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BS: HELP math probability question

03 Apr 01 - 09:37 AM (#431974)
Subject: HELP math probability question
From: John Hardly

I am having WAY too much trouble trying to express the nature of a math problem/practical dilemma.

My wife runs our dogs in agility trials (think obstacle courses for dogs). I could describe the courses but that part is immaterial to the math question.

The dog runs the course for accuracy (on the obstacles) and TIME. Time is where the math problem comes up.

The course is measured for distance in feet and there is a fixed chart to determine the time UNDER WHICH THE DOG MUST COMPLETE THE COURSE in order to qualify.

Unfortunately, though the judge is a paid professional, the timer is usually a volunteer from the hosting training club.

It is sometimes hard for the judge to convey to these volunteers how critical it is that the time for each dog's run be read to the judge in EITHER seconds, or MINUTES AND SECONDS---but it MUST BE CONSISTENT. For instance 1:02 is ONE MINUTE and TWO SECONDS, or it is SIXTY-TWO seconds.


The courses are always less than 2 minutes, but rarely less than one minute.

Here's the question.
What is the range of course time to relative dog's running time that will create the most plausible wrong readings when the volunteer timer reads the times inconsistently?

For instance, a dog that runs an 85 second course in 65 seconds but has the timer read it to the judge "one-oh-five", rather than coming in 20 seconds under time, instead gets credited with a 20 second over time run.

One other factor that contributes to the confusion. The dog has to score 170 out of a possible 200 points. If he is over time he may still qualify, as he will only recieve a point-per-second deduction.

Clear as mud?

thanks in advance (I didn't know who else to turn to and knew several of you have hashed out math problems before).---JH

03 Apr 01 - 09:45 AM (#431981)
Subject: RE: BS: HELP math probability question
From: Murray MacLeod

Mmmm, I think I understand what it is you are asking, John, but my initial reaction is that the volunteers should be instructed to report all the times in SECONDS only. How difficult would that be?

Murray

03 Apr 01 - 09:48 AM (#431983)
Subject: RE: BS: HELP math probability question
From: Murray MacLeod

I mean, of course, the actual running time in seconds

Murray

03 Apr 01 - 10:03 AM (#431990)
Subject: RE: BS: HELP math probability question
From: Bert

I would guess around 9/59

03 Apr 01 - 10:06 AM (#431991)
Subject: RE: BS: HELP math probability question
From: UB Ed

Impossible to assign probability without know percentage of time they are wrong versu total number of trials. But, there is the simple relationship whereby there should be a consistent 40 second differential. If the absolute time is 60 seconds and the timer calls out one, oh, oh (100) and the score keeper records 100 seconds (and does this consistently enought ot be discovered), the correct time could be calculated by merely subtracting 40 seconds. If the absolute time is 90 seconds and the call is "one thiry" and 130 is recorded, subtract 40.

03 Apr 01 - 10:12 AM (#431994)
Subject: RE: BS: HELP math probability question
From: campfire

John -

I had to read your post twice before I realized how "one-oh-five" could mark a dog twenty seconds over.It might help if you included the "obvious" sentence that you've left out, that "one-oh-five" could be interpreted as 105 seconds when only heard, not written out.

If the volunteers are from the club, do they also have dogs competing? If their dogs get scored incorrectly a few times, they'd probably be more careful. ;)

Maybe have a session with the volunteers with examples of how confusing it could be - you could call out times to the volunteers and have them interpret what you meant. Then tell them the "correct" answer. Sometimes seeing the problem first hand is what it takes to correct it.

Or develop a format of always using minutes and seconds, even if the score is then "O minutes, 59 seconds".

It's not feasible for practice meets, but the bigger trials have a large digital clock that the judge (and the audience) can see, eliminating any confusion.

Unless you just wanted a math answer to the question, in which case the time will always be 40 seconds over the real time if the score is between one minute (60 seconds) and two minutes (120 seconds) and 80 seconds over if the dog runs over two minutes, say, in 2:02 (122 seconds, not 202 seconds).

I'm not sure what you mean by the "most plausible" error - one the judge won't catch on his own? I would suppose that the closer to one minute the dog runs, if the judge is watching at all, he would realize that the timer meant 1:02, not 102, and that for the slower dogs, the error might not be detected.

Still clear as mud.

campfire

03 Apr 01 - 10:19 AM (#432003)
Subject: RE: BS: HELP math probability question
From: Bert

The problem is rather loosely defined. My guess was based on...
Times, generally range from one minute to less than two minutes which gives a 59 minute range.
Therefore there is no chance of error for numbers greater than 119.
One minute would normally be called as such.
So errors could only be made on calls from 101 to 119
If calls are randomly inconsistent about half in the range of 101-119 could be misconstrued.
So thats 1/2 of 19 divided by 59. Strictly speaking, 9 and a half, divided by 59. Somewhat less than 1/6th.

