# Math Help - Library Contest Edition

May 10, 2012 7:34 AM Subscribe

Math Help! We're doing a big inventory project in my library this summer and we want to attach weekly prizes to it to help motivate the poor students who have to do all the scanning. Trick is, students do not work the same amount of hours per week, so we would like some way of weighting each student's output so that those that work less feel like they can compete with those who work more while not disadvantaging those with longer hours by requiring them to go insane in order to keep up. How to keep things fair and sane?

Here are the details:

I have 8 students competing.

Students are scheduled to work from 21 to 35 hours per week.

There is only so much inventory work a student can perform in a day before their brain leaks out their ears.

The output of the process includes:

Total linear inches of material inventoried.

Total amount of time spent inventorying in minutes.

Number of errors located during the process.

While total number of books is a possible output, the inventory system is prone to crashing, which means that information could be easily lost. We can set an average of 13 books/foot, though.

I'd like to be able to give out weekly prizes, plus grand prizes at the end of the project.

Is there some way of working the scoring system so that things are balanced between longer and shorter shifted students? Just dividing linear feet inventoried by hours worked probably won't cut it. For example, I don't want to end up in a situation where someone only works one 6 hour shift in a given week (vacation, illness) and inventories for 4 hours, thus handily beating the 35 hour student who spent 20 hours inventorying.

Here are the details:

I have 8 students competing.

Students are scheduled to work from 21 to 35 hours per week.

There is only so much inventory work a student can perform in a day before their brain leaks out their ears.

The output of the process includes:

Total linear inches of material inventoried.

Total amount of time spent inventorying in minutes.

Number of errors located during the process.

While total number of books is a possible output, the inventory system is prone to crashing, which means that information could be easily lost. We can set an average of 13 books/foot, though.

I'd like to be able to give out weekly prizes, plus grand prizes at the end of the project.

Is there some way of working the scoring system so that things are balanced between longer and shorter shifted students? Just dividing linear feet inventoried by hours worked probably won't cut it. For example, I don't want to end up in a situation where someone only works one 6 hour shift in a given week (vacation, illness) and inventories for 4 hours, thus handily beating the 35 hour student who spent 20 hours inventorying.

Does everyone work the same shift? Give two prizes (1) Most inventoried in one week, and (2) Most inventoried in any one shift during that week.

posted by muddgirl at 7:39 AM on May 10, 2012

posted by muddgirl at 7:39 AM on May 10, 2012

I think you should just go with number of errors discovered. Students who do more inventory will find more errors than students who work more hours. If you reward them by shelf-inches inventoried, you're giving them an incentive to rush.

Another idea: have a "inventory is over!" party to celebrate when you're done.

And recruit students to help with weeding while they're inventorying - maybe give prizes for the "worst condition" book, the "most outdated" book, and the "most politically incorrect" book, udged by an independent panel of librarians? It makes it a little more fun and could help identify subject areas with bad collection coverage.

posted by mskyle at 7:42 AM on May 10, 2012 [3 favorites]

Another idea: have a "inventory is over!" party to celebrate when you're done.

And recruit students to help with weeding while they're inventorying - maybe give prizes for the "worst condition" book, the "most outdated" book, and the "most politically incorrect" book, udged by an independent panel of librarians? It makes it a little more fun and could help identify subject areas with bad collection coverage.

posted by mskyle at 7:42 AM on May 10, 2012 [3 favorites]

Different shift lengths - some work 4 or 5 one day then 8 the next, while others may work 9 hours a day but only for 3 days.

posted by robocop is bleeding at 7:42 AM on May 10, 2012

posted by robocop is bleeding at 7:42 AM on May 10, 2012

I wouldn't try to gameify this. That can get pretty demoralizing, in that horrible "you _must_ have fun!!1!!1" way that's so soul destroying.

I would:

posted by mhoye at 7:43 AM on May 10, 2012 [13 favorites]

I would:

- Give them free coffee,
- Let them pick the office background music and
- Bring in a box of donuts for whoever's there every few days, and
- Thank them at the end of their shift

posted by mhoye at 7:43 AM on May 10, 2012 [13 favorites]

Can't you just give one entry to each person who works in a given week? If the goal is parity (rather than giving an advantage to those who work more), just give each one entry.

Alternatively, if you want a more nuanced approach to incentives, give each person 100 entries per set category--i.e., feet of shelving categorized, errors, etc--whatever are your metrics.

Each person starts with 100 entries per category, assuming perfect performance, and you assume certain targets (i.e., 5 feet per hour). You then subtract out from that 100 the percentage shortfall (and possibly give bonus points).

So Person A worked for 10 hours and cleared 50 feet--gets 100 points. However, they had a 15% error rate, so subtract 15 from the error category. Total: 185 points between the two categories.

