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Futility

The acquisition of Marlon Anderson made me think about the pointlessness of acquiring a bench player this late in the season. With only a month to go, it's likely that Anderson would only get 20 at bats the rest of the way. With this in mind, I wondered what the odds were that a lesser player would out perform Anderson.

To do this, I made a simple program. You put in two averages and a number of at bats each player will get. The program then generates a random number from between 0 and 1. If the number is less than or equal to a players batting average, that player gets a hit. After all the at bats are generated, compare the number of hits between the players, and then the higher total gets a win. Now, repeat this process 100,000 times. Admittedly, this is a simplified process, but considering that Anderson doesn't have much patience or power, I didn't feel as though they needed to be figured in. If you want, you can assume that the other player has the same patience and power. The results are as follows.

Anderson avg. Player Two Avg. AB Anderson Win% Player Two Win% Tie%
.267 .220 50 65.48% 29.60% 4.92%
.267 .220 20 41.48% 39.71% 18.81%
.267 .220 10 45.96% 39.54% 14.50%
.267 .170 50 87.40% 7.27% 5.33%
.267 .170 20 70.01% 18.80% 11.19%
.267 .170 10 80.73% 6.11% 13.16%
.267 .100 50 98.34% 0.43% 1.26%
.267 .100 20 84.98% 6.22% 8.79%
.267 .100 10 67.57% 9.42% 23.00%

What conclusions can be drawn from this? Acquiring a guy like Anderson for the bench is completely pointless. Through no fault of his own, Anderson would get out hit by a guy who hits .100 six percent of the time if he's only given twenty at bats. If you narrow that gap to a .220 average, Anderson would only make a difference once every 20 years or so. Even when he does make a difference, how many times would he get five hits to the other guys four?

These numbers also show how random this truly is. For example, the .100 hitter actually out performed the .170 hitter over 100,000 trials. Just for fun, I ran these numbers a few more times, and came up with vastly different results each time. In some trials, Anderson actually was worse than the .220 hitter over 20 at bats, in other trials, he won over 65% of the time. It takes bumping the program to one million trials to get something resembling stable numbers. If the results of over 100,000 seasons are near random, you might as well just flip a coin if you're looking only at one season.

When you consider that the Dodgers have Delwyn Young, a man that's probably better than Marlon Anderson, this trade looks even more pointless. It's not that losing a guy like Jhonny Nunez is no problem, but you should at least gain something in a trade, right?