E. Linacre 
1/'99 
A convenient measure of the quality of a forecast of daily maximum temperature, for instance, is the Priestley Skill Score (PRSK), which involves a comparison of the variance of such temperatures at this time of year (V), with the mean square of the error in forecasting the temperature (E), thus
PRSK = 1  E / V
The variance V is the arithmetic mean of the squared deviations from the average value. It is calculated as follows for this set of measured daily maximum temperatures Tx in ºC 
Day 
1 
2 
3 
4 
5 
6 
7 
8 
9 
mean 
Tx 
24 
25 
22 
26 
23 
20 
23 
26 
27 
24, i.e. Tm 
Tx  Tm 
0 
1 
2 
2 
1 
4 
1 
2 
3 
 
(ditto)2 
0 
1 
4 
4 
1 
16 
1 
4 
9 
4.4, i.e. V 
forecast 
25 
25 
26 
29 
24 
20 
22 
25 
26 
 
errror 
1 
0 
4 
3 
1 
0 
1 
1 
1 
 
(ditto)2 
1 
0 
16 
9 
1 
0 
1 
1 
1 
3.3, i.e. E 
This set of forecasts shows a forecasting skill of (1  3.3/4.4) i.e. 0.25. That positive number implies that the forecasts are better than chance estimates. However, the degree of skill is modest. If it were perfect, E would be zero and the PRSK would be unity.
It is also interesting to calculate the skill achieved by two other methods of forecasting. First, one might assume that the value for each day was always the average value (i.e. the ‘climatological forecast’). Then E by definition would equal V, and thus the skill works out as zero. Alternatively, the ‘persistence forecast’ involves assuming that tomorrow’s value will be the same as today’s proved to be. Therefore, the table above becomes the following 
day 
1 
2 
3 
4 
5 
6 
7 
8 
9 
mean 
Tx 
24 
25 
22 
26 
23 
20 
23 
26 
27 
24, i.e. Tm 
Tx  Tm 
0 
1 
2 
2 
1 
4 
1 
2 
3 
 
(ditto)2 
0 
1 
4 
4 
1 
16 
1 
4 
9 
4.4, i.e. V 
forecast 
 
24 
25 
22 
26 
23 
20 
23 
26 
 
error 
 
1 
3 
4 
3 
3 
3 
3 
1 
 
(ditto)2 
1 
1 
9 
16 
9 
9 
9 
9 
1 
8.0, i.e. E 
In this case, the skill works out as minus 0.8, which is appalling. It would have been better to use a climatological forecast. However, this is not always the case.
In summary, 
PRSK = 1 
perfect forecast 
PRSK > 0 
better than chance (has skill) 

PRSK = 0 
climatology 

PRSK < 1 
worse than climatology 