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