apx-bonus-distance-use.tex

% !TEX TS-program = xelatex
% !TEX encoding = UTF-8 Unicode
\documentclass[gap.tex]{subfiles}
\begin{document}
\label{sec:bonus-distance-use}

\begin{quote}
    For all distance point calculations, including the difficulty calculations
    in hang-gliding (see ~\ref{sec:difficulty-calculation}), these new stopped
    distance values are being used to determine the pilots’ best distance
    values.  Time and leading point calculations remain the same: they are not
    affected by the altitude bonus or stopped distance values. 
\end{quote}

This appendix, expands on this brief but broad statement (see
~\ref{sec:distance-stopped-tasks}) showing how and when bonus distance or real
distance is used in calculating validities and weights and when allocating
points in FS.

Launch validity doesn't depend on distance. Distance validity and stop validity
depend on real distance but time validity depends on bonus
distance\footnote{Time validity and stop validity depend on distance only if no
pilot makes it to the end of the speed section.\label{fn:repeat}}. Task validity depends
transitively on bonus distance through time validity.

Arrival weight, departure weight and distance weight do not depend on distance.
Time weight and leading weight depend on bonus distance.

Departure point allocation doesn't depend on a pilot's distance. Distance point
allocation depends a pilot's bonus distance but arrival, time and leading point
allocation depend on a pilot's real distance.

As available points depend on task validity and this depends on bonus
distance\footref{fn:repeat}, all point allocations depend on bonus
distance indirectly.

\begin{table}[!ht]
    \begin{tabularx}{\textwidth}{|l|X|c|c|}
    \hline
        \textbf{Aspect of Scoring}
        & \textbf{Part of Aspect}
        & \textbf{Real}
        & \textbf{Bonus}
        \\
    \hline
        \multirow{5}{*}{Validity}
        & Launch
        &
        &
        \\
    \cline{2-4}
        & Distance
        & $\checkmark$
        &
        \\
    \cline{2-4}
        & Time
        &
        & $\checkmark$
        \\
    \cline{2-4}
        & Stop
        & $\checkmark$
        &
        \\
    \cline{2-4}
        & Task (Day Quality)
        &
        & $\checkmark$
        \\
    \hline
        \multirow{5}{*}{Weight}
        & Arrival
        &
        &
        \\
    \cline{2-4}
        & Departure
        &
        &
        \\
    \cline{2-4}
        & Distance
        &
        &
        \\
    \cline{2-4}
        & Time
        &
        & $\checkmark$
        \\
    \cline{2-4}
        & Leading
        &
        & $\checkmark$
        \\
    \hline
        \multirow{5}{*}{Allocation}
        & Arrival
        & $\checkmark$
        &
        \\
    \cline{2-4}
        & Departure
        &
        &
        \\
    \cline{2-4}
        & Distance
        &
        & $\checkmark$
        \\
    \cline{2-4}
        & Time
        & $\checkmark$
        &
        \\
    \cline{2-4}
        & Leading
        & $\checkmark$
        &
        \\
    \hline
    \end{tabularx}
    \caption{Use of bonus distance and real distance in scoring.}
    \label{tab:gap-defaults}
\end{table}

\begin{lstlisting}[style=base, caption={Launch validity doesn't depend on distance inputs.}]
double launch_validity =
    CalcLaunchValidity
        ( sp.No_of_pilots_flying
        , sp.No_of_pilots_present
        , sfg
        );
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Distance validity depends on \textcolor{blue}{real} distance inputs.}]
double <@distance_validity<@ =
    CalcDistanceValidity
        ( sp.<@Sum_real_dist_over_min<@
        , sp.No_of_pilots_flying
        , (double)sfg.Nom_goal
        , sfg.Nom_dist
        , sfg.Min_dist
        , sp.<@Best_real_dist<@
        );
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Time validity depends on \textcolor{red}{bonus} distance input.}]
double @>time_validity@> =
    CalcTimeValidity
        ( time_validity_time
        , (double)sfg.Nom_time
        , sp.@>Best_dist@>
        , sfg.Nom_dist
        );
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Stop validity depends on \textcolor{blue}{real} distance inputs.}]
sp.<@Sum_flown_distances<@ += p.<@_real_distance<@;
<@distances<@[distance_counter++] = p.<@_real_distance<@;

double <@avg_distance<@ = sp.<@Sum_flown_distances<@ / sp.No_of_pilots_flying;
double <@sumOfDerivation<@ = 0;
for (int i = 0; i < distances.Length; i++)
{
  <@sumOfDerivation<@ += <@distances<@[i] * <@distances<@[i];
}
double <@sumOfDerivationAverage<@ = <@sumOfDerivation<@ / sp.No_of_pilots_flying;
double <@stdev_distance<@ = Math.Sqrt(<@sumOfDerivationAverage<@ - (<@avg_distance<@ * <@avg_distance<@));

double <@stop_validity<@ =
    CalcStopValidity
        ( sfg
        , sp.Last_start_time
        , task_state.TaskStopTime
        , sp.<@Best_real_dist<@
        , sp.Launch_to_ess_distance
        , <@avg_distance<@
        , <@stdev_distance<@
        , sp.No_of_pilots_landed_before_stop
        , sp.No_of_pilots_flying
        , sp.No_of_pilots_reaching_ES
        , task_state.IsStopped
        );
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Task validity depends on \textcolor{red}{bonus} distance (and \textcolor{blue}{real} distance).}]
double @>day_quality@> =
    CalcDayQuality
        ( @>time_validity@>
        , launch_validity
        , <@distance_validity<@
        , <@stop_validity<@
        );
\end{lstlisting}

