Student Sociodemographic and School Type Differences in Teacher-Predicted vs. Achieved Grades for University Admission

In England, students apply to universities using teacher predicted grades instead of their final end-of-school A-level examination results. Predicted rather than achieved grades therefore inform how ambitiously students apply to and receive offers from the most selective courses. The Universities and Colleges Admissions Service (UCAS) encourage teachers to make optimistic predictions to motivate students to apply ambitiously and achieve higher grades. However, little is known about variations in optimism across students and schools, as well as the mechanisms behind such variations. If certain groups of students or schools are predicted more optimistically than others, this may distort application, offer, and acceptance rates between these groups. Such distortions have the potential to impact efforts to promote wider participation and enhance social mobility. In this study, we use newly linked administrative education data to show predicted grades are differentially optimistic by student sociodemographic and school characteristics. These variations are often substantial and can only be partially explained by differences in students’ prior achievements, the subjects they studied at A-level, the degree subjects they pursue, and their choices of university and courses. We find less educationally advantaged students are in general more rather than less optimistically predicted, although there are important exceptions to this trend. Our findings contribute to the growing consensus advocating for reforms to the admissions system, including whereby students can continue to revise their course choices until they receive their achieved grades, and universities only make offers after that date.


Introduction
In England, students submit their university applications for undergraduate courses with predicted grades provided by their teachers, rather than their final A-level exam results.
Consequently, teacher predicted grades play a crucial role in determining the level of ambition with which students apply for competitive courses and whether they are granted admission offers.The Universities and Colleges Admissions Service (UCAS) promotes the practice of teachers providing optimistic predictions to inspire students to pursue selective courses and attain better grades.An important concern is that certain students and schools might receive more optimistic predictions than others and that this might impact the way different students apply to, receive offers from, and ultimately enrol in the courses that best suit their needs.Murphy and Wyness (2020), for example, show that students predicted more optimistically, all else equal, are more likely to apply to more selective courses.Such distortions, would then have important implications for perceptions of fairness (Boliver, 2013), especially if they exacerbate the known underrepresentation of ethnic minority (Boliver, 2016;Noden et al., 2014;Shiner & Modood, 2002) and socioeconomically disadvantaged students in higher education (Boliver, 2017;Dilnot, 2018;Harrison, 2011;Gorard et al., 2019;Marginson, 2016), particularly at the most prestigious universities (Del Bono et al., 2022).If any distortions do play out in this way, they would work against efforts to promote widening participation (Archer & Hutchings, 2000;Chowdry et al., 2013;Greenbank, 2006;Harrison, 2011;Younger et al., 2019) and more fundamentally higher education as a championed route to increased social mobility (Blanden & Machin, 2013;Britton et al., 2021;Shiner & Noden, 2015).
In this study, we analyse recently linked administrative education data from the 2018/19 UCAS applicant cohort (the final cohort prior to .Our aim is to investigate and quantify the extent to which predicted grades exhibit varying degrees of optimism across student sociodemographic and school characteristics.Additionally, we seek to understand to what extent these disparities across groups can be attributed to differences in their GCSE prior achievements, A-level subject selections, chosen degree programs, universities, and courses.Our contribution is two-fold.Firstly, we present results based on a notably broader collection of student, school, and application data compared to prior studies. Secondly, we provide a comprehensive interpretation of these optimism variations, shed light on the potential mechanisms underpinning them, and propose solutions to mitigate these effects.Ofqual (2020), the exams regulator in England, reviewed previous studies comparing teacher predicted and achieved A-level grades (BIS, 2011(BIS, , 2013;;Delap, 1994;Murphy & Wyness, 2020;Shiner & Modood, 2002;UCAS, 2016).They conclude that optimism is higher for Black and some Asian subgroup students and is higher for more socioeconomically disadvantaged students, except perhaps among the highest achieving students.In contrast, Ofqual concludes that evidence is more mixed in terms of any age or gender effects, and while there are some effects of A-level subject and school type, they deem these effects small.

