. Third, the scoring rules for men’s artistic gymnastics are revised after each 4-year Olympic cycle. Because this study spans multiple cycles, the various versions of the Code of Points may involve different difficulty values and deduction criteria. This study did not differentiate between Olympic cycles. Future research could conduct more fine-grained comparative analyses across different Olympic cycles to better understand how changes in scoring regulations influence competition outcomes.