\pagebreak

\begin{lstlisting}[style=base, caption={Arrival weight and departure weight don't depend on distance inputs.}]
double dummy_arr_weight = 0;
if (sfg.Use_arrival_time_points && !sfg.Use_leading_points)
    dummy_arr_weight = (1.0 - sp.Distance_weight) / 4.0;
else
    dummy_arr_weight = (1.0 - sp.Distance_weight) / 8.0;

if (sp.No_of_pilots_reaching_ES > 0)
{
    if (sfg.Use_arrival_points)
        sp.Arrival_weight = dummy_arr_weight;

    if (sfg.Use_departure_points)
        sp.Departure_weight = dummy_arr_weight * 1.4;
}
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Distance weight doesn't depend on distance inputs.}]
sp.GoalRatio = 0;
if (sp.Best_time > 0 && sfg.Use_time_points)
{
    sp.GoalRatio = sp.No_of_pilots_reaching_goal * 1.0 / sp.No_of_pilots_flying;
}
sp.Distance_weight =
    0.9
    - 1.665 * sp.GoalRatio
    + 1.713 * Math.Pow(sp.GoalRatio, 2)
    - 0.587 * Math.Pow(sp.GoalRatio, 3);
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Time weight depends on \textcolor{red}{bonus} distance through leading weight.}]
sp.@>Time_weight@> =
    (1 - sp.Distance_weight)
    - sp.Arrival_weight
    - sp.Departure_weight
    - sp.@>Leading_weight@>;
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Leading weight depends on \textcolor{red}{bonus} distance.}]
if (sp.No_of_pilots_reaching_goal == 0
    && sfg.Use_proportional_leading_weight_if_nobody_in_goal)
{
    sp.Leading_weight = Math.Min(sp.@>Best_dist@> / sp.Task_distance * 0.1d, 0.1d);
}
else
{
    sp.Leading_weight = dummy_arr_weight * 1.4;
    if (sfg.Double_leading_weight)
        sp.Leading_weight *= 2;
}
\end{lstlisting}

\pagebreak

\begin{lstlisting}[style=base, caption={Arrival point allocation depends on \textcolor{blue}{real} distance.}]
double arrival_points = 0;
double time = p.Result.Ss_Time_Dec_Hours;
if (time > 0) // reached ES
{
    double x = 0;
    if (sfg.Use_arrival_position_points)
    {
        x = 1 - (p.Result.Finished_ss_rank - 1.0) / sp.No_of_pilots_reaching_ES;
        x = 0.2 + 0.037 * x + 0.13 * Math.Pow(x, 2) + 0.633 * Math.Pow(x, 3);
    }
    else if (sfg.Use_arrival_time_points)
    {
        x = Math.Round(
          Math.Pow(
            1 + (2.0 / 3.0) * (sp.First_finish_time.Utc_time - p.Result.Finished_ss.Utc_time).TotalHours
            , 3)
          , 4, MidpointRounding.AwayFromZero);
        if (x < 0) x = 0;
    }
    arrival_points = x * sp.Available_points_arrival;
    if (p.<@_real_distance<@ < t.DistanceExact)
    {
        arrival_points *= (double)sfg.Time_points_if_not_in_goal;
    }
}
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Distance point allocation depends on \textcolor{red}{bonus} distance.}]
if (use_difficulty)
{
    double linear_fraction = dist / 2.0 / @>best_dist@>;

    int kmx10 = (int)(dist * 10);
    double difficulty_fraction = dsd100ms[kmx10]._score_percent;
    if (dsd100ms.Length > kmx10 + 1
       && dsd100ms[kmx10 + 1]._score_percent > difficulty_fraction)
        difficulty_fraction += (dsd100ms[kmx10 + 1]._score_percent - difficulty_fraction) * (dist * 10.0 - kmx10);
    return (difficulty_fraction + linear_fraction) * available_points_distance;
}
else
{
    double linear_fraction = dist / @>best_dist@>;
    return linear_fraction * available_points_distance;
}
\end{lstlisting}

\begin{lstlisting}[style=base, caption={Time point allocation depends on \textcolor{blue}{real} distance.}]
double time_points = 0;
double time = p.Result.Ss_Time_Dec_Hours;
if (time > 0)
{
    time_points
      = 1 - Math.Pow
        (
          (
            (time - sp.Best_time)
            / Math.Sqrt(sp.Best_time)
          ), 2.0 / 3
        );
    if (time_points < 0) time_points = 0;
    time_points -= time_points_stop_correction;
    time_points *= sp.Available_points_time;

    if (p.<@RealDistance<@ < t.DistanceExact)
    {
        time_points *= (double)sfg.Time_points_if_not_in_goal;
        p.Result.Got_time_but_not_goal_penalty = true;
    }
}
\end{lstlisting}

\end{document}