# Test error of probability “prediction” for little league soccer

Background: I have multiple sets of team's little league soccer scores made up only of whole numbers [0-12 inclusive], eg:

A: 1, 2, 4, 7
B: 0, 0, 0, 1, 1, 1, 4, 7
C: 0, 1, 2, 2, 2, 3, 4


Due to a positive skew, I would like to improve upon using the mean for prediction of next score.

• At about 4 or more pieces of data for a set, I can make a fairly accurate prediction using the mean average of the set, [diminishing returns for reducing error starts very rapidly]. But is definitely open to improvement at a fundamental level.
• Most sets will be made up of 4-60 numbers and have a very nice bell shaped distribution for 90% of the data from 0-5 inclusive but have a positive skew for the remaining 10% from 6+. The data points from 6+ are not outliers necessarily but they most certainly do interfere with the mean for future predictions [consistently over predicting on average by about 5-7%].

Using the mean of previous scores as a rudimentary prediction. "Next" is the next score achieved by the team in the set.

    Mean - Next - Error
A:  3.50    4     0.50
B:  1.75    2     0.25
C:  2.00    0     2.00


Issue: How does one test the error of a probability based prediction without a specific number to compare against like a mean / median / mode?

Probabilities are rounded [may not total to 100].

     0   1   2   3   4   5   6   7 -  Next - Error - Intuition / aim?
A:   0  25  25   0  25   0   0  25      4      ?       3.0
B:  38  38   0   0  13   0   0  13      2      ?      ~0.8 ??
C:  14  14  43  14  14   0   0   0      0      ?       2.0


Obviously predicting probabilities like the above even with slightly larger sets that form smoother distributions is meant for a very different kettle of fish predictions eg Set C: ~71% chance of scoring less than 2.5 goals.

• Ideally a method to output a simple as possible [tacky is great] not necessarily best practise, it could be an estimated prediction of what a team will score higher than 50% of the time and lower than 50% of the time so that an error can be produced similar to the mean prediction and hence compared, or...
• Some other way without producing an exact prediction for the probabilities for each set but would allow direct comparison of error with the mean prediction.
• Most of the sets have 22-42 scores but the solution needs to work effectively even with a very limited number of data points [eg 4-9] if using the probabilities to infer some sort of approximate prediction.