03 Apr 01 - 10:36 AM (#432018)
Subject: RE: BS: HELP math probability question
From: John Hardly

campfire,

I think you are right. The quote from you (below) Is VERY important to the understanding of the dilemma.

"I had to read your post twice before I realized how "one-oh-five" could mark a dog twenty seconds over.It might help if you included the "obvious" sentence that you've left out, that "one-oh-five" could be interpreted as 105 seconds when only heard, not written out."

Also important is that the error is not caught if the dog qualifies. The owner/handler may have though he scored a better time but will probably not question it if his dog still qualifies. That's why when this happens it often goes undetected.

Murray,
ALWAYS reading is absolutely the best way. But I remember my experience as a timer once trying to explain the importance of this to both judge (obviously no math wiz) and scoring table alike and getting that look from everyone that says "Why are you making such a DEAL about this?!"

My 9 1/2 year-old boy (not much time left in his life to get his final title)is now "running for points" and just got robbed by this this weekend. Fortunately, we have a video of it and I am going to try to appeal it to the United Kennel Club.

I do think there is a range of dog's running time to the course time that is least likely to "raise red flags" that something is amiss. I'm just not sure how to express it. I had noticed the 40 second constant discrepancy, I just don't know where the course time relative to the switching from misunderstanding seconds for min/sec readings causes the most plausible (wrong) time. I know it has to do with the 30 second lee-way allowed for a run to still qualify.

THANKS AGAIN!!!

03 Apr 01 - 12:22 PM (#432123)
Subject: RE: BS: HELP math probability question
From: Peter T.

You obviously need a watchdog. Sorry, I couldn't resist, this is the one time in my life when I get to use this joke.

yours, Peter T.

03 Apr 01 - 12:48 PM (#432145)
Subject: RE: BS: HELP math probability question
From: Murray MacLeod

Or perhaps a Clocker Spaniel

Murray

03 Apr 01 - 02:17 PM (#432259)
Subject: RE: BS: HELP math probability question
From: Mary in Kentucky

John, I'm still not sure that I understand your question or the problem.

Are you trying to explain it to one person or a committee? Is it for a specific appeal or a campaign for rule and procedure changes due to anticipated errors? Seems to me like you want to give a persuasive speech in which case I'm not sure you really want to get into mathematical illustrations. If it's an appeal, just show where there was a mistake.

I understand the 40 second discreptancy. That is, in a 1 to 2 minute race, a misinterpreted time will always be 40 seconds off. How can this not be noticed immediately? It seems that the audience would realize a 40 second (out of 2 minutes) mistake immediately. Is the total time (running time) not publicly reported? (perhaps just a score which takes into effect other factors?)

Your question as to whether there were ranges or instances where this wasn't as noticeable....I would have to have specific information on just how the scoring was determined. Then you could always write an equation and find maximum and minimum times. (determine the slowest time coupled with whatever other scoring points there are that would still give a passing score.) For illustration purposes you could just write down the rule (function) then just "plug and chug" numbers to observe what happens. All this data in a table would illustrate trends which don't have to be analyzed with calculus. If you are making a persuasive speech, this may be the best tactic.

Clear as mud? It you want more info, let me know. I think we could do all kinds of things with this illustration, but I suspect a persuasive speech is more in line with what you really need.

I could also send along some Yorkshire Terrorists to help. Or do you need some Whippets to whip up on 'em? (Your're not coursing Whippets are you?)

03 Apr 01 - 02:24 PM (#432263)
Subject: RE: BS: HELP math probability question
From: Amos

This is not a problem in math so much as in process engineering. ONE standard of communication for allparticipants in a given dialogue usually works better than having to introdice a real-time analyze-and-translate-if-necessary loop. Why not have a standard report in SECONDS ONLY and require the timer to write it down before h/she reports it, so there is no fuzziness about the step from the stopwatch to the reported number?

A

03 Apr 01 - 02:55 PM (#432289)
Subject: RE: BS: HELP math probability question
From: GUEST

It's not really a maths problem, simply becauase to tackle it mathematically is quite complex, and the easy way to do it is, as was suggested earlier, to make all readings in seconds; train up your volunteers to be able to do this. You gave us only one example - of an 85 second target. Here though errors could be made by taking one o five to be one hundred and five seconds, the dog would still qualify by getting 180 points ie a time penalty of 20 points. The only dogs that would lose out would be those with times of one sixteen to one twenty, since they would get time penalties over thirty points. Since these could in fact be times of seventy six to eighty seconds, ie reasonably close to the target timee, it seems to me that it would disadvantage mostly the better dogs in the race.

The proportion of dogs disadvantaged in a race targetted as , say 95 seconds would be different.A dog 'on target' here, with given time one thirty five, could be given a time penalty of 40 points, which would eliminate it. Don't your timers use standard stopwatches? Surely that could solve the problem, since the recorded times could be read after each event without undue pressure.

