Wednesday, April 24, 2013

Games of the Price is Right: The Wheel (Part III)

The last few times I've discussed The Wheel on The Price is Right I've talked about some of the odds that you face as the first or second contestant.  A lot of the discussion has been based simply on how The Wheel is designed and played, and not necessarily on actual data.  

For today's post, I'd like to talk about what it actually takes to win at The Wheel.  

I've watched and coded a bunch of episodes at this point, and have a good deal of information on what people spin at The Wheel.  There's a lot we can look at that might take a bit more data, but for now I thought it would be the most interesting to just put together a chart like this:

What this chart is showing is the distribution of contestants' winning totals at The Wheel.  What is quickly evident is that a lot of people who win at The Wheel win by walking away with a dollar total.  That's not to say that they hit a dollar on their first spin, but just that they totaled a dollar by some combination of one or two spins.  95 cents is also a bit winner - almost accounting for as many winners as a dollar itself.  

If any of the contestants hits a dollar total, the other contestants only have a 1 in 20 (5%) of forcing a tie and spin-off each time they spin.  Those aren't great odds.  95 cents isn't much better - there's a 1 in 20 (5%) chance of forcing a tie and spin-off, and a 1 in 20 (5%) chance of simply winning.  

The odds of straight out winning against any given score actually double from 95 down to 90.  While the odds of forcing a tie and spin-off stay constant (5%), the chances of winning straight out go from 1 in 20 (5%) to 2 in 20 (10%).  This might account for the larger gap between 90 and 95 cents on this graph.  

What should also be evident is that not many contestants make it as a winner at The Wheel with scores much below 70 cents.  Two contestants managed to eke out that win at 65 cents, but the singular winner with 40 cents is actually an interesting fluke.  

It was a situation where the first and second contestants had gone over a dollar and lost - the third contestant had a single spin at the wheel to see if they could hit a dollar in one spin.  Good trivia for The Price is Right - in such a situation the third contestant does not get another spin at the wheel no matter how they do on their first.  It is the only realistic situation where someone could win at the wheel with a spin of 5 cents.  The value they come up with is completely random, as it is based on just one spin.  

This brings up an important point, though.  How do things look if we break them down by contestant?  

Of the 72 events at The Wheel (36 episodes with 2 events per episode), the breakdown of wins by placement is actually starting to look fairly interesting.  I looked at it after the last post with a smaller sample, and things seemed to be a bit more biased toward later spins.  The numbers as they break down now are:

Contestant 1:  23 wins
Contestant 2:  23 wins
Contestant 3:  26 wins

Those wins are distributed as follows:

I was initially expecting the wins for contestant 1 to come a bit higher up the scale - perhaps a disproportionate number of wins from the 95 to a dollar range.  Interestingly enough, contestant 1 as a place in line seems to be taking home a lot of wins right around the 70-75 cent region.  

Now, this is still a small sample (so I'm going to keep coding), but 70-75 does seem to be the area where contestant 1 generally starts to feel safe enough to stay.  If a first spin is below 70 the odds are that they are either: going to stay and get beat, use a second spin to fail to get to 70 and get beat, use a second spin to get into the 70+ region, or spin big and go over a dollar.  I'd like to see how this continues to play out with more examples, but if this effect sticks around that might be a start of what's going on.  

In terms of dollar wins, everyone seems to be pretty close to equal footing.  If you spin a dollar you pretty much have things wrapped up, no matter where you are in line.  The best someone can do is also spin a dollar and take you to a spin-off.  

Speaking of, we can also take a look and see how many of these wins resulted in a spin-off win.  The way I have things coded is which contestant won (overall), what value they won with (enough to make the last chart), but also if there was a tie and what happened during the tie.  The winner of the tie is who made it into these charts, so if contestant 2 and contestant 3 tied at 75, went to a spin-off, and contestant 2 won, then contestant 2 gets credited with the win and the winning value is logged as 75.

[To be fair I also have information on every spin that occurred, not just who won, so there's a lot of things I can look at in future posts.]

Basically, we can simply add this information to the counts from earlier:

Contestant 1:  23 wins (6 through spin-offs)
Contestant 2:  23 wins (2 through spin-offs)
Contestant 3:  26 wins (4 through spin-offs)

The first contestant is relying a bit more on winning in spin-offs, but hardly enough in comparison to really make any strong claims about it.  If we simply negated wins from spin-offs the ordering would still stay similar, though contestant 1 would take a bit of a hit, with:

Contestant 1:  17 wins
Contestant 2:  21 wins
Contestant 3:  22 wins

In any case, the small sample still seems to be limiting things a bit, but we're also starting to get into the range where some potential trends could be emerging.  If there's one takeaway, it seems that your chances of winning with a spin below 70 - for any contestant - are fairly low.  Your odds at winning with a spin below 65 are virtually nonexistent.       

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