Subject:      A treatise on the statistics of dumping
 From:         James=Parinella%sdl%msdtwk@vines.msd.ray.com (James C. Parinella)
 Date:         1996/01/26
 Newsgroups:   rec.sport.disc
 
 
 I have looked a little more in depth at the statistics of dumping (the
 frisbee, well, I've also looked at the stats of the other dumping.  I average
 about 3 PGD's if I've been drinking beer and coffee, 2 otherwise).
 
 Method:
 I estimated throwing percentages (with a high stall count) for three
 categories of thrower (great, average, and poor) for four different length
 passes (40,20,10, and -5, with four different rates for the dump), then
 estimated scoring rates for three types of teams (great, average, and poor)
 from 5 different spots on the field (10,20,40,60, and 70 yards away from
 scoring).  I thus estimated the team's chances of scoring for each choice of
 throw.  I included a penalty for short turnovers to reflect the fact that the
 other team will have less ground to cover to score.
 
 The percentages I uses:
 
 Chance of scoring from the x yard line
 Yard line   70  60  40  20  10
 Great team  .5 .57 .71 .86 .93
 Average     .3 .4  .6  .8  .9
 Poor        .07 .2 .47 .73 .87
 
 Chance of a player completing a y yard pass
 Yards   40  20  10  -5 (4 different ones)
 Great   .4  .75 .85 .98 .95 .9 .8
 Average .3  .6  .75 .98 .95 .9 .8
 Poor    .2  .45 .6  .98 .95 .9 .8
 
 At first glance, these completion rates may appear low.  However, they were
 chosen to reflect the difficulty of completing a pass at a high stall count,
 which is when the dump should be used.
 
 Simplifying assumptions:
 1.  Scoring rate is 100% at epsilon yards away from the goal line, and
 decreases linearly with every yard further away.
 
 2.  Completion rate for a particular throw is independent of location on the
 field.
 
 3.  Everything is linear.
 
 Other relevant data:
 At Nationals this year, the Open division had a completion rate of 88%, and
 the Women completed 82.5%.  Goal scoring rate was about 90% once a team
 crossed the 10, about 35% from their own goal line.
 
 Results:
 I have the full matrix available (perhaps I'll post it later if there is any
 interest), but I'll summarize the trends.
 
 1.  In almost all situations, when the dump completion rate was at least 90%,
 the better team strategy was to dump.  The primary exception was when the
 thrower was in a class higher than the team (great thrower on average team,
 for example).
 
 2.  A great thrower on a poor team will help the team more by throwing it
 downfield at 75% or 85% than by taking a 100% dump.
 
 3.  On a great offensive team, even a great thrower will help the team by
 dumping it.  Even if he can complete 85% of his 10 yard stall 8 throws, which
 is extremely unlikely, he would only need to complete 95% of his dumps to
 come out ahead.  If he is deciding between a 75% 20 yarder and a dump, the
 break even point is between 91 and 93%.
 
 4.  Poor teams tended to benefit more by dumping near the goal line, and
 taking the riskier throws away from the goal line.
 
 
 Conclusions:
 Being able to dump will increase a player's value to almost every team.  A
 high percentage dump pass, even though the team is further away from scoring
 than before and thus will have a lower likelihood of scoring, is often the
 best option available.
 
 In general, if a team is likely to score, a conservative option should be
 chosen.  If a team is unlikely to score, the higher risk, higher gain pass
 should be taken.
 
 If you reran the numbers using completion rates at all stall counts, the dump
 would probably be advantageous only for poor players on good teams.  But this
 article is looking at the use of the dump as a high stall count option.
 
 Comments and discussion are appreciated.  Recommended topics:  validity of
 assumptions and how they would affect the results, completion percentages,
 scoring percentages.  Effect of defending the dump.
 
 Jim Parinella
 
 
 ---End of forwarded mail from Daffyspond@aol.com
 
 
 

Wil Stark, wstark04 (at) pobox _dot_com

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