Gruber, and Blake showed that survivorship bias is larger in the small-fund sector than in large mutual funds (presumably because small funds have a high probability of folding). They estimate the size of the bias across the U.S. mutual fund industry as 0.9% per annum, where the bias is defined and measured as: Additionally, in quantitative backtesting of market performance or other characteristics, survivorship bias is the use of a current index membership set rather than using the actual constituent changes over time. Consider a backtest to 1990 to find the average performance (total return) of S&P 500 members who have paid dividends within the previous year. To use the current 500 members only and create a historical equity line of the total return of the companies that met the criteria would be adding survivorship bias to the results. S&P maintains an index of healthy companies, removing companies that no longer meet their criteria as a representative of the large-cap U.S. stock market. Companies that had healthy growth on their way to inclusion in the S&P 500 would be counted as if they were in the index during that growth period, which they were not. Instead there may have been another company in the index that was losing market capitalization and was destined for the S&P 600 Small-cap Index that was later removed and would not be counted in the results. Using the actual membership of the index and applying entry and exit dates to gain the appropriate return during inclusion in the index would allow for a bias-free output. Michael Shermer in Scientific American and Larry Smith of the University of Waterloo have described how advice about commercial success distorts perceptions of it by ignoring all of the businesses and college dropouts that failed. Journalist and author David McRaney observes that the "advice business is a monopoly run by survivors. When something becomes a non-survivor, it is either completely eliminated, or whatever voice it has is muted to zero". In his book The Black Swan, financial writer Nassim Taleb called the data obscured by survivorship bias "silent evidence". History Diagoras of Melos was asked concerning paintings of those who had escaped shipwreck: "Look, you who think the gods have no care of human things, what do you say to so many persons preserved from death by their especial favour?", to which Diagoras replied: "Why, I say that their pictures