The Apperent Negative Associations Between Early and Adult Performance in elite performers Arise from Colider Selection Bias and Baserate Neglect

The Apperent Negative Associations Between Early and Adult Performance in elite performers Arise from Colider Selection Bias and Baserate Neglect Michel Nivard Güllich et al. argue that among elite performers there is a negative association between early and adult performance, a pattern they link to distinct developmental causal mechanisms for early, and adult elite performance. Using simple simulations, we show that this pattern arises naturally from collider bias when selection into elite samples depends on both early and adult performance, and/or from other biases like base rate neglect. We then revisit the data leveraged by Güllich et al. and highlight how in numerous instances early and late peak performance are highly positively correlated. While associations estimated within elite samples are descriptively accurate for the selected population, they are causally misleading, and should not be relied on to infer developmental mechanisms of elite performance without explicit modeling of the selection processm, accounting for base-rates and minding other statistical biases. Güllich et al.(Güllich et al. 2025) recently review the causal mechanisms by which the most exceptional (academic, athletic, professional) talent arises. Based on their reading of the literature, they conclude that: “Across the highest adult performance levels, peak performance is negatively correlated with early performance.” This observation is likely explained by collider bias, also known as Berkson’s paradox, a wellknown but frequently misunderstood bias in epidemiology and the social sciences(Griffith et al. 2020; Holmberg and Andersen 2022; Cole et al. 2009; Munafò et al. 2017) and base rate neglect. If selection into a sample (here: elite performers) is caused by both the exposure (early performance) and the outcome (adult performance), conditioning on that selection induces a 1 spurious negative association, even when early performance and adult performance are highly positively correlated in the population. Furthermore the analysis of small elite groups of individuals, risks base rate neglect. Consider how Güllich et al.(Güllich et al. 2025) report only 8% of people in the top 5% of income bracket are people from elite high-schools. The underlying references reports that the 1.3% of pupils are at elite high-schools (Tatler) and they later form 9.5% of the top 5% earners, an incredible 7 fold enrichtment over the expected number, in fact 37% of Tatler elite high-school pupils are in the top 5% earners(Sullivan et al. 2018). We will first briefly outline simulation to make the process of collider bias more intuitive, and then review the data used by Güllich et al.(Güllich et al. 2025) for signs of collider bias and base rate neglect. Collider bias We simulate a data-generating process in which early and adult performance share a common latent cause (i.e. talents, training, opportunities, social and psychological support) and both early and adult performance contribute to selection into an elite group of athletes use for analysis. −5.0 −2.5 0.0 2.5 5.0 −2.5 0.0 2.5 5.0 Early performance Adult performance Figure 1: Relationship between early and adult performance in the full population (black) and elite performers (red). Conditioning on elite status induces a negative association despite a positive population relationship. 2 It becomes clear from Figure 1 that although early and adult performance are positively related in the population, conditioning on elite status reverses the association. The negative slope among elite performers is therefore not evidence against a causal role of early performance; it is the mechanical consequence of selection. The implications extend beyond bivariate associations. Whenw e further five causal variables contribute equally to early and adult performance the bias persists to the effects of these variables on performance in the selected sample. In the full population, the effects are recovered accurately. In the selected (elite) sample, however, estimation is strongly attenuated, and severely biased and may even suggest opposite effects on early versus adult performance. Given the risk of bias the analysis Güllich et al.