FiveThirtyEight has an interesting column, Riddler column, which I follow with great interest. In this post we will take a look at another statistics puzzle published as Riddler Classic puzzle for April 29th.

## Puzzle

In short (see the original post for a more detailed formulation), we have two teams (e.g., "red" and "blue") playing a game of $$200$$ possessions ($$100$$ possessions for each team). Let us allow only two-pointers in this game. Furthermore let us assume that if the teams are tied, scoring probability for either team is $$0.5$$, but if one team is ahead then loosing team concentrates and starts shooting better: scoring with $$0.5 + x$$ probability. Likewise winning team looses concentration and starts shooting worse: scoring with $$0.5 - x$$ probability.

Organizer, who knows $$x$$ (from empirical observation?), has done the math and came to conclusion that after $$200$$ possessions there is $$50 \%$$ chance that the game will be tied. How big is the losers advantage $$x$$? Under these assumptions is there first possession (dis)advantage?

## Solution

Analytical solution is possible, but will merit its own post. Here let us share interactive app, which may be used to solve the problem. The input parameters are self-explanatory, while the plot shows progression of a single game. Overall record is shown in the top label of the interactive app below.

Can you find the $$x$$?