While gymnastics does not conform to an offense-defense structure like basketball or football, opportunities do remain for strategic decision-making. One area of particular interest for college teams is lineup construction–selecting the right six gymnasts and sorting them in the right order to best optimize the event total on the day.
As with strategic questions in other sports, there are different schools of thought regarding lineup decisions. For instance, teams may arrange their gymnasts in terms of ascending scoring potential to save their best gymnasts for last or adopt the so-called ‘Bridgeying’ technique (explained in this article). In either case, teams work off the widely-held belief that scores build over the course of a rotation.
But do scores truly rise across lineups? How exactly have teams approached lineup decisions? And finally, what relationship, if any, does a team’s lineup decision have with scores? In this Data Deep Dive, we look at data from the 2023 and 2024 seasons in search of answers.
Data Overview
As no source for consolidated lineup information was readily available, we collected the data manually from official score sheets, supplementing it with information from additional sources such as live score pages and meet videos where necessary. Even so, lineup data could not be reliably constructed for a handful of meets, which are thus excluded from this analysis. At meets where teams did not compete enough gymnasts for a team score (i.e., at least five gymnasts per event), that information was excluded.
Early Impressions
Once the data had been compiled, we began our exploration by looking at the median and interquartile range (IQR)* of scores by lineup position. These statistics appear to confirm the common assumption of scores building, since median scores were generally higher for positions later in a lineup. Moreover, IQRs generally decreased over a rotation, indicating that the scores that anchor gymnasts were given across a season tended to be bunched more closely than those of lead-off gymnasts.
*IQR is a measure of the spread of a set of values, calculated as the difference between the 25th percentile (i.e., the value that is higher than 25% of the set of values) and 75th percentile.
Moving from measures of center and spread to understanding the shape of the distribution as a whole, the following chart visualizes scores given to hit routines (i.e., scoring 9.500 or higher) by lineup position. The width of the pink area indicates the frequency at which the score occurred for the given lineup position. For example, the most frequent score for hit lead-off routines on vault was about 9.750. Of note, this chart suggests that routines earlier in a rotation have a lower maximum score–the highest score notched by a lead-off performer in the last two seasons has been a 9.950 on vault and a 9.975 on each of the other events; no competitor in the second spot on vault, or in the second or third spot on floor, has achieved a perfect score.
To consider trends within a single lineup, we represented each lineup by a single line in the chart below. Darker lines indicate trends that are observed more frequently, and scores below 9.000 are omitted. Note that to achieve an apples-to-apples comparison–to avoid comparing gymnasts in the fifth of six spots with anchors of a five-person lineup, for example–we limited our analysis to full lineups (i.e., six gymnasts with non-zero scores) only. We applied this limitation throughout the rest of our analyses as well.
As shown, the most common trend is a gentle upward slope over the course of the lineup, seemingly in-line with the common assumption. Mid-lineup dips are likely explained by falls and major errors, a phenomenon which, unsurprisingly, occurs most frequently on beam.
Refining the Analysis
While the preliminary results above seem to confirm that scores build over the course of a rotation, we questioned if these findings would hold when controlling for different variables, such as the particular lineup or individual gymnast being studied. The refined analysis below investigates both of these control variables separately.
Analyzing Particular Lineups
Lineup Frequency Trends
Before studying the effect of lineup position on gymnasts in fixed sets of lineups, we looked at the frequency at which each lineup occurred. As the chart below indicates, on nearly every team and event more than six gymnasts competed scoring routines over the course of a season. In other words, most teams experimented not only with lineup order, but also with the set of gymnasts who composed the lineup, often having anywhere between one and four alternates. Notable exceptions include Ball State in 2023, where no alternates made lineups on bars, beam, or floor across all meets; and Alaska and Penn in 2024, where 12 gymnasts made the bars and beam lineups over the season.
Furthermore, the next chart shows the frequencies at which any given lineup–that is, a given set of gymnasts, arranged in a given order–was repeated. Each lineup is represented by a faint bar; a darker region indicates that more lineups were repeated with that frequency. As shown, many lineups serve an experimental role, staying in place for a single meet. In contrast, as represented by the faint but long tail on the right of each chart, a handful of teams had particularly stable lineups on certain events. For example, in the 2024 season:
- Minnesota never once changed its vault lineup across 14 meets.
- Oklahoma used the same lineup on bars in 14 of 16 meets, and California used the same lineup on beam in 16 of 17 meets. In both cases, there was a core group of five gymnasts that competed in every meet, in the same relative order, and a sixth gymnast who was replaced in one or two meets by an alternate, not necessarily in the same lineup spot.
- Illinois State put up the same floor lineup in 12 of 14 meets, and both meets in which the team experimented with different lineups occurred in January.
Moreover, for each season and event, each team had at most one ‘stable’ lineup–that is, a lineup which stayed in place for six or more meets across the season. In the next section, we analysed the performance of the gymnasts who comprised these stable lineups, to better understand trends in the lineups that teams repeated most frequently.