Previous research
Ofqual's review stresses the importance of exploring not just simple mean differences in optimism by each student sociodemographic characteristic, but to explore whether each mean difference persist once the influence of other variables is taken into account.The review notes that optimism decreases with increased achieved grade due to a ceiling effect in the A-level grade scale.The A-level grades are A*, A, B, C, D, E, U, where an A or higher is considered excellent, a C or higher is good, while a U is an unclassified or failed grade.Thus, while a B student could potentially be predicted two grades higher, an A student can only be predicted a maximum of one grade higher, and an A* student cannot be optimistically predicted at all: there is no A** grade.So, while it may seem fairest if all student groups are, on average, overpredicted by the same amount, for example, by 1 grade, the ceiling effect prevents this.Thus, mean optimism will, in general, be lower for higher achieving student groups.It is therefore important to move beyond simple mean differences to establish whether these differences persist after one has adjusted for the A-level scale ceiling effect and other potentially justifiable explanations for differences in optimism.Delap (1994), for example, shows that the ethnic group simple mean differences seen in their univariate analyses disappear once they control for achieved grades and other variables.In contrast, a gender effect, whereby mean optimism is higher for male versus female students, only becomes apparent upon control.
The subtle point alluded to above that among the highest achieving students, disadvantaged students are predicted slightly less optimistically than their more advantage peers was made by Murphy and Wyness (2020).They also show that among this subgroup, state school students received less optimistic predictions than their independent school peers.
They argue that these two distortions may be deterring high achieving disadvantaged students from applying to the most selective courses as their predicted grades are misinforming them as to their potential relative to more advantaged but similarly high achieving students.
A limitation with all previous studies and which will also apply to our study is that optimism is defined by comparing predicted to achieved grades, but achieved grades will to some extent be positively influenced by the degree of optimism applied to the predicted grades.Indeed, this influence is part of the motivation for encouraging optimistic predictions.
A preferable analysis might be to compare predicted grades to the grades that students are on track to achieve at the point predictions are made, but no such data is available.Interestingly, the above studies offer few explanations for differences in optimism beyond the A-level scale ceiling effect noted above.An exception is Murphy and Wyness (2020) who suggest three possibilities: teacher unconscious bias, differential growth in achievement over the last six-months of A-level studies, and differential effect of predicted grades on motivation and effort.A further explanation implicit in the advice that UCAS provide to teachers (UCAS, 2023b) is that predicted grades should not be "affected by student, parental, guardian, or carer pressure", or "influenced by university or college entry requirements or behaviours".Thus, it may additionally be the case that some student groups place more pressure on their teachers to predict high than other student groups or if certain student groups tend to apply to more selective courses than others, their teachers may respond to this difference by predicting them more optimistically than their peers to make sure they still have a good chance of receiving offers.

Background on UCAS
Most students apply to university via UCAS in their final year of secondary schooling (year 13, age 17/18), some six months before their end-of-school A-level examinations and some nine months before they intend to start their preferred courses.Given these constraints, students apply with teacher predicted grades for their three A-level subjects rather than the actual grades they go on to achieve.While students also submit their General Certificate of Secondary Education (GCSE) examination results (year 11, age 15/16), other student background data, a personal statement, and a school-provided written reference, predicted grades are nevertheless the main information provided on students' suitability for different courses.As a result, predicted grades play a crucial role in shaping students' selection of their five courses and the level of aspiration associated with these choices.These predicted grades then influence whether these chosen courses make offers, and subsequently, which offers students declare as their preferred "firm" offer (with typically higher entry requirements) and "insurance" offer (with typically lower entry requirements).This approach is taken with the anticipation that students accept their "firm" offer after their actual grades are revealed.In the 2018/19 cohort that is our focus, 34.1% of UK 18-year-olds entered university with 73.6% placed on their preferred course (UCAS, 2019).See UCAS (2023a) for further detail about the application process.
In their advice to teachers, UCAS (2023b) state that predicted grades should be "aspirational but achievable" or in other words the grades students are "likely to achieve in positive circumstances".Their argument is that "stretching predicted grades can be motivational for students" presumably as they increase students' chances of applying to and receiving offers from more selective courses with higher entry requirements and this in turn will lead students to work harder towards these higher grades.Thus, where students do fulfil their potential, they will be able to attend an appropriately selective course rather than having to reapply (via Clearing).UCAS, however, do not give any numerical guidance as to just how optimistic predictions should be, although they do warn that excessive optimism can disadvantage rather than advantage students as then "applicants may receive offers they are unlikely to meet" or may "gain admission to courses which they cannot succeed in".In 2018/19, 79% of accepted 18-year-olds missed their predicted grades (UCAS, 2019).

Data Source
The data are provided by the Grading and Admissions Data for England (GRADE) data sharing project, a joint open data initiative initiated between UCAS, Ofqual, and the Department for Education (DfE) in 2020 (GRADE, 2021).The first student-level linked data was made available via the Office for National Statistics (ONS) Secure Research Service (SRS) in spring 2022.The data contain student A-level results and university applications for the 2018/19 student cohort in England linked to their sociodemographic and school characteristics and their earlier GCSE qualifications.The data therefore do not include any mature or international students.They also do not include any non-A-level or non-GCSE qualifications.

