What statistic test to use? Stats problem?

Question

In these hypothesis a field of thousands of players pick the outcomes (win or loss) of sports contests. I have access to each players picks and historical record but I do not have access to the entire group's results such as average winning %, etc. One of my assumptions is on each pick each player has a 50% chance of picking the winner.

Hypothesis one:

A player that has picked 85% winners in the last 100 picks (85/100) will FAIL to pick at least 50% (<50/100) winners in the next 100 picks.

Hypothesis two:

You have 10 players picking one outcome at a time independently and have picked 8 winners in a row. Less than half of these players will pick a winner on the 9th pick.

Answer 1

UPDATE:

Then the numbers for your second test don&#039;t add up. The sample size is just way too small to infer anytghing. To look at just one pick, you&#039;d need  500 or so players who had already picked 8 winners in a row. If &quot;winning&quot;  is truly random (which I really doubt), the probability of winning 8 in a row is about 1 in 256, so you&#039;d have to start with a pool of 128,000 to have a decent chance of finding that many.

For the first, you need a group of folks that meet your initial criteria for prior wins. Then you need their winning percentage for the next 100. Strictly speaking, this is a binomial distribution problem, but as long as the group is relatively large (&gt;30) and there are lots of picks (e.g. 100), then you can get away with a simpler test on a smaller sample.

You will need the winning percentage of each player. You will need to calculate both the mean and standard deviation.

You would do a one sample t-test (with alpha = .05), comparing the average number of wins of the group to your target percentage. (However, most people would do a 2 sample test to compare against the mean of another random group.)

Your null hypothesis will be that the mean &gt;= .5, and the alternate is that it is &lt;.5. Depending on your sample size and standard deviation, the number will need to be something less then .5 in order to make such a claim (and then, couched in probablistic terms).

UPDATE END

Sounds like you&#039;re investigating &quot;regression to the mean.&quot;

If I understand the situation correctly, there are no statistical tests involved, because you appear to be using whole populations instead of samples. That is, the folks you are investigating don&#039;t represent some larger group of people about whom you&#039;re inferring something.

If the numbers say it, then it is so -- at least for those people.

But note that I wouldn&#039;t say things like &quot;&lt;50%.&quot; I would say something like &quot;not much greater than the mean.&quot; If &quot;picking winners&quot; is strictly a matter of &quot;luck,&quot; then one would always assume that anyone will score around the mean, regardless of any other circumstances.