(Güllich et al. 2025) perform to elucidate the (seemingly distinct) causes of early and late elite performance cannot be interpreted mechanistically. The analysis requires a formal model that fully accounts for selection. Table 1: True and estimated covariate effects in the presence of simulated collider bias in the full and selected samples Whole sample Selected sample Early Adult Early Adult Covariate True � SE � SE � SE � SE X1 0.3 0.300 0.005 0.297 0.005 0.092 0.028 0.044 0.027 X2 0.3 0.290 0.005 0.295 0.005 -0.013 0.028 0.032 0.027 X3 0.3 0.297 0.005 0.301 0.005 0.075 0.031 -0.006 0.029 X4 0.3 0.299 0.005 0.293 0.005 0.055 0.031 0.039 0.029 X5 0.3 0.299 0.005 0.300 0.005 0.000 0.029 0.047 0.028 Results of the multivariate simulation are presented in Table 1, these clearly reveal that while estimates in the full population are unbiased, conditioning on elite status produces attenuated, unstable, and even sign-reversed estimates of the effects of causes of performance. This is not a failure of measurement or modeling, but a direct consequence of selection on a collider. In the presence of collider bias the negative associations between early and adult performance among elite performers are descriptively correct but causally uninformative. Interpreting such patterns as evidence for distinct developmental processes for early and adult skill acquisition is therefore unwarranted. Any attempt to infer causal mechanisms within selected elite samples must explicitly model the selection process—or risk mistaking bias for insight. re-evaluation of emperical results presented by Güllich et al.(Güllich et al. 2025) Acedemic 3 The academic samples considered in Güllich et al.(Güllich et al. 2025) concern pupils in highly sleected highschools and colleges. They clearly note that elite schools are at best proxies for performance, but go on to claim the following: “Even using proxies, combining longitudinal prospective and retrospective analyses demonstrates that early and later exceptional performers are largely discrete population” Below in Table 2 we reproduce data from Sullivan et al. (Sullivan et al. 2018) on top earners and University “quality” where STEM is an acronym for Science, Technology, Engineering, and Mathematics, and LEM an acronym for Law, Econimics and Management. In total 29.8% of top 5% earners went to elite universities in this UK sample and among those elite graduates 17.4 to 31.7% goes on to be among the top 5% of earners at age 42. These data are entirely consistent with long standing observations on social and professional stratification and income inequality across educational backgrounds. Table 2: Degree status distribution and income Degree status Share (%) Share OF top 5% income Share IN top 5% income No degree 75.6 33.7 2.3 OSSAH, ordinary uni 8.7 8.9 5.2 STEM, ordinary uni 4.8 13.0 13.8 LEM, ordinary uni 3.7 14.6 20.5 OSSAH, elite uni 3.6 12.1 17.4 STEM, elite uni 2.7 11.7 22.2 LEM, elite uni 1.0 6.0 31.7 Similarly in Table 3 we see that more selective high schools (a poor proxy for abilities due to socio-economic stratification) is highly predictive of later income. The observation that most people in the top 5% income bracket were not in select schools is a function of a low base rate (very few people are in elite schools) not some individual level mechanism. Table 3: Secondary school type distribution and income Secondary school type Share (%) Share OF top 5% income Share IN top 5% income Comprehensive 81.0 61.9 3.9 Secondary modern 8.7 2.9 1.7 Grammar 4.3 9.5 11.4 Private (all schools) 6.0 25.7 22.3 Private (non-Tatler) 4.7 16.2 18.1 Private (Tatler) 1.3 9.5 37.0 4 These are some of the same data used in the article, while non of the claims made are false, theirpresented wihtout baserate. YEs among those in the top 5% of incomes at age 42 in the UK only ~9% are from elite highschools, but this i actually an astounding over representation as 1.3% of pupils in the study attend those elite highschools. Even if all pupils from elite highchools ended up in the top 5% of earners, they would at most comprise ~26% of top earners simply due to their low numbers, the low baserate. While both top 5% earning and elite highschools are poor proxies for elite cogntivie/profesisonal performance its reasonable to seek proxies. It also noteworthy that there is evidence cogntition plateu’s among the top earners based on swedish constription IQ data and tax data(Keuschnigg, Rijt, and Bol 2023). This is a process worth studying, but to conclude it is reflection of two distinct early and late developing processes overlooks alternative explanations. On inspection there is a clear and positive relation between early and late proxies of academic and career performance. While it is also true (due to low base rates) that highly selected pupils never compose a (somewhat wide) peak income bracket, this is entirely consistent with a strong positive relationship between early and late performance. Chess We proceed to analyze FIDE chess ranking data for the period between 2001 ans 2019 obtained online. based on ratings in months where a player played at least 1 game (as the results of games are the basis for updated ratings) and based on classical chess rating. We correlated the FIDE ratings of all players between the ages of 15 and 45. Retaining correlations based on at least 50 observations, we found that ratings were very highly correlated to later ratings across this 19 year span. We note this is a simplified analysis, Figure 2: correlations between age stratified chess ratings for all FIDE rated players 5 Whiile most players in the database rate over 2000, suggesting at minimum an expert level chess players, we can narrow our analysis to those who at any point became grand masters (> 2500). The correlations attentuate (as expected due to selection) but remain high if we select individuals who at some point attain a rating > 2500, the range of “Grand Master”. The correlations suggest that even in the presence of conditional selection, early and late performance are highly correlated. Figure 3: correlations between age stratified chess ratings for all FIDE rated players who at any point rate /> 2500 Arguably Güllich et al.