Sample selection
The initial sample consists of 234,774 students from 2,772 schools with 531,294 Alevel qualifications.We make various sample restrictions leading to a final sample of 170,750 students from 2,490 schools with 465,723 A-level qualifications.The data contain one row per A-level subject per student.Most students apply with three A-level qualifications.

Variables
Predicted grades, achieved grades, and grade optimism Predicted and achieved A-level grades are letter grades to which we assign numeric values (A* = 6, A = 5, B = 4, C = 3, D = 2, E = 1, U = 0).We define grade optimism as predicted grade minus achieved grade.

Student sociodemographic characteristics
Student sociodemographic characteristics include gender, ethnicity, socioeconomic status (SES), and disability.Ethnicity includes six and 15 group versions.SES is captured via three measures: the national statistics socioeconomic classification (NS-SEC), the index of multiple deprivation (IMD), and the participation of local area (POLAR).NS-SEC is an ordinal measure of students' parents' employment status and occupation.IMD and POLAR are middle supper output area (MSOA) quintile measures of deprivation and the proportion of young people aged 18 or 19 who participate in higher education, respectively.MSOAs are mid-sized geographic areas used for reporting small area statistics.

School characteristics
School characteristics include region, county, type, and gender.Type distinguishes state schools (free) from independent schools (fee-paying).State schools are further distinguished into academies (relatively autonomous), grammar schools (which have entrance exams), and sixth form and further educational colleges (only teach students aged 16 and over).

Student GCSE prior achievement
Student GCSE prior achievement is a continuous point score derived by summing across each student's eight best GCSE examination grades (most students take eight to ten GCSEs).We categorize this into 25 quantiles.

A-level subject studied
We observe predicted and achieved grades across 32 subject areas.For some analyses we focus on so-called facilitating subjects: English literature, maths and further maths, biology, chemistry, physics, geography, history, modern languages, classical languages.
These subjects are traditionally the most asked for in course entry requirements to Russell Group universities (Russell Group, 2019), a self-selected association of 24 universities traditionally viewed as the most prestigious for students to attend.

Application characteristics
For each student, we observe the number of courses applied to, the predominant degree subject area applied to, the proportion of applications that are Russell Group applications, and whether an application was made to Oxbridge (University of Oxford or University of Cambridge, traditionally considered the two most elite institutions).

Methodology
Our interest lies in whether, how, and why grade optimism systematically varies by student sociodemographic and school characteristics and the extent to which any such differences can be understood in terms of the different GCSE prior achievement, A-level subject, and application characteristics of these student and school groups.
First, we describe the overall predicted grade, achieved grade, and grade optimism distributions.Next, we calculate mean optimism and show how this varies by each student sociodemographic and school characteristic in turn.Then, we shift to a series of linear regression models to explore how mean optimism by each characteristic changes as we increasingly statistically control for other characteristics.Model 1 replicates the unadjusted mean difference in optimism by regressing optimism on the characteristic of interest and so provides our baseline.Model 2 controls for student GCSE score and number of A-levels studied.Model 3 additionally controls for A-level subject studied.Model 4 adds in application characteristics (less than five applications, degree subject, number of Russell Group applications, applied to Oxbridge).Model 4 adds in other student sociodemographics (gender, ethnicity minor, NS-SEC, IMD, POLAR, disability).Model 6 adds in school characteristics (county, type, gender).Model 7 adds in school fixed-effects (FE) dummy variables.All models are estimated with school cluster robust standard errors.We present the results by plotting predicted mean optimism by each characteristic against model number.

Predicted Grades, Achieved Grades, and Grade Optimism
Figure 1 shows the predicted and achieved grade distributions.Predicted grades are optimistic: the predicted distribution is notably more concentrated in the highest A* and A grades relative to the achieved distribution.Teachers overpredict 60.7% of grades, accurately predict 31.8% of grades, and underpredict just 7.5% of grades.Almost one in four predicted grades (23.8%) are overpredicted by two or more grades.The optimism distribution (predicted minus achieved grade) is approximately symmetric with a mean of 0.84 grades per subject (SD = 1.05).Summing across three A-levels, students are therefore, on average, overpredicted by 2.52 grades.Thus, students who achieve, for instance, BBB are, on average, predicted AAB or AAA.Importantly, mean optimism will decrease as a function of achieved grade due to the A-level scale ceiling effect and it follows that mean optimism will therefore also be lower for higher achieving student and school groups, a point we will return to once we have described simple mean differences in optimism by each student and school characteristics.

