Tag Archives: statistics

Yodely GuyThese days, Sue and I usually have lunch together over an episode of The Price is Right.  It is just and proper that we do so — we are both over sixty, we enjoy Drew Carey, and we like to compete with each other.  After a few months of comparing our guesses in the showcase round, I proposed that we have an official 100-showcase tournament: Sue and I would make our guesses for each showcase, and the person closest to the actual price without going over would win that showcase.  If we both overbid, there would be no winner. Here are our results, along with my rules-of-thumb for guessing showcase prices and a few other interesting findings.

How we guessed our guesses

A showcase generally comprises a low-priced item ($1000-$3000), a mid-priced item or bundle ($5000-$8000), and a high-priced feature item like a car or boat ($15,000-plus).  Sometimes, instead of offering a big-ticket item, the producers will put together a package of variously-priced vacations. The key to a good guess is knowing the rules-of-thumb for pricing vacations and the more expensive items.  I based the following rules on personal experience — the TPIR episode database does not go into enough detail for me to provide item-by-item price statistics.

VACATIONS:  Showcase vacations range from three-night stays in nearby cities such as Las Vegas or San Fransisco to six-night trips halfway around the world.  A reasonable starting point for a TPIR vacation price is $4000, plus $1000 for every time-zone change from Los Angeles to the destination.  You might add $1000 for big cities like New York, London and Paris.  For showcase purposes, I figure six nights for two people to Cancun is about $5000; Boston or New York at $7000-$8000; the Caribbean at $8000; Europe at $11,000-$12,000; and Fiji, Bali, Thailand or New Zealand at $13,000-$14,000.

Fridge with three doors and bow tieKITCHEN APPLIANCES: For the standard set of stainless-steel appliances (dishwasher, range, microwave and refrigerator), I start at $5500-$6000.  I may add another $1000 if the fridge has a third door or the range has custom features.

MOTORCYCLES: My rule-of-thumb is $2500 per 200cc of engine size.

JET SKIS: Some showcases may include one large jet-ski (always with trailer) or two smaller jet-skis, but either way I throw in $8,000.

BRAND NEW CARS: Someday, inflation will make this rule-of-thumb obsolete, but right now a very good baseline guess for showcase car prices is $10,000 per liter of engine size.  If the trim-line is L (luxury) instead of S (standard), add another $1000.  If the car is made by a German corporation (BMW, Mini Cooper, Volkwagen), add $2000 — they are always more expensive than they look.  For a Kia or Dodge, subtract $1000, as they are cheaper than they look.  For SUVs, add $3000-$5000, depending on the manufacturer.

BOATS: I have had a hard time coming up with a pricing rule for this category.  There are sailboats, pontoon party boats, jet boats and motor boats.  They are almost always 15 to 17 feet long, so pricing by the foot ($1000 per foot, plus $1000 for the trailer) only takes you so far.  I usually add $2000-$4000 if the boat has a big motor, looks especially muscular, or the announcer includes the word “deluxe” in the description.

100 Showcase Tournament ResultsAnd the winner is…

After 100 showcases (click chart at right), I had won 43 (just call me champ), Sue had won 30, and we both overbid on 27.  I overbid more often than Sue, but my guesses were usually closer to the actual price.

You know me: I had to go full-costume nerd with our tournament data, and in doing so gained some insight on bidding behaviors.  I started by plotting the over-under errors of our guesses vs. the actual prices, and was surprised to see that our data clusters looked pretty similar.  [On the graph below, the bold horizontal line denotes zero error — overbids are plotted above the line, underbids below.]  Our trend lines (blue and gold) show how we both tend to overbid lower-priced showcases and underbid higher-priced ones.

Showcase Error vs Actual PriceWhile I was a bit more accurate than Sue at the high end, we were both prone to overbid on showcases less than the median price ($26,897).  I think I can explain this as an example of anchoring, a cognitive bias first described by Tversky and Kahneman (1974). Anchoring takes place when a typical price or price range is established ahead of time.  The anchor price sticks in one’s mind and influences one’s later estimates.

In the weeks before our tournament, Sue and I obviously obtained a feel for the price of a typical showcase.  I surmise that, with this anchor price in our minds, we unconsciously adjusted our lower bids up toward the anchor and our higher bids downward, so that they deviated less from the norm.¹  In fact, I recall that, when making some of my high guesses, I found myself thinking, “It can’t be worth that much!”

It would be interesting (to me, anyway) to see whether other experienced players would reproduce this over-under tendency.  My guess is yes.

That’s too much!

