Programming

In[79]:=

spread[lis_]:=Drop[FoldList[Plus,0,lis],1] (* spread[{a,b,c}] *)

In[80]:=

pvector[s_,r_]:=With[{d=Switch[r,
                               18,0.40,
                               30,0.80,
                               50,0.80,
                               60,1.22,
                               70,1.22,
                               90,1.22
                               ]},
                   pvector[d/r,s,x10arrow/2/r]]

In[81]:=

(* s is the mrad of the shooter's ability, and r is meters to the target *)

getweights[s_,r_]:=spread[pvector[s,r]]
       
(* this function returns a vector of the cumulative probabilities starting with the X ring *)
       

In this function we provide the cumulative probability vector (determined above) and "roll" a shot that's consistent with the shooter's skill.  The way we simulate (say) an end of three arrows is to "roll" three times!

In[86]:=

(* provide a weight vector and this function "rolls" one arrow *)

roll[wv_]:=With[{r=Random[]},
                Which[(*r<=wv[[1]], 11,--only use this for testing X's*)
                      (* this is the fastest order of evaluation *)
                      r<=wv[[2]], 10,
                      r<=wv[[3]], 9,
                      r<=wv[[4]], 8,
                      r<=wv[[5]], 7,
                      r<=wv[[6]], 6,
                      r<=wv[[7]], 5,
                      r<=wv[[8]], 4,
                      r<=wv[[9]], 3,
                      r<=wv[[10]], 2,
                      r<=wv[[11]], 1,
                      True, 0]]

In[88]:=

(* this rolls n arrows and returns their sum *)

roll[wv_,n_]:=Sum[roll[wv],{n}]

In[90]:=

(* this "rolls" a male FITA, at 30m, 50m, 70m, and 90m *)

rollfita[male,s_]:=roll[getweights[s,30],36]+
                   roll[getweights[s,50],36]+
                   roll[getweights[s,70],36]+
                   roll[getweights[s,90],36]

In[92]:=

rollfita[female,s_]:=roll[getweights[s,30],36]+
                     roll[getweights[s,50],36]+
                     roll[getweights[s,60],36]+
                     roll[getweights[s,70],36]

In[93]:=

<<Graphics`Graphics`

In[94]:=

SetAttributes[hello,Listable]

In[104]:=

hello[sex_,score_]:=With[{s=findmrad[sex,score]/1000},
                    Module[{histo=Array[0&,1440]},
                         Do[With[{e=rollfita[sex,s]},histo[[e]]++],{20000}];
                         With[{m=mean[histo],
                               sigma=Sqrt[sigma2[histo]]},
                         Print[sex, " ", score, " shooter, ", N[1000 s,2], "mrad"];
                         Print["simulated tournaments: ", Total[histo]];
                         Print[" mean is ", N[m,4], " points, sigma is ", N[sigma,3], " points"];
                         Print[" 68% of the time the score is within ", N[m - sigma,4], " and ", N[m + sigma,4]];
                         Print[" 95% of the time the score is within ", N[m - 2 sigma,4], " and ", N[m + 2 sigma,4]];
                         With[{p1=ListPlot[converttopoints[histo],
                                           DisplayFunction->Identity],
                               p2=Plot[Exp[-((sc-m)/sigma)^2/2]/sigma/Sqrt[2 Pi],
                                  {sc,m-3 sigma, m+3 sigma},
                                  DisplayFunction->Identity]
                                  },
                              Show[p1,p2,DisplayFunction->$DisplayFunction]
                         ]]]]

In[96]:=

mean[histo_]:= Sum[i histo[[i]], {i, Length[histo]}]/Total[histo]

In[97]:=

sigma2[histo_]:=With[{m=mean[histo]},
                     Sum[histo[[i]] (i - m)^2,{i, Length[histo]}] / Total[histo]]

In[98]:=

converttopoints[histo_]:=Module[{res={},
                                 count=Total[histo]},
                                Do[If[histo[[i]]>0,
                                      res=Prepend[res,
                                                 {i,histo[[i]]/count}
                                                 ]
                                      ],
                                   {i, Length[histo]}];
                                res]

Created by Mathematica  (June 28, 2005)