Student Sociodemographics
Figure 2 shows how mean predicted grade (top line) and mean achieved grade (bottom line) vary by gender, ethnicity (major and minor), SES (NS-SEC, IMD, and POLAR), and disability.We present these mean scores with 95% confidence intervals.We sort the categories of each sociodemographic characteristic by their mean achieved grade.
Visually, mean optimism is depicted by the vertical distance between the two lines, and we report these values on the plot.
Mean optimism varies across the categories of each student sociodemographic characteristic except gender where mean optimism is 0.83 grades per subject for males versus 0.84 for males (range = 0.01).For all other characteristics, the degree of mean optimism noticeably reduces with increased achieved grade (the line plots converge as we move from left to right).This pattern is consistent with the A-level scale ceiling effect.However, the profiles of the predicted grade lines also differ from those of the achieved grade lines showing that there is more to differential mean optimism than just this mechanical explanation.
In terms of optimism differences across major ethnic categories, mean optimism ranges from 0.77 for white students to 1.07 for black students (range = 0.30) with Asian students overpredicted, on average, by 1.00 grade per subject.However, within each major ethnic category, there is variation across minor ethnic subcategories, especially for Asian students where mean optimism ranges from 0.81 for Chinese students to 1.08 for students from other Asian backgrounds (range = 0.27).Importantly, mean predicted grades do not increase monotonically with increasing mean achieved grade.We see notably lower mean optimism for White and Black Caribbean, White and Black African, and White students versus what we might expect given their mean achieved grades and the overall trend between mean predicted and mean achieved grades for the 15 ethnic groups (the predicted line noticeably drops down for these three ethnic groups relative to the achieved line).
Turning attention to SES, mean optimism is negatively associated with increasing SES whether we measure this by NS-SEC, IMD, or POLAR.For example, in terms of IMD, mean optimism ranges from 0.72 in the least deprived areas to 1.01 in the most deprived areas (range = 0.29).
Mean overprediction also varies by disability, ranging from 0.68 for students with learning difficulties to 0.89 for students with mental health disabilities or deaf/partial hearing (range = 0.21).In contrast, mean optimism for the 90% of students with no disabilities is 0.84.We see lower mean optimism for learning difficulty versus what we might expect given their achieved grades and the overall trend between mean predicted and mean achieved grades.

School Characteristics
Figure 3 shows how mean predicted grade, achieved grade, and optimism vary by region, county, school type, and school gender.
Mean optimism ranges from 0.72 in the South East to 0.97 in London (range = 0.25).
Relative to other regions, mean optimism appears higher in London versus what we might expect given their achieved grades.Turning attention to counties, mean optimism ranges from 0.57 in East Sussex to 1.05 in Staffordshire (range = 0.48).Mean optimism is noticeably lower in Leicestershire and noticeably higher in Rutland relative to what one would expect given the mean achieved grades in these two counties and the overall relationship between mean predicted and mean achieved grades.By school type, mean optimism ranges from 0.72 in independent schools to 1.09 in Other schools (range = 0.37), though we note that there are relatively few of the latter.The lower mean optimism in independent schools (and single-sex versus mixed-sex schools) is expected given the especially high achieving students these schools teach.

Application Characteristics
The variation in mean optimism by student and school characteristics will to some extent be explained by differences in GCSE score, A-level subjects, and application choices made by these groups.To facilitate our interpretation when we control for these variables, we first briefly describe mean optimism for each of these sets of characteristics.

Student Prior Achievement Characteristics
Figure 4 shows how mean predicted grade, achieved grade, and optimism vary by GCSE score and number of A-levels.Mean optimism narrows dramatically with increased GCSE GCSE score quantile.This is the clearest illustration of the A-level scale ceiling effect.

A-Level Subject Characteristics
Figure 5 shows how mean predicted grade, achieved grade, and optimism vary by Alevel subject.Mean optimism is higher in facilitating subjects.In terms of individual subjects, as mean optimism increases, we see a general shift from creative art subjects to social sciences, then humanities and modern languages, then maths, and lastly psychology and the traditional sciences.Particularly noteworthy is that the high optimism seen in the sciences and the low optimism seen in the arts are higher and lower than what we might expect given the mean achieved grades and the overall trend between mean predicted and mean achieved grades for the 32 subjects.

Application Characteristics
Figure 6 shows how mean predicted grade, achieved grade, and optimism also varies by different application specific characteristics.Here we see some agreement with the findings for A-level subject (Figure 5) in that sciences (and now associated subjects, including medicine, dentistry, engineering, and architecture) show the highest mean optimism, with social sciences and arts showing lower optimism.Turning attention to where students apply, mean optimism is lower for those who apply exclusively to Russell Group universities and those who apply to Oxbridge versus other applicants.As one would expect, these last two characteristics are strongly correlated with mean predicted and mean achieved grades.