Our showcase overbid rates (40% for me, 32% for Sue, 27% double-over) were well above the 25% overbid rate and the 6% double-over rate of last year’s TPIR contestants.  Why?  What does this say about our bidding?  Can these questions even be answered?

In my effort to explain our overbids, I must have read (or slept through) over two hundred articles and lectures on game theory; I learned about probability density, the Liebniz rule and Bayesian auctions; and I scratched out page after page of calculations (most of which were dead ends).  I even programmed a showcase simulator to help me test strategies.

In the end, I finally did find the optimum TPIR showcase bidding strategy — but it is far too detailed to describe in this post.  I intend to publish my solution in the next few weeks, as soon as I finish my analysis of showcases involving opponents of different skill levels.  In the meantime, however, I can offer my readers the following first-order approximation: when the players have roughly equal estimation skills, each should bid the lowest possible price that his or her showcase could be worth.  Why?  Because it is far worse to overbid your showcase (instant loss) than it is to underbid and hope that your opponent will either overbid his showcase or underbid his by more than you did yours.

But what about players with unequal estimation skills?  In this case, the less-skilled player will have to bump up her bid (and accept the risk of overbidding) if she wants to maximize her chance of winning.  The worse her relative skill level is, the closer her bid should be to her midpoint estimate.

The specifics will be discussed in my upcoming paper.  You will assuredly be notified here when it is ready.

One last comment about overbid rates.  If the population of TPIR contestants were equally divided between minimum-bidders and midpoint-bidders, and the showcase players were drawn from this population at random, then the long-term individual overbid rate would be 25% and the chance of both players overbidding would be about 6%.²  This is very close to the game statistics cited above.  Coincidence?  Probably.  Without doing post-showcase interviews, it would be impossible to say what bidding strategies the players actually used.

I can say this about my relatively high overbid rate: unlike actual contestants, I did not bid conservatively.  I didn’t fear going over, as real players do, because there was no money at stake, nothing to lose.  In fact, it was far more rewarding to me when I made a really close bid (within a few hundred dollars) than it was to win with a bid that was off by thousands.  It’s akin to how I play Scrabble — the fun part is playing killer seven-letter words and the score is secondary.  So it makes sense that my overbid rate would be greater than that of typical contestants.

Punch a bunch of hundreds

Finally (as George Gray likes to say when introducing the big-ticket item), we come to the last pearl of wisdom in this post.  In our 100-showcase tournament, Sue rounded her guess to the nearest thousand dollars (as most contestants do) a total of 99 times.  I did so only 10 times — in my other 90 bids, I added an arbitrary number of hundreds.  There is a good rationale for this, and it has to do with the double-showcase rule — if a contestant’s bid is within $250 of his or her showcase (without going over), the player wins both showcases.

In our tournament, we did not award ourselves double points for bidding closer than $250, but doing so was an ego-boost nonetheless.  As it turned out, I would have won a double-showcase four times out of the 100 showcases that we bid on.  (I overbid by less than $250 another four times.)   For comparison, last season on the show there were only five double-showcase winners among 380 players.  This means I was three times more likely to be a double-winner than were the contestants on the show.

Final Showcase DigitsAs I mentioned earlier, this is partly due to my aggressive bidding, but I also found that it is just as important to avoid bids that are rounded to the nearest thousand.  The chart at right (click to zoom) is a breakdown of the final three digits of the showcase prices in our tournament.  Note — there was not one showcase whose price ended in 250 or less.   Coincidence?  Not this time!

The producers of the show obviously caught onto the fact that most players round off their guesses to the nearest thousand — so the easiest way to keep players from winning both showcases is to make sure all showcase prices end in something more than $250.  The last time a player won a double-showcase with an even-thousands bid was in 2011.  Since then, most double-showcase winners made bids that ended in $500.  My recommendation is to finish off your guess with $251, until the producers catch onto this trick too.

Hope you liked this, because it’s the last post we have

Well, it’s the last post for this year anyway.  I hope your last ten minutes spent here were informative and will help you make better showcase bids the next time you are sick and staying home watching daytime television.  Credit for TPIR game statistics is due to the fan websites The Price is Right Stats and The Price is Right Wiki.  Have your pets spayed and neutered and let’s try to make it through 2017 without going over.

______________
[1] Interestingly, the anchoring effect also implies that an experienced player may be at a disadvantage compared to someone coming in cold who is familiar with prices but unaware of previous game results.
[2] If the population of players were evenly split between min-bidders and mid-bidders, there would be a 25% chance that two given showcase contestants are mid-bidders, a 50% chance that Player A will overbid, and a 50% chance that Player B will overbid.  The product of those probabilities is 6.25%.
More in  Life | Tagged , , , , | Be the next to comment  | Subscribe