Over the course of the season a ballplayer will bat about 650 times. In order for this player to hit .250, which is decent, he will need 163 hits. In order for this player to hit .300, which is the guy you want on your team, he will need 195 hits.
If we did not keep stats, you might think you would be able to tell the difference between the guys who hit .250 and those who hit .300. Thirty hits is a generous margin. Except over a season each player will have about 25 at bats a week. The .250 hitter, the Matt Weiters, will have six or seven hits a week. The .300 hitter, the Austin Jackson, will have seven or eight.
Unless you are Lisbeth Salander you would not be able to see the difference in one hit every week. Not to mention that is on average, for players on the same team. Good luck trying to watch every at-bat of multiple teams.
That is why in a nutshell (and mostly stolen from Bill James) why statistics are important. And just as important, it is key that we look at players over a period of time, rather than just a week or two to judge how good a player is.
I am not saying that watching a player means nothing. Only that watching a player for the few games you are able to attend in person or catch on TV is not something you should base your whole opinion of a player on. There were games this past year in which Miguel Cabrera and Mike Trout went 0-for-5. There was also a game in which Hideki Matsui went 2-for-3, scored a run, and drove in another. Cabrera and Trout do not suck and Matsui is not that good of a hitter. We know this, why? Because we do not base our opinions of them on one game.
So the next time they flash up on the scoreboard that Craig Wilson is 4-for-5 against left-handed pitchers on Tuesday afternoons when the wind is blowing to left-center, ignore it. Five at-bats does not tell you anything. And the next time you see a hitter go 2-for-12 and strike out five times over a three game home stand, check his stats to see how he his season is actually going, before demanding a trade.