Oxbridge
The variation in mean optimism by nearly all student sociodemographic characteristics (Figure 2) and school characteristics (Figure 3) is considerable.However, there is greater variation by GCSE score (Figure 4) and academic subject (Figure 5) and important variation by application characteristics (Figure 6).These latter variables will be strongly associated with student sociodemographic and school characteristics.In this section we therefore explore how student sociodemographic and school characteristic differences in mean optimism change when we adjust for these factors.We focus on the most interesting results.The plot shows that while there is no overall gender mean difference with males and females overpredicted 0.83 and 0.84 respectively (model 1, d = 0.01, p = .230;see also Figure 2), as soon as we adjust for GCSE score (model 2) and especially A-level subject (model 3), a gender difference appears with male and female students now overpredicted 0.75 and 0.90 respectively (d = 0.15, p < .001).In contrast, subsequent adjustments for application characteristics, other student sociodemographics, and school characteristics make little further difference to the results.Recall that the SD of optimism is 1.05 grades and so the gender difference of 0.15 grades equates to 0.14 of a SD and is therefore meaningful.

Gender
The intuition for this suppression effect is that, on average, females show higher GCSE scores than males which we have shown are associated with lower optimism (Figure 4).Furthermore, females are more likely than males to study subjects associated with lower optimism (Figure 5), put simplistically, arts and social sciences rather than sciences.Indeed, the percentage of female students increases from 53% to 64% as we move from the lowest to the highest GCSE score quantile.Similarly, the percentage of female students increases from 49% in the five highest mean optimism subjects to 73% in the five lowest mean optimism subjects.The intuition why further adjustments (models 4-7) make no impact is that, in contrast to GCSE score and A-level subject, gender does not strongly correlate with application, student sociodemographics, or school characteristics and so these characteristics cannot predict why females are predicted more optimistically than males.

Ethnicity
Figure 8 shows how mean optimism for each major ethnic group changes with statistical control.We highlight the three largest groups, White, Black, and Asian students.
Mean optimism is 0.30 grades higher for Black students (p < .001)and 0.23 grades higher for Asian students (p < .001)versus White students (see also Figure 2).As White students account for 71% of all applications, mean optimism moves less with statistical control than for Black (5.6%) and Asian (15.8%) students.In contrast to the results for gender, here adjusting for GCSE score (model 2) and A-level subject (model 3) do explain some of the differences in mean optimism between ethnic groups (as Black students have lower mean GCSE scores than White and Asian students and Asian students and to a lesser extent Black students study subjects where mean optimism is in general higher than White students: sciences rather than arts).Also, and again in contrast to the results for gender, adjusting for other student characteristics (model 5) narrows the mean differences further (as Black and to a lesser extent Asian students are, on average, lower SES than White students).Nevertheless, even in the most complex models (Model 6 and 7), Black and Asian students continue to be, on average, predicted more optimistically than White students.

IMD
Figure 9 shows that while mean optimism is, on average, 0.29 grades higher for those in the most deprived areas compared to those in the least deprived areas (model 1, p < .001),adjusting for GCSE score, A-level subject, then application characteristics (model 4) narrows this to 0.17 grades (p < .001).However, this is still equivalent to almost one in five poorer students being predicted one grade higher than otherwise observationally equivalent richer peers.While adjustment for other student sociodemographics (model 5) narrows this to 0.08 (p < .001),we note that these sociodemographics include adjustments for NS-SEC and POLAR, two competing measures of SES.So, in maintaining a common set of controls for comparability across each focal characteristic, in this instance we are perhaps over adjusting the IMD mean differences.

County
Figure 10 shows how mean optimism in each county changes with statistical control.
The overall impression is that, in contrast to gender (suppression) and ethnicity and IMD (explanation), we see relatively little change in differences in mean optimism across counties as we apply statistical control.Indeed, as we move from model 1 to model 6 the range in mean optimism across the 47 counties only drops from 0.50 (= 1.05 -0.55) to 0.40 (= 0.99 -0.59) and the correlation is very high at 0.91.