Person B worked for 5 hours, but only cleared 20 feet, so gets 80 points in the speed category. He had 15% errors, too, so gets another 85 points--a total of 165.

Then you draw the prizes based on the cumulative point entries.

posted by Admiral Haddock at 7:45 AM on May 10, 2012

Alternatively, if you want a more nuanced approach to incentives, give each person 100 entries per set category--i.e., feet of shelving categorized, errors, etc--whatever are your metrics.

Each person starts with 100 entries per category, assuming perfect performance, and you assume certain targets (i.e., 5 feet per hour). You then subtract out from that 100 the percentage shortfall (and possibly give bonus points).

So Person A worked for 10 hours and cleared 50 feet--gets 100 points. However, they had a 15% error rate, so subtract 15 from the error category. Total: 185 points between the two categories.

Person B worked for 5 hours, but only cleared 20 feet, so gets 80 points in the speed category. He had 15% errors, too, so gets another 85 points--a total of 165.

Then you draw the prizes based on the cumulative point entries.

posted by Admiral Haddock at 7:45 AM on May 10, 2012

Another risk of gameifying something like this, is that chances are a lot of the students won't care about that aspect, which defeats the point of making it into a game. I think letting them pick the music is a good idea. Maybe some weird weekly prize for the weirdest/best thing they find in the collection.

posted by kendrak at 7:47 AM on May 10, 2012

posted by kendrak at 7:47 AM on May 10, 2012

The students are the ones who came up with the idea of prizes - they just had a shelving contest with all the year end books. I surprised the winner with some movie passes and they seemed to really like it.

They knew that the inventory project would be a big part of their work if they got hours this summer, so it's not a huge surprise.

posted by robocop is bleeding at 7:51 AM on May 10, 2012

They knew that the inventory project would be a big part of their work if they got hours this summer, so it's not a huge surprise.

posted by robocop is bleeding at 7:51 AM on May 10, 2012

So, how was the shelving contest organized, since it seems like that was pretty successful?

posted by mskyle at 8:00 AM on May 10, 2012

posted by mskyle at 8:00 AM on May 10, 2012

I'd suggest a raffle. For every unit of output (and I'd ask the staff how they'd like the output measured. They know best), you get a raffle ticket. Each week, a ticket is drawn, and a prize is given, and then at the end, all the tickets are put into a big drawing for a big prize. That way, even people who work less are motivated by knowing they have a chance at winning, but more work ups your odds of winning. If you make it purely output-based, people who work less don't get to have any of the fun, and if you make it totally random, then it's not a contest, but a raffle with earned tickets strikes a balance between the two.

posted by decathecting at 8:04 AM on May 10, 2012 [1 favorite]

posted by decathecting at 8:04 AM on May 10, 2012 [1 favorite]

You could have two metrics: the amount of stuff done, and the rate at which it's done. In particular, maybe have

score1 = Total linear inches of material inventoried per hour (a rate)

score2 = number of errors detected

the guys who work many hours will have a higher score2 than those with few hours, b/c they'll have spent more time looking for errors. The guys with few hours are hopefully able to work faster, though, so they'll have a high score1, while the guys with many hours get burnt out and slow down.

One easy option is to have two prizes per week and two grand prizes: rate-based and magnitude-based. Another option is to scale these by their expected values:

score = ( score1 / expected score 1 + score2 / expected score 2 ) / 2

where the expected scores you somehow know. Expected score 1 is inches / hour you would be able to do yourself, maybe? expected score 2 is the average number of errors you would personally find?

posted by bessel functions seem unnecessarily complicated at 8:04 AM on May 10, 2012 [1 favorite]

score1 = Total linear inches of material inventoried per hour (a rate)

score2 = number of errors detected

the guys who work many hours will have a higher score2 than those with few hours, b/c they'll have spent more time looking for errors. The guys with few hours are hopefully able to work faster, though, so they'll have a high score1, while the guys with many hours get burnt out and slow down.

One easy option is to have two prizes per week and two grand prizes: rate-based and magnitude-based. Another option is to scale these by their expected values:

score = ( score1 / expected score 1 + score2 / expected score 2 ) / 2

where the expected scores you somehow know. Expected score 1 is inches / hour you would be able to do yourself, maybe? expected score 2 is the average number of errors you would personally find?

posted by bessel functions seem unnecessarily complicated at 8:04 AM on May 10, 2012 [1 favorite]

You could also seed some random Golden Tickets in a few of the books on the shelves and whoever happens to work that shelf would find it and get a prize. I wouldn't use this for the entire premise of the contest, but it might be a fun aspect to add in.

In general, though, I would let the kids decide what the rules of the contest should be. If they designed the shelving contest on their own, they can probably design this too.

posted by CathyG at 8:45 AM on May 10, 2012 [3 favorites]

In general, though, I would let the kids decide what the rules of the contest should be. If they designed the shelving contest on their own, they can probably design this too.

posted by CathyG at 8:45 AM on May 10, 2012 [3 favorites]

Some questions:

- Do you want to reward thoroughness or speed?

