We definitely need a 'gold relinquished' stat.

It can be buried in the post-game or advanced web generation stats.

The fact that tanks are on average going to have more deaths/gold relinquished than other people doesn't diminish the value of the statistic.

It should simply show how much money you gave to the enemy team by dying, which is your number of deaths + cumulative gold from dying with kill/assist streaks. Which we know is already tracked, just show it.

Most damage does not matter if you are running 12 deaths and your carry is running 2, in a game where for most roles any number of deaths over 6 makes you a liability to your team. (with the caveat that the number of deaths goes up or down by 2 for each tier, so 6 is at gold, 8 silver, 12 bronze, 4 plat and higher, etc.)