Explanation of KS4 scoring system

Capped and uncapped total points score

At Key Stage 4 two different average points scores (APS) are calculated. Unlike at Key Stages 1-3 where almost all pupils take the national assessments, at Key Stage 4 pupils take different numbers of courses, so choices need to be made about how to compare performance. One way is through meeting thresholds, such as the percentage of pupils attaining 5+ A*-C. Another way is through points scores. Because of the different number of courses pupils take, the points score method is based on the total of a pupil’s points scores; it is not based on the average points score per subject, as is the case at Key Stages 1-3. First of all, the average total points score per pupil for all of the courses is calculated, so in schools where pupils are entered for a large number of courses this may be higher than in schools where pupils are entered for fewer, depending upon the grades they obtain.

For example in School A, if pupils take 10 full GCSEs and in each obtain grade C, which has a points score of 40 (see table below), their total points score will be 10 x 40, which is 400. If all pupils in the school had the same results, the school’s average total points score would be 400. In School B all pupils might take only 8 GCSEs but in each attain grade B, which has a points score of 46. The school’s average total points score would be 368. So School A has a higher average total points score than School B. The quantity of courses has had a slightly higher weight than the difference of one grade.

In order to compare the grades more closely, the capped average total points score was introduced. It caps the total number of courses that can be included at the equivalent of 8 full GCSEs, because the vast majority of pupils take at least this number of courses. There is no requirement for it to contain English and mathematics. For School A the capped average total points score would be for 8 grades C, a total of 8 x 40, which is 320. For School B, where pupils only took 8 GCSEs the capped score is the same as the average total points score, 368. So School B now has a higher score then School A when capped average points scores are compared. It places higher weight on the grades within the core of 8 subjects than on the quantity of courses.

To distinguish these two approaches, they are referred to as capped APS and uncapped APS. Looking at the national figures can give an indication of the grades and number of courses they represent. In 2004 the national uncapped total APS was 340 and the national capped total APS was 282. The difference is 58 points, or roughly one extra GCSE at grade A* or two extra GCSE at grade E per pupil. The capped APS represents roughly 8 x 35 points which is just above an average of grade D in all 8 subjects. If the uncapped APS also represented the same average score, 35, it would show that on average pupils took a number of courses equivalent to 9.7 full GCSEs.

New scoring system for 2004

From 2004, the DfES has introduced a new scoring system at Key Stage 4. It includes the results of pupils in all qualifications approved for use pre-16, such as entry level qualifications, vocational qualifications, and AS levels taken early. Firstly there is a new points score system linked to the old points score for GCSE by the formula:

new points = old points x 6 + 10

|Level |2 |
|48 points |one grade in all eight subjects for all pupils |
| |two grades in all eight subjects for half of the pupils |
|24 points |one grade in four subjects for all pupils |
| |one grade in all subjects for half of the pupils |
|12 points |one grade in two subjects for all pupils |
| |one grade in all subjects for a quarter of the pupils |
|6 points |one grade in one subject for all pupils |
| |one grade in all subjects for one eighth of the pupils |
|3 points |one grade in one subject for half of the pupils |
| |one grade in all subjects for one sixteenth of the pupils |
|2 points |one grade in one subject for one third of the pupils |
| |one grade in all subjects for one twenty-fourth of the pupils |
|1 point |one grade in one subject for one sixth of the pupils |
| |one grade in all subjects for one forty-eighth of the pupils |

Differences between the scoring systems

The table below shows the points equivalence for each grade for each type of GCSE.

|Grade |A* |A |B |
|Half GCSE |10 |0.5 |3 |
|Full GCSE |20 |1.0 |6 |
|Double GCSE |40 |2.0 |12 |

If, instead of improving their grade in a GCSE course, the pupil took an extra full GCSE course and obtained a grade G, they would add 16 points to their total points score. In other words, they can add more points by taking an additional subject than by improving an existing subject by one grade. They would need to improve their existing subject by three grades (18 points) to increase their points score by the same amount as they could by obtaining grade G in one extra subject. This is an illustration of how the new points scoring system gives more weight to the quantity of courses than did the old system.

One way of analysing this effect is to look at the relationship between the points score for the highest and the lowest grades. We can calculate the proportion of the highest grade that each lower grade represents.

The points differential between low grades and high grades is lower in the new points system than in the old. For example, in the old system a single A* grade was worth the same number of points as eight grades G. Now, an A* is worth 58 points, and eight grades G are worth 128 points. This means that the points value of grade G relative to A* has more than doubled.

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The effect is similar with GNVQ, but because there are fewer grades it is less noticeable.

We can calculate the points score differential by dividing the number of points awarded to the highest possible pass by the number of points awarded to the lowest possible pass. This is shown in the table below. For GCSE, the differential shows the number of grades G that give you the same points as a single A*. For GNVQ it shows the number of ordinary passes that give you the same points as a distinction.

|Type of Exam |Old Differential |New Differential |
| | | |
|Full GCSE |8 |3.6 |
|GNVQ Foundation |2.7 |1.8 |
|GNVQ Intermediate |1.5 |1.4 |

The table shows not only that low passes count for more relative to high passes in the new system than the old, but that the largest proportional change in the differential is at GCSE. The new differential is less than half of the old one.

