Total Skill Index
The Total Skill Index (or TSI) is an official measure of a player's abilities. The formula used for the calculation is unknown, but several somewhat successful attempts have been made in approximating the true function. It is rumoured that HT-Bjorn proclaimed he'll change the TSI calculation formula as soon as someone figures it out.
As a general rule, the higher the TSI, the better the player.
However, there are problems with this theory. A player who is average in several skills(eg inadequate in defending, passing, scoring with excellent stamina) will often have a higher TSI than a more specialized player (eg excellent defending, but everything else poor or lower). TSI also increases with training and it can also increase and decrease with form. Sometimes your TSI will drop even though your form does not. This is an easy way of spotting that a background form change has occurred, and your form sub-level has decreased.
TSI for goalies is a different matter. The highest TSI for a goalie the better. Since a goalie only specializes in one skill it can be measured and you can see how close your goalie is to the next level by entering your TSI into http://www.hottrick.org/hattrick_keeper_tool.php. Also keepers have higher TSI than their specialized equavalents.
A common theory is that both form and stamina have a multiplying effect on the TSI, whereas the other skills (for keepers, goaltending only) contribute as a sum of exponential functions.
For Goalkeepers an approximated formula for TSI calculation is:
TSI = [(0.025f)+0.1][10(s-1)]^(3.4)/1000
With f = Form and s = Skill ranked from 1 (disastrous)