School Type
Figure 11 shows how mean optimism by school type changes with statistical control (we omit the very small Other category).We highlight State schools (21% of students), Independent schools (9.6%), and sixth-form colleges (SFCs; 21.3%).The general impression once again differs from those drawn for the earlier characteristics studied.With statistical control, we see a noticeable reordering of how optimistic the school types are.While the unadjusted mean optimism scores show optimism is lowest in independent schools (0.72 grades, model 1), once we adjust for the full set of covariates, mean optimism is highest in independent schools (0.90 grades, model 6).Adjusting for GCSE score leads mean optimism in independent schools to increase.This is driven by the very high mean GCSE score of students attending this school type.Adjusting for A-level subject raises mean optimism further.As an aside, mean optimism in grammar schools also increases when adjusting for GCSE scores but decreases when adjusting for subject.This is because, although grammar schools have similarly high GCSE scores to independent schools, they concentrate more on facilitating subjects where mean optimism is higher than for non-facilitating subjects.Further adjustment for student sociodemographics sees another large increase in mean optimism for independent schools (and to a lesser extent grammar schools) reflecting the very socioeconomically advantaged nature of their students.For state schools, the successive adjustments pull their mean optimism towards the overall sample average of 0.84 (in particular, as they show below average GCSE score).SFCs on the other hand do not converge towards the overall average.That is, in contrast to independent schools, the covariates do not explain why this school type shows such low optimism.SFCs are much larger than other school types (the mean SFC has 270 students vs. 68 in the average school), so one explanation may be that predicted grades and therefore optimism are internally moderated more in larger institutions.Their greater size may also lead to less personal teacher-student relationships making teachers less likely to feel pressured to predict optimistically.

Oxbridge
Finally, Figure 12 shows how mean optimism by whether students apply to Oxbridge changes with statistical control.Here we see an even more exaggerated version of the story seen for independent schools versus state schools.While the unadjusted mean optimism scores show optimism is lower among Oxbridge applicants (0.62 grades, model 1) versus non-Oxbridge applicants (0.86, d = 0.24, p < .001),once we adjust for GCSE scores we see that mean optimism is higher for Oxbridge applicants (model 2, 0.88 vs 0.83, d = 0.05, p < .001).Further adjustment for the remaining covariates does little to alter this result (models 3-7).

Predicted Grades Are Optimistic
Teacher predicted A-level grades are optimistic.Our analysis of the 2018/19 UCAS cohort of applicants shows that 61% of grades are overpredicted with the average student predicted 0.84 grades higher per A-level subject than they go on to achieve.This is equivalent to being overpredicted 2.5 grades across their three subjects.For example, a BBB achieving student would, on average, have been predicted AAB or AAA.This is higher than the 1.7 grades reported by Murphy and Wyness (2020) in their analysis of the 2012/13-2014/15 UCAS cohorts, which is in line with the understanding that optimism has increased rapidly in recent years (DfE, 2021).UCAS encourage teachers to predict optimistically arguing that stretching grades are motivating for students (UCAS, 2023b).Questions that arise are, therefore, "How optimistically should teachers predict?" and "Is 0.84 grades per subject optimal?"However, UCAS give no such numerical guidance.UCAS do warn that excessive optimism may lead students to receive offers they are unlikely to meet or to gain admission to courses which they then struggle on (UCAS, 2023b).However, here too they do not quantify at what point desirable optimism strays into excessive optimism.These concerns are by no means the only ones.For example, excessive optimism may also lead certain students to experience undue stress in pursuit of unattainably high predicted grades (DfE, 2022).Other students may be demotivated by excessively optimistic predicted grades, undermining the central argument for optimism in the first place.Other students again may receive unconditional offers (whereby students are offered places on courses regardless of what grades they go on to achieve) when they would not have done with more realistic predicted grades.This may demotivate these students from achieving their best grades.
Finally, if stretching grades are indeed motivational, then students not applying to university would appear to be missing this benefit.

Groups
Our main finding, however, is not that optimism is high in general, but that it is differentially high across student and school groups, often substantially so, and with greater optimism among less educationally advantaged groups.Importantly, this trend while diminished remained even after adjusting for GCSE scores and therefore the A-level scale ceiling effect.Furthermore, even after additional adjustments for A-level subjects and application related factors, differences in optimism across student and school groups often remaining sizeable.These findings suggest that the reliance on predicted grades, rather than achieved grades, in the application process may distort students' applications, the offers they receive, and ultimately which students are accepted at the most prestigious universities and courses (Murphy & Wyness, 2020).Further quantitative and qualitative work is needed to explore this and other potential consequences of the differential optimism patterns which we have found.
In terms of our specific results, these mainly support the Ofqual (2020) review on previous research comparing teacher predicted and achieved grades, namely that optimism is higher for Black, Asian (Figure 8), and low SES students (Figure 9).However, in contrast to Ofqual's conclusions, we find many large A-level subject effects (Figure 5) and we view the school type differences we find as important (Figure 11).We also show many new results such as more optimistic predictions for girls that only becomes apparent once we control for GCSE score and A-level subject (Figure 7) and large persistent region and especially county differences in optimism (Figure 10).We note that our ethnic group findings and our finding that girls are predicted more optimistically than boys both contradict those reported by Delap (1994) suggesting that patterns of differential optimism have changed over time, though we note there may be other explanations.
While, in one sense, any differences in optimism among student groups might appear unfair, particularly after accounting for GCSE score and A-level subject, many might perceive the finding of higher optimism among less educationally advantaged groups as a potentially positive result.This is because it may be encouraging historically underrepresented groups to aim higher than they might otherwise, thereby supporting initiatives aimed at widening participation and enhancing social mobility.However, if we are to accept and support this argument, it would be better for this differential optimism to be intentionally set via advice and guidance, rather than depending on its emergence in the current ad hoc and unmonitored manner.Yet, given our previous discussion about excessive optimism, it is not certain that greater optimism for less educational advantaged groups really is a positive.We also note that while optimism is, in general, greater for less educationally advantaged groups, there are notable exceptions.In particular, once we control for GCSE score and A-level subject, we find greater optimism being applied in independent schools (Figure 11) and among Oxbridge applications (Figure 12) and so to some of the most educationally advantaged students in the country.