The following examples illustrate the differences between the scoring systems.

Example 1

Pupil A takes three GCSE courses and obtains A* in all of them
Pupil B takes four GCSE courses and obtains B in all of them
Pupil C takes a Full Intermediate GNVQ and obtains a merit

Under the old system, all three pupils would have a total points score of 24. Under the new system, Pupil A has 174 points, and Pupils B and C have 184.

Example 2

Pupil D takes 5 GCSE courses and obtains B in all of them
Pupil E takes 6 GCSE courses and obtains C in all of them
Pupil F takes a full Intermediate GNVQ and obtains a distinction

Under the old points system they would all have 30 points. Under the new system Pupil D has 230 points, Pupil E has 240 points, and Pupil F has 220 points.

At school level the differences can be marked. A school’s national percentile ranking can change between the systems. About one third of schools go up or down in rank by between roughly 2 and 15 percentile points and the remainder stay almost the same. In schools in which the rank falls most between the old and new scoring system, pupils took a relatively small number of GCSE courses and gained grade C or above in almost all of them. In schools in which the rank increases most between the old and the new scoring system, pupils took more GCSE courses and gained lower grades in them, with few at grades A* or A.

The differences in capped total points score can be seen in the table below, in which a pupil’s total points are calculated for each number of GCSE courses from 1 to 8. This shows that, if a pupil took only four full GCSE courses, and their total points score in the old system was n, then the score in the new system would be 6n+40.

|GCSE 1 |GCSE2 |GCSE3 |GCSE4 |GCSE5 |GCSE6 |GCSE7 |GCSE8 | |Old score |p |q |r |s |t |u |v |w | |New score |6p +10 |6q+10 |6r+10 |6s+10 |6t+10 |6u+10 |6v+10 |6w+10 | |Total old score |p |p+q |p+q+r |p+q+r+s |p+q+r+s+t |p+q+r+s+t+u |p+q+r+s+t+u+v |p+q+r+s+t+u+v+w | |Total new score |6p+10 |6(p+q)+20 |6(p+q+r)+30 |6(p+q+r+s)+40 |6(p+q+r+s+t)+50 |6(p+q+r+s+t+u)+60 |6(p+q+r+s+t+u+v)+
70 |6(p+q+r+s+t+u+v+w)+80 | |
Number of full GCSE courses |1 |2 |3 |4 |5 |6 |7 |8 | |Old total points score |n |n |n |n |n |n |n |n | |New total points score |6n+10 |6n+20 |6n+30 |6n+40 |6n+50 |6n+60 |6n+70 |6n+80 | |
You can work out if the pupils had 8 subjects contributing to their capped total points score, by multiplying the old score by 6 and subtracting it from the new score. If the difference is 80, then all pupils took the equivalent of 8 full GCSE subjects. For example, if the capped APS were 45 in the old system and 345 in the new system, you could work out 345 – (6 x 45) or 345 – 270, which is 75. On average, pupils contributed 7.5 full GCSE equivalent courses to the capped total points score, or perhaps half of the pupils contributed eight and half of them contributed 7.

These graphs for rough conversion between old and new scoring systems were prepared by the Fischer Family Trust and are available on the targets section of the DfES Standards website. They are based on school results from 2004 and are not intended for use at pupil level. Schools may use them to convert their estimates under the old scoring system to estimates in the new system.

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Value added between key stages

The value-added median graphs in the PANDA report show the value added you can expect for a pupil with each average points score at the beginning of a key stage. For example, for all pupils with KS2 APS of 27, one point is plotted on the graph where the capped average points score of the median (middle) pupil nationally at KS4 falls, which is at roughly 39. Points are plotted for the median pupil with each possible KS3 APS and then joined up with straight line segments. That is why the word ‘median’ is in the title. You can use the graphs to evaluate individual pupils’ progress. They are not suitable for comparing school and national APS which are averages of pupils’ points scores. These graphs use the old scoring system at KS4.

Value-added median graph for KS2 in 1999 to KS4 in 2004

Value-added median graph for KS3 in 2002 to KS4 in 2004

The value-added median graphs below, from the DfES performance tables site, use the new scoring system. There are separate graphs for mainstream and special schools. More information about them can be found on: http://www.dfes.gov.uk/performancetables/schools_04/sec3b.shtml

Value-added graph for KS2 in 1999 to Age 15 in 2004 in mainstream schools

Value-added graph for KS2 in 1999 to Age 15 in 2004 in special schools

Value-added graph for KS3 in 2002 to Age 15 in 2004 in mainstream schools

Value-added graph for KS3 in 2002 to Age 15 in 2004 in special schools

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Information sheet 2