Ranking Stable Lineups
For our analysis of stable lineups, we studied how the median and IQR of scores achieved differed by lineup position. Median scores were ranked from 1 to 6, with 1 being the highest and 6 being the lowest. These ranks were then charted against the corresponding lineup positions, using a reversed vertical axis so that higher ranks appear towards the tops of the charts. Similar to the trend observed in the median scores calculated for each lineup position in the initial exploration, median scores generally increased with lineup position. One counter to this trend is the generally higher medians for lead-off performers as compared to gymnasts in the two-spot on beam which is due to the specifics of the event itself. Since beam is a nervy event, teams may opt to put a consistently-solid performer in the lead-off spot to start the team off on the right foot.
Turning to the spread of scores, the lowest IQR–which is suggestive of the gymnast with the most consistent scores–was ranked as 1 and the highest IQR was ranked as 6. As above, the chart below shows the ranks in reverse order. In this case, the trend observed in the initial exploration does not come across as strongly when zeroing in on stable lineups; no coherent trend of improving consistency across the lineup emerged. In fact, within stable lineups lead-off performers generally had an equal or smaller spread of scores than anchors, suggesting that lead-off reliability may be a motivating factor for coaches when solidifying lineups.
Analyzing Particular Gymnasts
When controlling for particular gymnasts, we were interested in gymnasts for whom sufficient data was available in multiple lineup positions, defined as gymnasts who competed at least five times each in two different lineup positions in a given season. Included among these gymnasts were those who only saw one lineup position change across the entire season, as well as those who frequently flip-flopped between their two lineup positions. The chart below visualizes the distribution of the number of lineup position changes on each event.
On all four events, gymnasts who competed in one lineup position for the first chunk of the season, made one switch, then stayed in their new lineup position throughout the rest of the season were most common. This was particularly the case on bars, where over half of the gymnasts with substantial experience in two lineup positions followed this pattern. We focused the rest of our analysis on this group of gymnasts.
To understand potential motivations for this change in lineup positions, we studied the direction of the change (earlier, for instance from the three-spot to the two-spot, or later) and each gymnast’s performance before and after it. For ease of comparison, we quantified performance as follows: we ranked each gymnast’s score within their team for each relevant meet. Next, these ranks were translated into ‘implied’ lineup positions when operating under the assumption that scores build over a rotation–the highest score on the team would have an implied lineup position of six. We then took the median of these implied ranks over the course of the season, and classified gymnasts as underperforming, performing as expected, or overperforming if the median was lower than, equal to, or higher than their actual lineup position respectively.
From the table above, gymnasts who were initially underperforming or performing as expected were moved earlier in the lineup more often than later. In these instances, they commonly went on to outperform their new lineup positions. One particularly noteworthy example is Jaly Jones, who anchored the beam lineup for Lindenwood to open the 2024 season, then moved earlier in the lineup to the fourth spot for the next six meets, and yet earlier to the third spot for the last six meets. Comparing her two main lineup positions, her performance was markedly improved after moving earlier in the lineup by one spot, in both relative and absolute terms. Whereas she underperformed in the fourth lineup spot with a median implied lineup position of 2.5, she overperformed in the third, with a median implied lineup position of 5.0. Moreover, the median of her scores increased from 9.650 to 9.788.
On the other hand, gymnasts who were initially outperforming were moved later in the lineup (47) more often than earlier (31), perhaps in recognition of their strong performance. However, these moves had mixed results, with gymnasts spread across underperforming, performing as expected, and outperforming their new lineup positions. In contrast, the gymnasts who were moved earlier in the lineups overwhelmingly continued to outperform their lineup positions, even after moving.
To get a sense of the magnitude of these changes, we looked at the change in implied lineup position against that in the actual lineup position. In the chart below, the size of each point encodes the number of gymnasts with the corresponding pair of change values. Note that the largest point corresponds to a change in actual lineup position of -1 and a change in implied lineup position of 0–that is, gymnasts who moved one position earlier in the lineup, but saw no change in the median rank of their score within their team.
Together, these findings suggest that moving a gymnast earlier in a lineup may not have a negative impact on their performance. Instead, gymnasts may continue to rank similarly (relative to their teammates) even after being moved earlier, potentially due to having established a preconception of their rank based on past achievements.
Conclusion
Based on the findings above, there does appear to be some merit in the assumption that scores build over the course of the rotation. However, it should be noted that the correlation between a later lineup position and a higher score is not indicative of causation–that is, a later position does not necessarily cause a higher score. Instead, we have a chicken and egg problem, especially since the assumption that scores build has been widely-held for quite some time. It is possible that gymnasts are scored better in alignment with the common assumption due to their position later in the lineup, but it is also possible that coaches place gymnasts later in the lineup because they are notching higher scores.
Additionally, our analysis showed there are certain situations in which the common assumption may not hold as strongly (e.g., on beam, where having a solid lead-off may be more important than having scoring potential strictly rise from one lineup position to another), particularly when controlling for particular lineups or gymnasts. That said, the controlled analyses may have been subject to selection bias–for example, if there was a confounding factor among gymnasts who switched lineup positions, which would make the analysis controlled for particular gymnasts unique to such gymnasts, rather than generally applicable.
Lastly, our analysis was based on data from the 2023 and 2024 seasons only. To the extent that lineup strategies have and continue to evolve, the results above may not be indicative of the relationship between lineup positions and scores in the past, particularly at the inception of the common assumption of rising scores.
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Article by Dara Tan
