# Puts you back on the winning trail

So, The Price Is Right finally (mostly) wrapped up its season. There's another stray episode to air in mid-August, but we can consider that as part of the next season. That is, if I do keep up statistics-gathering about who wins the Showcase Showdown and how the winners of the Showcase are revealed. I admit I've started to realize I don't know why I'm keeping this data anymore, other than that I've been doing it for a long while: I went back through my records and discovered that while I could swear I'd been doing this for only a couple years, I actually started keeping track in the middle of November 2008 for crying out loud. (That's of Showcase Showdown winners; of the Showcase reveals, that goes back only to January of 2009.)

But since I've got that let me give the Showcase Showdown winners from the 2nd of June 2014 through to the 27th, plus the episodes aired the 2nd and 4th of July, in addition to what as best I can figure are the aggregate totals from the 10th of November, 2008, onward, less a couple episodes that I missed:

First Second Third
Month 6 13 15
Season 114 122 124
All Time 575 651 622

If there is anything interesting to be said about this it's it actually does appear that being the first spinner puts one at a tiny disadvantage, and that my ancient hypothesis that the second spinner has an edge might be justified. Based on this, the first spinner wins 31.11 percent of the time; the second spinner 35.23 percent of the time; and the third spinner 33.66 percent of the time.

If we suppose that, ideally, each contestant would have exactly one chance in three of winning, that would imply there ``should'' be 616 wins for each contestant, with a standard deviation (based on the binomial distribution, with p = 1/3 and N = 1848) of about 20.265. The first spinner is just a tiny bit more than two standard deviations below the expected value, and the second spinner not quite one and three-quarters above. This is suggestive but I can't say it's quite compelling, statistically speaking. That said I'm not sure it's worth gathering another season's data to make or break my null hypothesis.

(See, if you run an experiment where you expect some outcome to come up one-third of the time, and run it 1848 times, you probably won't get that thing to turn up exactly 616 times. It'll be a little low or a little high, the same way if you flip a fair coin ten times it'll sometimes turn up tails only three times or as many as eight times, without the coin being unfair. You would expect that the thing would turn up somewhere between 576 and 656 times --- two standard deviations below and above the expected value --- nineteen times out of twenty that you do an 1848-trial run. So this is really just at the point where it starts to be a fair question whether the first spinner has got a one-in-three chance of winning and has just been unlucky these past few years.)

Is the first- or the second-revealed showcase the winner? For June, for the 2013-14 season, and for all time since I started keeping track (which is only from September 2009 for all this data, I find), I make it out as:

First Revealed Second Revealed Double Overbid
Month 14 7 1
Season 91 74 18
All Time 516 330 73
Unforced Month 4 7 -
Unforced Season 22 58 -
Unforced All Time 222 254 -

I can't resist the conclusion: if your showcase is revealed first, and you didn't overbid, chances are, you're the winner. (If we assume the first-revealed has a 50 percent chance of winning, then over the course of the 919 cases shown we should expect 459.5 first-revealed winners; the standard deviation is just over 15, so, the first-revealed wins more often than expected, and the second-revealed way less often than that.) If neither of you overbid (or bid a dollar, or had a double showcase win, things that generally force the order of the revelations) it's a toss-up; the second-revealed is the winner more often but not by so very much more that it's implausible it should be just chance.

So with that, I sign off the last of my reports on The Price Is Right for this season, and possibly for good. I'll see if I can get used to just watching the show without worrying that I've missed writing down data about it. If I can't just relax and watch it I might gather data anyway just to have something to do.

Trivia: Christopher Columbus's edition of the Geography of Ptolemey was printed in Rome as published in 1478. (The first printed edition dates to Bologna in 1477.) Source: The Fourth Part of the World, Toby Lester.

Currently Reading: Sputnik: The Shock of the Century, Paul Dickson.

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