- Are the number of errors discovered mainly a function of the student's thoroughness?

- Is it the case that some sections will have a greater proportion of errors?

- Are some sections going to easier or quicker to process? (e.g. fatter volumes)

I suspect you'll want a simple system, with a number of different prizes.

Maybe a student has to put in a minimum of 20 hours to be eligible that week, and there are prizes for most inches, most errors, and greatest inches per hour.

Maybe the number of weekly prizes you earn could add up to some grand prizes at the end of the whole process.

posted by philipy at 8:54 AM on May 10, 2012

- Do you want to reward thoroughness or speed?

- Are the number of errors discovered mainly a function of the student's thoroughness?

- Is it the case that some sections will have a greater proportion of errors?

- Are some sections going to easier or quicker to process? (e.g. fatter volumes)

I suspect you'll want a simple system, with a number of different prizes.

Maybe a student has to put in a minimum of 20 hours to be eligible that week, and there are prizes for most inches, most errors, and greatest inches per hour.

Maybe the number of weekly prizes you earn could add up to some grand prizes at the end of the whole process.

posted by philipy at 8:54 AM on May 10, 2012

Every book shelved gives you 1xp. Start at Level 0 and level up every 100xp (adjust as appropriate - maybe have each level get further apart?). Every level gives you one extra ticket in the raffle at the end of the week. Maybe if you retain levels between weeks, have all the people who didn't win the main prize(s) get some random event (A dragon attacks! Gain 15xp!).

Ha actually decathecting already suggested essentially the same idea without the RPG gamification.

posted by EndsOfInvention at 8:55 AM on May 10, 2012

Ha actually decathecting already suggested essentially the same idea without the RPG gamification.

posted by EndsOfInvention at 8:55 AM on May 10, 2012

What about varying the prize metric each week? Week one is most errors caught, week two is fastest correct inventorying (I'm assuming you're scanning barcodes so it would be obvious if someone tried to speed their way through and skipped a bunch of books?), week three is most linear feet scanned, week four is total inventorying time.... And maybe keep the actual week/prize schedule unpublicized, since you wouldn't want the kids who aren't scheduled for many hours to totally slack on the week they don't have a shot at the most inventorying time?

Also, the random Golden Ticket idea is awesome. Maybe those could be entries into a raffle grand prize at the end?

posted by banjo_and_the_pork at 9:42 AM on May 10, 2012

Also, the random Golden Ticket idea is awesome. Maybe those could be entries into a raffle grand prize at the end?

posted by banjo_and_the_pork at 9:42 AM on May 10, 2012

I would suggest multiplying hourly productivity (linear inches / hours spent inventorying) by a score booster for each shift depending on shift length. For example, if you assume that the rate at which someone can work is constant for the first two hours and then decreases linearly down to zero at 12 hours, you get:

For shifts longer than two hours, scoring boost = 20/(22 - hours worked). This only works if you know how many linear inches were completed each shift, and tally the score for each shift separately.

posted by Earl the Polliwog at 9:56 AM on May 10, 2012 [1 favorite]

For shifts longer than two hours, scoring boost = 20/(22 - hours worked). This only works if you know how many linear inches were completed each shift, and tally the score for each shift separately.

posted by Earl the Polliwog at 9:56 AM on May 10, 2012 [1 favorite]

As far as error handling, I would just subtract a fixed amount of linear inches per error - corresponding to the amount of effort to correct an error. This would have to be done before scaling.

posted by Earl the Polliwog at 11:06 AM on May 10, 2012

posted by Earl the Polliwog at 11:06 AM on May 10, 2012

Why not divide every person's efforts by the hours they log? Then you're looking at the rate of work, not the total work.

This might be unfair to people working 8 or 9 hour days, because as you said, "There is only so much inventory work a student can perform in a day before their brain leaks out their ears." If this starts to seem unfair to people who work shorter days, go with different goals per week or two.

posted by filthy light thief at 2:10 PM on May 10, 2012

This might be unfair to people working 8 or 9 hour days, because as you said, "There is only so much inventory work a student can perform in a day before their brain leaks out their ears." If this starts to seem unfair to people who work shorter days, go with different goals per week or two.

posted by filthy light thief at 2:10 PM on May 10, 2012

Keep the game simple - two levels ought to suffice. One level can be the 'golden ticket' idea - it's random, it's spontaneous, and completely random. The other level can be based on units per hour. You can always award a prize to the one that works the most hours - or find a way to reward every student for the most, best, or something else.

posted by chrisinseoul at 8:03 AM on May 11, 2012

posted by chrisinseoul at 8:03 AM on May 11, 2012

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