Looking for a ranking algorithm that favors newer entries
You could use any function that gives a lower weight to older entries. For example, if data consists of scores, $s_1,\ldots,s_n$, where the index  corresponds to the 'time of arrival' of the entry, that is, newer entries have larger indices, then you could use a weight function that increase as $i$ increases. So any 'increasing' function will do. Examples include:


$f(x)=e^x$
$f(x)=\log x$
$f(x)=x$
$f(x)=x^2$


etc.

Then your function will be

$\dfrac{\sum_{i=1}^n s_i\cdot f(i)}{\sum_{i=1}^n f(i)}$.

Actually, it makes more sense to give the newest entry the lowest index and make the weight function decreasing. This way you can tune it by setting the weighting that you want to give to the first element. 

Wikipedia has an entry on weight functions, some examples can be found on the page about weighted means.