Explanations for Differential Optimism Differential Impact of the A-Level Scale Ceiling Effect
The most fundamental explanation for differential optimism appears to be a mechanical one, namely that higher achieving student and school groups have less potential to be predicted optimistically due to the A-level scale ceiling effect (see also Ofqual, 2020).
However, this will be by no means the sole explanation, especially as we have shown that mean predicted grades rarely increase monotonically with increasing mean achieved grades across the various student and school characteristic categories (Figures 2 and 3).

Differential Focus on Different A-Level and Degree Subjects
A second explanation for differential optimism is that different student and school groups study different A-level subjects and mean optimism varies greatly by subject (Figure 5).We saw, for example, that girls' A-level subject choices are more concentrated in arts and social sciences while boys are more concentrated in sciences and maths.But why might mean optimism vary across A-level subjects in the first place?We found mean optimism was higher in facilitating subjects, especially sciences and maths, and lower in non-facilitating subjects, especially the arts and social sciences.One potential explanation is that students studying A-level sciences or maths apply to similar degree subject areas and these degree subject areas tend to have very high entry requirements.This may place greater pressure on their teachers to predict optimistically versus teachers in other subject areas.Furthermore, science and maths degree courses often specify the specific grades students should have in these subjects.For example, to apply to many Physics degree courses, students must often not only study Physics A-level but achieve an A grade in that subject.In contrast, students studying Sociology A-level who apply to Sociology degree courses will typically face lower entry requirements in general, with no specific grade requirement in that subject or often even the requirement to have studied Sociology at all.Another explanation for the optimism ordering of A-level subjects may be that, in contrast to science and maths A-levels, creative arts subjects often have substantial coursework components.Many of these components may have already been marked, or at least teachers are aware of their quality by the time predictions are made.This results in reduced uncertainty and limited room for optimistic predictions regarding students' remaining components and therefore their overall grades.

Differential Progress
A third explanation for differential optimism is that predicted grades are based on how students are performing at the point at which predictions are made, but some student and school groups will progress more rapidly than others over their next and final six months of study.For example, the result that girls are predicted more optimistically than boys (Figure 7) might reflect boys, on average, going on to achieve higher grades than expected, given their current and past performance.This explanation would be consistent with the stereotype that boys work less steadily than girls over their A-level studies, but cram effectively just before their exams (Times, 2017).If teachers do not consider this future behaviour, then, on average, boys are more likely to achieve results closer to their predicted grades compared to girls.As a result, boys will then appear less optimistically predicted than girls.More generally, the progress of many student and school groups may change over the last six months of A-level studies.These changes may not just reflect different study approaches, but also different levels of home support, parental pressure, and the differing responses of different groups to their optimistic predicted grades.

Differential Ambitiousness
A fourth explanation for differential optimism is that different student and school groups may apply more ambitiously than others to Russell group and Oxbridge courses, which tend to have higher entry requirements.Teachers naturally want to support their students' chances of being offered a place on their preferred course and this would lead them to predict higher for more ambitious student groups than others.There may also be student and school differences in the extent to which students and their parents directly pressure their teachers to predict high (DfE, 2022).Importantly where students are offered places many students are often still admitted if they only slightly miss their entry requirements (DfE, 2022;UCAS, 2019).Thus, teachers may view predicting higher grades for more ambitious or forceful student groups as a beneficial action for those specific students, not realizing that this practice may be distorting the application system more generally.
Different school groups may also be differentially ambitious.For example, the higher mean optimism seen in independent schools, once we have adjusted for GCSE score (Figure 7), could potentially stem from the fact that independent schools more aggressively promote their accomplishments in getting students into Oxbridge.Independent schools may therefore be disproportionally making optimistic predictions for their current students each year.

