Here are a number of analysis with much bigger models.

http://www.baseballprospectus.com/article.php?articleid=2656

The statistical studies of clutch have supported this point. David Grabiner did the seminal work more than a decade ago, defining clutch as performance in the late innings of close games. From the article:

The correlation between past and current clutch performance is .01, with a standard deviation of .07. In other words, there isn't a significant ability in clutch hitting; if there were, the same players would be good clutch hitters every year.

A study by Ron Johnson, which is not currently online but is quoted here, covered a 15-year period and concluded that just two players, Paul Molitor and Tony Fernandez met the statistical criteria to be considered clutch hitters. (Johnson didn't argue that the two had this trait, just that of the players in the study, they were the only two whose performance with runners in scoring position showed a statistically significant improvement.)

https://www.bsports.com/statsinsights/debunking-myth-playoff-vs-regular-season-hockey#.VP9tguHcjYg

http://research.sabr.org/journals/the-statistical-mirage-of-clutch-hitting

WE HAVE BROKEN the data down by league and computed the correlation coefficient for both the overall batting average and the Elias clutch rating (late-inning pressure minus overall average) for every possible pair of years, i.e., 1984-1985, 1984-1986, 1984-1987, 1985-1986, 1985-1987, and 1986-1987. Since we have six pairs of years and two leagues, we can compute twelve correlation coefficients using a cutoff of 25, 50 and 75 late-inning pressure at bats. We can then determine the degree of significance of each of these correlations. For the same correlation, the significance increases as the number of data points (players, in this case) increases. The level at which a correlation is significant tells us what chance there is that this is not a result of random chance. For example, there is a 99 percent chance that something at the 99 percent confidence level did not occur by chance, and thus we would feel pretty confident that is a real signal. For twelve correlations, we would expect one of them to be significant at the 11/12 (91.7%) confidence level just by random chance. Table 1 summarizes the results of the correlation calculations. It gives the number of players (n) involved in each pair of data sets (i.e. for AL 1984-1985, there are 127 players who had at least 25 late-inning pressure at bats each year, and 78 who had at least 50), the correlation coefficient (r) between the two data sets (i.e. - 0.049 for the AL 1984-1985 with 25 pressure at bats), and the confidence level at which this correlation is significant (only confidence values greater than 90 percent are given).

TO PUT IT SUCCINCTLY, year to year values of the Elias "clutch" rating are uncorrelated. This is in contrast to overall batting average, which is highly correlated in all pairs of seasons. This latter conclusion is simply a reflection of the fact that people like Ty Cobb always hit for a high batting average and people like Mario Mendoza never do. In both the 25 and 75 at bat levels, there is the one correlation significant at the 91.7 percent level predicted by random chance, while at the 50 at bat level, there are only two. Of the 36 correlations for the clutch average, 16 are negative (all 36 are positive for overall average), and, in fact, the most significant correlation, between the American League in 1985 and 1986 for a minimum of 75 pressured at bats, is negative. If this were a true indicator of the situation, it would mean that rather than showing that good clutch hitters repeat their performance from year to year, good clutch hitters have a tendency to be bad clutch hitters the next year. The results of these correlation calculations imply that while an individual's batting average is somewhat predictable from year to year, clutch hitting (by the Elias definition) is not predictable.

http://bleacherreport.com/articles/923262-debunking-the-myth-of-clutch-in-the-nba-once-and-for-all

There's a quote from the book Scorecasting that really sticks out in my mind:

"Over the last two decades in the NBA, including more than 23,000 games, the free-throw percentage of visiting teams is 75.9 percent and that of home teams is...75.9 percent--identical even to the right of the decimal point. Are these shooting percentages any different at different points in the game, say, during the fourth quarter or in overtime, when the score is tied? No.

Even in close games, when home fans are trying their hardest to distract the opponents and exhort the home team, the percentages are identical. Sure enough, as sluggishly as the Blazers played in San Antonio, they would make 15 of their 17 free throw attempts (88.2 percent) even with fans behind the basket shouting and waving.

The Spurs, by contrast, would make 75 percent of their attempts. Evidence of the crowd significantly affecting the performance of NBA players is hard to find."

The free throw is the most human of all events in a basketball game. It's just one man standing at the foul stripe and using his mind and skill to overcome all distractions and make a simple, uncontested shot. If there is neither a difference between home and away free-throw shooting nor at various points in the game, than that proves to me that as a whole, NBA players have learned to overcome nerves.

They're different than you and I, who may miss a last-second free throw during a pickup game because we have butterflies in our stomach. We don't spend hours a day in a gym honing our form, making repetition after repetition until we're perfectly confident in our abilities. Quite simply, we aren't professionals.