## Wednesday, 31 August 2011

### Discriminant Analysis: A different take!

Discriminant Analysis: A different take!

So, we were learning Discriminant Analysis using SPSS in class today. Now, I wonder, what is the real use of Discriminant Analysis for a layman? For all we know, a layman may perhaps never have heard of a Discriminant Analysis.  But, however, a lot of things that he sees around maybe influenced by Discriminant Analysis, and possibly we never pay heed to such a discriminating factor in our lives.

There have been several examples of Discriminant Analysis’ usage in sports, but this is a take which blew my mind:

(1979)... employed a statistical treatment called "discriminant analysis," which, based upon combinations of four variables (two for size, one for fat, one for strength), could place each player into his position with a very high degree of accuracy. This has important implications for selection of players when they make the transition from college to professional football. Finally, we again employed discriminant analysis within the positions, adding variables of muscle deficits, injury history, and playing time and were able to rank players into either the injured or noninjured categories. These equations had a sensitivity of 93.7 per cent and specificity of 96.1 per cent, with the overall injury rate of 38 per cent. This indicates that some characteristics may abet injury. The discriminant analysis allows for selection of variables to statistically profile the football player. This technique addresses the multiple factors that contribute to the success or injury of the player and should be of use in profiling any sport, especially on the professional level....

Talk about leaving fans’ hearts in their mouths based on Mathematics! Next time you go watch a game, you never know whether the selection has been Discriminant or not! If you feel your team is underplaying and is behaving strangely, don’t blame it on match fixing, blame it on Discriminant Analysis! However, on a serious note, the amount of study that the above gentlemen did, goes to show their determination of equalizing the 2 different entities, namely Sports and Mathematics. It was definitely a step forward!

Another Berkeley experiment research on “Predicting the Atlanta Falcons Play Calling using Discriminant Analysis” says:

“This study investigated the ability of discriminant analysis to predict the offensive play calling of the 2005 Atlanta Falcons. Data was collected on each of the 988 offensive plays run from scrimmage by the Atlanta Falcons during the 2005 NFL season. Independent variables included game location (home vs. away), down, yards to go, field position, score, offensive formation, opponent’s defensive rank against both the run and the pass, weather and field surface (turf vs. grass). The response variable was categorized into either a short pass (5 yards or less), medium pass (6 to 15 yards), long pass (more than 15 yards), run, or scramble (by Michael Vick).

A linear discriminant function was developed to predict play calling based on the independent variables. Based on a cross validation procedure, the model was able to correctly predict the play called 40.38 percent of the time. While this rate is not high, the model was able to predict each play with greater accuracy than the relative frequency that each play was run. Considering that the Falcons coaches said they only use frequencies, the use of discriminant analysis is an intriguing possibility for NFL coaches.”

The question is, how far can Mathematics and Statistical data go ahead in things like sports. Sports is usually a very emotion-centric way of life, and is prone to both human emotions and errors. What is right this season, can vary next season. If however, such models come to exist in everyday circumstances, they can surely put a gag on the thriving betting business!

Discriminant Analysis has been used far and wide, from measuring customer satisfaction of Airlines, Mobiles etc to Finding credit scores to analyzing players of Football. The question is, why should this knowledge be only kept to the seekers? If Airlines and Mobile Operators are doing such exercises, they should ensure that they are publishing it, so that the knowledge spreads. It Always Helps.

The Best application according to me, of Discriminant Analysis stands as thus. It is best used for Bankruptcy Calculation (at bankruptcy calculation)! This kind of information should go to the public, so that we precisely know when we are down under. See, my point stands vindicated. We really need this information to be spread in the public arena.

Sagnik Biswas
Marketing 2