I would like to share one final story that not many people know about Super Bowl XLI in Miami. It has nothing to do with who won or lost the game, the rarity of running back the opening kickoff for a touchdown, or how many points were scored. Before the game even started, at the mid field pre game coin flip, the Indianapolis Cots of the AFC called tails. After the coin was flipped, and heads was the winner, Jim Nantz of CBS Sports proclaimed that although the odds were more than 1000 to 1 against it, the NFC had now won 10 coin flips in a row.

Was Jim Nantz correct to announce this? Did he get his statistics right? In the PPC industry, people can use numbers to claim just about anything. It is up to you to decide which of the numbers actually mean something, and which do not. Everyday there are variations in your data, but you don’t get all worked up each day over the slightest change. It is up to you do decide when numbers are telling you something, and when they are just part of normal variation.

One way to gain an intuition into randomness is to take two people and play a coin flipping game. Tell one of them to flip a coin 100 times (or use this coin flipping simulator) and record the results. Tell the other to make a fake sequence of 100 coin flips that is supposed to look as though they had actually flipped the coin. Anyone trained in probability or statistics would be able to easily tell the difference between the two sets of 100 flips. The fake one will be almost too random, and will alternate too much between heads and tails. However, the real flips will contain a run or two of 5,6,7 or more in a row of all heads or all tails. Check the simulator if you don’t believe me.

In reality, are you more likely than not that in a series of 100 coin flips to see either a long run of heads or tails? To understand just takes a little bit of information about basic probability. The actual odds of flipping a coin 10 times and getting all heads are in fact 1024 to 1. So Jim Natz was correct, that would be equal to the odds of one side winning the coin flip 10 years in a row. However, those are the odds of picking up a coin and flipping it only ten times and getting all heads. If the Super Bowl is played for 100 years, there are actually 90 different sets of 10 flips in a row. So, if the Super Bowl is played with the coin flip in the same manner for 100 years, there will be 90 opportunities for one side to win 10 times in a row. Another way of looking at this is to say that the first flip of10 flips in a row happens 90 times. That means that in 100 years of the Super Bowl, the odds of one side or the other winning 10 times in a row are actually closer to 9%. In fact, if the Super Bowl is played for 375 years, there is actually a 50% chance that one side or the other would win 10 times in a row.

I like to play blackjack on my frequent trips to Las Vegas, so consider this example. For simplicity, let’s say the odds of winning a hand of blackjack are 50%, and you wager 15% of your total capital from after your last winning hand, on each hand you play. To run out of money, you would only need to lose 7 consecutive hands. Well with a 50% chance of winning, the odds of losing 7 times in a row would be 128 to 1. That would never happen! Right?

Well say thru the course of one sitting you play 4 shoes with 25 hands per shoe. That is a total of 100 hands. Calculated similarly to the odds of one side winning a coin flip 10 times in a row, in those 100 hands it would be more likely that not to go on a losing run of 7 hands in a row one time, and you would be out of money.

I bring this example to you to get you to think about the way people present numbers. Indeed, in after only 41 years of the Super Bowl, one side winning 10 times in a row is quite unlikely, but not totally unexpected. The point here is that over the long course of a strong PPC campaign, there is destined to be some serious variation. What will separate the best SEM’s from the rest will be those who can understand and interpret the statistics on their own, and those who cannot.