Differential Unconscious Bias
In contrast, unconscious bias does not appear an explanation for differential optimism.This is because we would expect unconscious bias to operate against least educationally advantaged groups (Burgess & Greaves, 2013), yet we have actually found greater optimism for these groups.

Given Differential Optimism, How Might Course Administrators, Students, and Teachers Respond?
A useful thought experiment is to explore how course administrators, students, and teachers might respond to learning that teachers predict girls more optimistically than boys.
We are not recommending the following responses; rather, we are presenting them solely to highlight the tensions that emerge from differential optimism.

Course administrators
From the standpoint of a course administrator, the understanding that teachers predict girls more optimistically than boys suggests that when an otherwise observationally equivalent boy and girl present with the same predicted grades, the admissions officer now has the knowledge that, on average, the boy is more likely to achieve their predicted grades than the girl.Consequently, the admissions officer might reasonably lean toward offering place to the boy.However, this action might be perceived as selection based on gender, a protected characteristic, and this categorized as discrimination (Equality Act, 2010).
However, an alternative perspective is that this action serves as a form of corrective measure against the underlying predicted grades, which is where gender-based discrimination truly originates.

Students
From a boy's standpoint, the knowledge that teachers predict girls more optimistically may seem unfair, and worse still consequential if it deters boys from applying to more selective courses compared to otherwise equivalent girls.This might suggest that boys should aim higher despite this penalty or try to remove this penalty by working harder earlier in their studies to reveal their true potential.This would then allow boys to benefit from the same higher predicted grades that girls are given.From a girl's perspective, the knowledge that they are less likely to reach their predicted grades than boys might suggest that they should be a little more cautious in just how ambitiously they apply to courses.

Teachers
From a teacher's perspective, they would want to correct the finding that they have been predicting girls more optimistically than boys.Thus, in future years they might try to factor into their predicted grades the increase in progress that boys tend to make in the final six months of study.

Potential Solutions to Differential Optimism Greater Guidance to Teachers
One response to differential optimism might be for UCAS to give teachers more guidance around setting predicted grades (UCAS, 2023b).For example, many of the practical suggestions made by Ofqual (2021) to teachers having to assign A-level grades to students in 2020/21 in lieu of their COVID-19 cancelled A-level examinations are also relevant to teachers assigning UCAS predicted grades.The general guidance from the Joint Council for qualifications (JCQ, 2023) is also relevant.Guidance could also be given on known patterns in differential progress across student groups.However, UCAS would but still need to define what the optimal degree of optimism is and explain how this must necessarily taper with increased achievement due to the A-level scale ceiling effect.So, while increased guidance may help, there would be challenges in articulating and implementing the concept of optimism.

Data Driven Predictions
Another response would be to replace teacher predicted grades with data predicted grades.For example, one could build a prediction model using the previous student cohort's data where achieved grades are known (Wyness et al., 2022).However, assuming that optimism was to be retained, UCAS would still need to quantify the degree of optimism that the prediction model should incorporate.The problem of the A-level scale ceiling effect would then also persist.Even if we put aside these challenges, however, this proposed response is unlikely to appeal to UCAS, ministers, or the public, considering the fallout from the Ofqual algorithm used to assign data predicted A-level grades to students in 2019/20 due to the cancellation of exams amidst the COVID-19 pandemic (Kelly, 2021).Perhaps, at most, data driven predictions might support rather than replace teacher predictions.

Post-Qualifications Admission System
The government recently consulted on potential post-qualifications admissions systems (PQA) which would remove or at least reduce the reliance on predicted grades (DfE, 2021).In their first model, students would only apply once they received their achieved grades with results day being brought forward to the end of July and degree courses pushed back to the start of October to make the system work.In their second model, students would continue to apply as they presently do.However, they would have the option to modify their choices at any point up to and including when their results are released.Only offers and decisions would be made post results day.A minority of respondents to the consultation thought that either model would be better than the current system.Key criticisms were that the contracted timescale would negatively impact course admissions using interviews, tests, or auditions (DfE, 2022).Furthermore, obtaining application data only after results day would create challenges for courses in terms of anticipating student numbers and hinder their ability to build relationships with students while they finalize their choices.Additionally, students would miss out on the substantial support, information, advice, and guidance that teachers offer, and this would particularly affect disadvantaged students.Ultimately, the DfE concluded that the present moment was not suitable for implementing reforms, as priority should be on educational and exam recovery from the repercussions of COVID-19 (DfE, 2022).What is certain, is that the debate around predicted grades and differential optimism

Figure 7
Figure 7 plots mean optimism for male and female students against model number