03 Apr 01 - 03:42 PM (#432337)
Subject: RE: BS: HELP math probability question
From: IvanB

A consistent way of announcing time would be great, but many stopwatches show elapsed time as minutes and seconds. Although it'd seem almost a no-brainer to add the 60 seconds on (for times over a minute) and announce the time in seconds, it opens another door for error. I'd suggest that times announced as minutes and seconds be read as "one dash oh five" (for 1:05). I suggest "dash" only because it seems easier than saying "colon." Anything that creates a mental split between the numbers would work.

03 Apr 01 - 03:51 PM (#432347)
Subject: RE: BS: HELP math probability question
From: Murray MacLeod

Ah, Ivan, you have stumbled on one of my pet hates. I can't stand it when the digit "zero" is referred to as "O". But yes, with that minor modification yours is a very sensible suggestion.

Murray

03 Apr 01 - 04:27 PM (#432385)
Subject: RE: BS: HELP math probability question
From: IvanB

Murray, I'm four square with you on the zero question, and, if reading a telephone number, zip code, etc., would always read it as "zero." However, it seems to be a well established convention that times, whether time of day or an elapsed time reading, is read as "blank oh blank" for anything under ten.

03 Apr 01 - 06:10 PM (#432493)
Subject: RE: BS: HELP math probability question
From: John Hardly

Mary and all

thanks. I was trying to come up with a way of proving to both United and American Kennel Clubs just what a problem not having this communication standardized can be.

I wanted to submit a proposal to change their rules to reflect this but I thought I could come up with a well reasoned example of the problem. As you suggested, all I could come up with was your suggested "plug and chug" with examples.

I'm pretty sure the only reason that the discrepancy often goes unnoticed is because only the 4 dogs who place seem aware of their times. The others only want to know if their scores qualified. The reason I sat up and took notice is that when a dog is "going for points" his window is narrowed from the 30 for qualifying, to only 5 (he must score at least a 195 to score points.)

Thanks for sharing your logic with me. I've always been kinda math-challenged :o)

03 Apr 01 - 06:18 PM (#432502)
Subject: RE: BS: HELP math probability question
From: GUEST

Get an electronic stop watch; read it directly. Needs no interpretation

03 Apr 01 - 06:57 PM (#432539)
Subject: RE: BS: HELP math probability question
From: Chicken Charlie

John--

This is not a probability problem; this is a communication problem. I mean, are you really interested in the percentage of mistakes made, or do you want to know which specific instances are ambiguous?? If you TRULY want a probability, it's just the number of errors divided by the number of trials. The answer will be a fraction. Multiply it by 100 to get the percentage.

Or get her a cat for Christmas?

04 Apr 01 - 07:54 PM (#433378)
Subject: RE: BS: HELP math probability question
From: raredance

I guess like the guest right above, I don't see why there should ever be a problem. Stop watches are calibrated in minutes (2 places) - seconds (two places) - and often hundreths of seconds (2 places). The numbers 6, 7, 8, and 9 do't even appear in the left most column for each of the units. Read the watch and write it down. Times of 61 or 75 or 90 do not occur on a stop watch. "one-zero-five" is always 1:05 because there aren't three digits in the seconds column. "one-forty-seven" is always 1:47 My son ran track for years in high school and college, I went to lots of meets where events were timed. It was never and issue. Read the watch and write it down. If you have to add or subtract something for style, do it after the time is written down. Olympic equestrian events use the same principle, record the time and subtract penalty seconds for knocking over jumps etc.

rich r

04 Apr 01 - 10:17 PM (#433423)
Subject: RE: BS: HELP math probability question
From: MichaelM

I work in the construction industry. There are a number of standard styles that everyone uses. I measure for window coverings with a tape that reads only in inches ( 12,13,14 ...) You always write down measurements width first. We had a printer do up a work order form for us and they inadvertantly reversed the length and width columns. We took them anyway but six months later (after a couple of episodes of working with expensive material that ended up as side drapes 96" wide and 30" long) I threw them all away. Your competition needs a standard timer. I can see why the difference between 59 seconds and 1.00 minutes looks dramatic.

Michael

05 Apr 01 - 12:38 AM (#433498)
Subject: RE: BS: HELP math probability question
From: GUEST,#1

An electronic stop watch that is thumb operated is a poor way to measure accurate times. You need a suitable light, good fast photocell, amplifier, then a Schmidt trigger or comparator to gate a counter of standard frequency quartz crystal oscillations (3rd rate here, use WWV for higher acuracy). Just use a decimal point after every two digits. hours.min.sec.sec/100.sec/10000.sec/1000000, etc.

Of course if the first is a millenium or so long you have to use more than two digits for the hours part. Just remember that all before the 1st decimal point is hours.