# Methods

## Automatically generated forecasts

A set of different automated systems are participating in the wetterturnier as well. These will be divided into the three groups “automated Systems” (MOS), “reference tips”, and “mean tips”. They are highlighted by colors in the ranking tables: human players [white], automated systems [black], reference tips [blue], and mean tips [orange].

• automated systems: a majority of these are so called model output statistics (MOS) systems: statistically post-processed forecasts from a numerical weather forecast model
• reference tips: special tips like e.g., persistence, or others (see below).
• mean tips: there will be one mean tip including all submitted tips, and several group tips. The equation behind both is exactly the same. The only difference is, that the group tips are only including all active members of a specific group for a specific tournament

### Persistencies (Thursday and Friday)

The persistency forecasts (“all parameters remain unchanged”) participates as a reference, and for statistical tests. For the persistency of Thursday (Donnerstag) and Friday (Freitag). A mean over both stations of each tournament cities is calculated. We use the following observations:

• Minimum-temperature (TTn) of Friday 6 UTC
Cloud cover (N), wind direction (dd), wind speed (ff), weather state forenoon (Wv), atmospheric pressure (PPP), and dew point temperature (TTd) of Friday, 12 UTC
• Weather state afternoon (Wn), and maximum temperature (TTm) of Friday, 18 UTC
• Amount of Precipitation (RR) of Saturday, 6 UTC.

### Petrus

“Petrus” is the mean forecast of all participating contestants and methods of the weekend. The following parameters are averaged arithmetically and rounded mathematically (to even numbers):

N, ff, PPP, TTm, TTn, TTd

• For sunshine duration (Sd) a majority decision about whether or not the sun should shine is made. If at least 50% of the player were IN FAVOR of sunshine, all of their values are averaged. Otherwise Sd = 0.
• For wind direction (dd) an average vector weighted with the corresponding wind speed (ff) is computed.
• For wind gusts (fx) a majority decision for or against wind gusts is made. If no absolute majority in favor of fx = 0 is reached, all values larger equal 25 are averaged.
• The weather conditions (Wv, Wn) are decided by majorities. The following decisions are taken in a row (in case of no majority the higher code number is taken):
• Decision dry / not dry weather conditions (0, 4 vs. 5, 6, 7, 8, 9)
• In first case simple decision between 0 and 4.
• In second case decision stratiform vs. convective (5, 6, 7 vs. 8, 9)
• In case of stratiform precipitation decision liquid vs. snow (5, 6 vs. 7), then decision between 5 and 6.
• In case of convective precipitation simple decision between 8 and 9.
• For precipitation amount (RR) firstly, a decision is made between dry cases and cases with observed precipitation. If there is an absolute majority FOR dry weather, -3.0 is given. If not, an analogous decision between “no measurable precipitation” (0.0) and “wet weather” is made. In case of the latter, the arithmetic mean of all participants who forecasted any precipitation is computed for RR.

### Moses

“Moses” is an automatic forecast based on the “model output statistics” (MOS) method. Carsten Raymund wrote his bachelor thesis in the year 2017 about this method. The bachelor thesis with the title “Regressionsanalysen zur Ableitung einer Optimal-Vorhersage, basierend auf der Kombination von Kurzfristvorhersagen der Teilnehmer am Berliner Wetterturnier” can be downloaded here [click]. Moses started its participation on 5.1.2001 with the equation following:

• Moses = 0.5 * Dummschwätzer + 0.25 * Gatzen + 0.14 * Schmelzi + 0.11 * Frank

These coefficients are computed once a week with the results from the latest rounds/tournaments. If one of the users included in the equation does not participate it will be replaced by Petros. Worst case (if all players do not take part) Moses would be identical to Petrus. The current Moses equations can be found here:

### Sleepy

Sleepy is no player. Sleepy defines the points a user gets in the ranking (total ranking) for the weekends where he has not participated in the tournament. The points Sleepy gets for a full weekend are mean points minus the ‘mean absolute residual’ to the mean points of all players. If $$p_c$$ are the user-points for a given weekend and a given city $$c$$ (max 200 points), and $$N$$ the number of players for a given city, Sleepy (for city $$c$$) gets:

$$p_{sleepy,c} = \bar{p}_c – mean( | p_c – \bar{p}_c | ),~~\text{with}~~\bar{p}_c = \frac{1}{N} \cdot \sum_{i=1}^N p_i$$

NOTICE: Since 2018 $$p_c$$ only contains bets of human players or automatons, so no group bets or reference bets like Petrus anymore!