Distribution of 3Play Scores
by Kirk Allen
January 26, 2000
I assume that most of you do the ESPN 3Play.
Hey, it's like a free lottery ticket, so why not? After "playing" it almost every day for the past
6 or 7 months, I somehow became intrigued by the distribution of my scores. I figured it was probably
somewhat normally distributed (bell curve) since most things seem to be. I decided to investigate.
Looking back through the history of my scores, I decided I would look at my daily percentile
ranking. I did this instead of the raw score because, for example, a score of 1000 might be 40% one day
and 65% the next day. It just depends on the nature of the sports going on that day. ESPN obviously
makes an adjustment also since the daily bonus threshold changes.
About 7 months of nearly daily play gave me 184 scores to work with. A sample anywhere over
50 would probably be sufficient, so this is more than enough. I was a bit surprised by the results,
presented graphically below..
The average percentile turned out to be 48.48, which is close enough to 50. The range with
the greatest number of scores was the 45-49.9 range, which is also fairly centered. These results
were expected. What surprised me was the overall spread of the data. Except for 3 large spikes
near the mean, the distribution is seemingly random.
I believe the reason for his seeming randomness is the all-or-nothing nature of 3Play. This
is especially relevant with hockey and baseball players. If you get Mark McGwire and he's 0-4,
you get zero points. Even if he hits a double and gets 2 walks, you probably get zero. But if he
hits a homerun, you may get 500 points, which is usually enough to put you into the 20 percentile
range. Similarly, hockey players are usually awarded points only for goals and assists (maybe a
few points for taking a shot). The results are not so extreme in basketball because points, rebounds,
etc. are easy to come by in small numbers, so even a bad game by your player will get you something.
This seems to explain the distribution pretty well. Out of your 3 players, you have to figure
at least one will get you at least something (20 percentile range). Maybe you have one big game or
two average games (50 percentile range). If you're lucky, you can get all three guys to produce
(75 percentile). If you're REALLY lucky, you'll get maybe 3 great games to reach over 90 percentile.
Obviously, your chances of winning are miniscule considering the number of people who play. This
was basically done just out of curiousity with the sole of intent of curing a little boredom.
March 26, 2000
I had a little more free time, so I added my scores for the last few months (243 total scores).
Here is the updated chart, in the same format as above..
The data perhaps became slightly less centered, but there is not alot of movement overall.
The mean is 49.3, slightly closer to 50 than before. The 45 - 49.9 range remains the largest, but
two other ranges are barely behind. To examine how centered the data was, I also tried using larger
ranges..
Now it appears that there is very little centering of the data. The two middle ranges (40 - 49.9
& 50 - 59.9) are still highest but only by a slight margin. In the future, I may examine the
predictive nature of 3Play scores. For example, if you do good one day, does this increase/decrease your chances
the next day? Does it affect your bonus card? Or is it truly random? I am pretty sure it's random, so I doubt I can
prove otherwise..
3Play is a copyright of ESPN Internet Ventures
copyright 2000, Kirk Allen