Repdigit Numbered Teams

FIRST General Forum
1

Repdigit numbers are those expressed by a single repeated digit, such as 11, 22, 33, …, 111, 222, …, etc.

Retention for all team numbers is somewhere in the neighborhood of 1226/2235 = 55% per today’s registration figures.

For repdigit numbered teams, retention is a bit higher. Six repdigit teams appear to be inactive: 44, 55, 77, 99, 666, and 777. Fourteen repdigit teams are active: 11, 22, 33, 66, 88, 111, 222, 333, 444, 555, 888, 999, 1111, and 2222. So retention for repdigit teams is 14/20 = 70%. Or 13/18 = 72% if we neglect 666 (which may never have existed) and 2222 (a 2007 rookie).

Are repdigit numbered teams more likely to succeed?

2

no

3

Just having the percentages isn’t really enough, you need to show that there is a statistically significant improvement over picking teams at random. That is, if I picked 18 teams at random, what is the variability of that group’s retention rate?

Come to think of it, that’s a pretty easy stats problem that I could do if it hadn’t been 2 years since my last stats course.

So basically, you are choosing 20 teams at random, each of which has a 55% chance of succeeding. We are asking “what are the chances of 14 or more of them being retained?”. So we have 20 independant trials, and want to know the chances that we will have 14 or more successes.

Probability(14 or more successes) = prob(14 successes) + prob(15 successes) + prob(16 successes) + prob(17) + … + prob(20)

The binomial distribution can tell us the probability of a given number of successes:
prob(k successes out of n) = (n choose k)(Probability of success)k(Probability of Failure)(n-k)
Example: prob(14 of 20) = (38760)(0.55)14(0.45)6 = around 0.07.

Repeat that for 15,16,17,18,19 and 20, then sum to find the answer.

Answer: The probability that a randomly chosen set of 20 teams has 14 or more of them still in the competition is 12.9%. So this really isn’t THAT unlikely. There are many numerical patterns (in fact, 12.9% of ALL patterns) you could pick that would have a similar retention rate. To show that your hypothesis of “Teams with patterned numbers retain longer” is more likely, pick more numerical patterns and see if the average retention rate is still high. If you can specify a picking pattern that results in a 70% retention rate after 50 or 100 teams, then the probability of something odd going on with those teams rather than random luck gets much higher.

4

Number in my opinion has nothing to do with it. It has to do with more of a team’s foundation and how they stand and their resources as to what number they are.

If you choose any random numbers between 11-2222 I bet that you will see that there are MANY gaps where there were teams and where they no longer exist.

Pavan.

5

Your assumption is correct, Richard – 666 was never assigned, as far as I’m aware.

6

All successful teams are repdigit numbered, when viewed from the right perspective. This is because any team number can become a repdigit, if it is expressed in base-N. Of course you need to choose the right N.

For example, 931 (base-10) becomes 777 (base-11). Or 111 (base-30). :cool:

7

Interesting…

Despite the statistics lesson; which was fantastic, thanks, Bongle; there might be another reason for a difference in the retention of repdigit teams as opposed to a random team, and that is that the repdigit teams are biased more towards the low numbers - there are 9 from 1-10 (which you neglected, Richard), 9 from 11-100, and 9 from 101 to 1000. This means that, for all teams started after 2000 (team number 200-something), the older a team is, the more likely it is to be a repdigit. In addition, for teams older than that, the earlier in the alphabet a team’s sponsor’s name is (or was in 2000), the more likely it is to be a repdigit. I’m not sure about backfilling team numbers after teams drop out, but that practice might have happened for a while, and then been abandoned. Anyone with more details care to comment?

8

It was never used.
http://www.usfirst.org/frc/map/index.lasso?page=teaminfo&team=666

9

there’s no correlation.

10

Wow! Richard, I think you have formally been out-statistic-ed! :ahh:
I never though I’d see that day! :smiley:

11

The last line of my starting post was in the form of a question, not a conclusion. :wink: The question contained a challenge, which Bongle nailed. :cool:

And my original post contained no mathematical reasoning; only some bare data, arranged as it might be seen in an advertisement.

For another example that illustrates how sound statistical reasoning trumps sloppy inference from bare data, see the birthday problem. Briefly, given a classroom with N students, what is the probability that two of them have the same birthday? Many a statistics professor has used this one on the first day of a new class. And many a student has been surprised by the result.

My inspiration for the challenge was a stochastic processes professor, long ago, who told our class that “gambling is a tax imposed on those with poor math skills.” The highest praise we could get from that professor was “you will be tax-exempt.”

Statistics won’t predict the future but they will tell you how you should bet. Most of us have a hunch that the form of a team’s number shouldn’t be predict the team’s performance. Bongle’s post showed that this is more than a hunch – it is mathematically defensible.

Playing hunches is reckless. Playing the odds makes you a gamer.

12

Repdigit numbered teams are not more likely to succeed, but sequential numbered teams are:

45, 67, 234 :wink:

Oh, maybe that is just because these are from the midwest powerpod and it has nothing to do with sequential numbers —

If FIRST goes back to a four team game, i hope to be partnered with teams 1, 567 and 890 -

How cool to hear Blair announce 1-234-567-890 !

13

What about partial repdigit teams–such as 330, 599, or 1197?

14

Any team in the 1100’s or 2200’s is sure to be one of those rep teams by default.

Perhaps we have to define a repitition team this way

x = digit a
y = digit b

x (1,4,5,7,8,9)
xx (11,22,33,66,88)
xxx (111,222,333,444,555,888,999)
xxxx (1111,2222)
xyy (100, 122, 133, 144, 155, 166, 177, 188, 211, 233, 244, etc.)
xyxy (1414, 1717, 1818, 2121, etc.)
xyx (101, 121, 131, 141, 151, 161, 171, 181, 191, 202, 242, 252, 262, etc.)

By these definitions, there are a large number of rep-digit teams. It does not always mean that they are successful, but they have interesting numbers that are awesome to look at and read (even if you don’t know their names).

15

how about them prime number teams? how well do they do?

16

Or xxyy, like … oh, wait a minute, I’ll come up with one.