(Güllich et al. 2025) would prefer to focus on even more extreme talents, as is their stated goal. So we the selected the top 100 players based on their max rating attained between the ages of ~15 and ~45 (based on birthyear and therefore the ages had somewhat fuzzy boundaries). We then compared the absolute best (1-25) to the contenders (26-100) as Güllich et al.(Güllich et al. 2025) do in their signature Figure. We chart the average ranking over time for these two groups in order to discern distinct early and late peaking patterns. 6 Figure 4: FIDE ELO ratings in months when at least 1 game was played for the top 100 players with the highest recorded ratings (includes players aged between 15 and 45 within the 2001 to 2019 window). Colors indicate top 25 and the contenders ranked 26-100. There is no evidence in Figure 4 that the group of absolute elites haven’t, on average, been ranked higher than the group of contenders from their early years onward. In this highly selected chess analysis correlations over development are attenuated. While there are salient individual exceptions, those do not negate the averages, which follow the inverse of the model proposed by the authors with peak performers leading in the early years. The analysis is cursory in that it ignores potential secular changes in chess development over birth cohorts (i.e. players professionalizing at younger ages) Conclusions Various biases, including selection on colliders and base-rate neglect, threaten the interpretation of groups of elite performers. A re-evaluation of some of the results and data considered by Güllich et al. [@güllich2025] highlights two key issues: (1) early and later performance are highly correlated, and (2) reporting the percentage overlap between two small populations neglects the influence of base rates. Güllich et al. [@güllich2025] study four key questions. First, 7 to what extent are early and later exceptional performers the same individuals across time? Their answer is essentially “not much.” However, based on some of the same data sources, the more accurate conclusion is that early performers are far more likely to become late performers than others; the two are strongly statistically linked. Especially in the context of elite education and later income, the examples they discuss are not direct measures of performance (as they themselves acknowledge). Concluding that elite schooling does not result in high income runs counter to decades of established sociological and economic literature.Second, did the world’s best performers already outperform their peers in their early years? Their conclusions and figures imply that this is not the case. Using FIDE chess ratings, we show that individuals who attain exceptional performance did, on average, perform better early on than those in the next-best performance group.Third, do predictors of early exceptional performance also predict later exceptional peak performance? The authors conclude that the causal factors differ. We believe that the risk of multiple statistical biases prevents a clear conclusion at this time. The very high correlations in chess ratings over time, even among grand masters, suggest that there are substantial shared causes. One of the leading causes of adult exceptional performance is very likely childhood elite performance, along with the advantages in training, guidance, opportunities, and supervision that accompany early elite status. Finally, the authors ask what factors predict the world’s best performers. Yet, as their own results show, even very strong correlates of peak performance (such as early performance) perform poorly when predicting exceedingly rare outcomes. Success in any domain has many partial contributory causes, none of which are individually strong; selection on the extreme all but guarantees a population in which there is no single shared common denominator. References Cole, Stephen R, Robert W Platt, Enrique F Schisterman, Haitao Chu, Daniel Westreich, David Richardson, and Charles Poole. 2009. “Illustrating Bias Due to Conditioning on a Collider.” International Journal of Epidemiology 39 (2): 417–20. https://doi.org/10.1093/ ije/dyp334. Griffith, Gareth J., Tim T. 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