I have previously shown the basic purpose of the binomial distribution and how to get MS EXCEL to calculate it for you.  Now let's use it in a meaningful way with respect to sports betting. 

A monkey throwing darts at the betting board (this is a euphemism for "purely random bet picking") has a probability of 0.5 for picking a winner against the spread.  Your bookie hopes you are a dart-throwing monkey.  You, however, hope to be a sharp sports bettor, with a 0.55 probability of picking winners against the spread.  You have developed a new system for picking winners and use it for picking 10 games.  You win 6 of them.  What is the probability that a dart-throwing monkey could have won 6 or more games?

Using MS EXCEL we are going to use the cumulative function to find 5 or fewer wins and subtract from 1.

This yields a (rounded off) probability of 0.6230 that our money picks 5 or fewer winners, or a (1 - 0.6230 =) 0. 3770 that our monkey could pick 6 or more winners.  Our results are not yet too impressive.

We continue for another 90 picks, making for 100 total bets.  We have 55 winners out of 100 - our vaunted 55% winners target.  Could our monkey have kept up?

First calculating for 54 or below we get a probability of 0.8159.  Converting to 55 and above (1 - 0.8159 =) 0.1841.  Our monkey is less likely to have kept up, but he still had a pretty decent probability.  Meaning, of course, that our own results might just be a random bit of good luck.

When do we make it to statistical significance?  That actually depends upon your personal threshold for how much risk you are willing to take that you are not just a lucky monkey.  At 55/100 wins you are going to be a lucky monkey 18.41% of the time.

Stanford Wong recommends a threshold of 0.0010 in his book Sharp Sports Betting.  Only one monkey in a thousand gets that lucky, and that is the confidence level Mr Wong recommends.  This threshold can be met by picking 549 winners out of 1,000 bets against the spread.  

You may choose to raise or lower this threshold, and consider your betting system proven to your satisfaction at any point you desire.  You should just be aware that the numbers don't lie, and if you lower the threshold you are assuming more risk that you are just being a lucky monkey.

Use the Binomial Distribution to Test the Touts.

Considering using a tout service?  (Touts sell or give away sports picks.)  All touts advertise their results in some form or another, trying to conince you that their winning record is impressive so you will use their service.  Plug his numbers into the BINOMDIST function box and see if he is posting results that meet your threshold for significance.