Baseball has a lot of different statistics, more than any other sport, because there are more different plays and happenings in baseball than in other sports. However, there are some important statistics that have been left out of stat lines by pretty much everybody, and it would be better if they were represented. The ones that I have in mind are:
Triple plays. One of the rarest and most exciting plays in baseball, turning a triple play (abbreviated TP) does wonders for a fielder's reputation and can be instrumental in the outcome of the ballgame. That said, I would like to see triple plays in stat lines for fielders and batters alike.
Steals of home. Like the triple play, attempted steals of home are among the rarest, most exciting, and most pivotal plays in baseball. I think that steals of home (and times caught stealing home) should be represented separately from total stolen bases in stat lines for baserunners, pitchers, and catchers. In a perfect world, there would be such separate documentation of stolen bases and caught stealing at second base, third base, and home plate.
Total runs produced. A handy little statistic that I thought up, total runs produced (TRP), is designed to rate how well a batter is at producing runs from wherever he may bat in the batting order. The formula is runs scored plus RBI's, minus home runs (because a home run counts as a run scored and an RBI for the batter). A leadoff hitter is expected to score a lot but drive in fewer runs, while a cleanup hitter won't score as much but will knock in the runners ahead of him. Total runs produced eliminates that fact and give clear data as to how influential the batter was to his team's offense. You can also take a player's total runs produced, divide it by two (giving you the average of his runs scored and his RBI's), divide that number by however many games the player played in his career, and multiply that by 162, giving you an average number of runs per season that the batter is responsible for. 100 runs scored and 100 RBI's are generally regarded as the standard goal for an entire season, so an average of 100 "adjusted total runs produced" would do just as well.
A statistic first invented to criticize Rocky Colavito, runs not batted in (RNBI) keeps track of how many runners a batter strands on base. It would be helpful to count how many such runners a batter strands in scoring position, and figure his ratio of RBI's to RNBI's to see who were really efficient at driving in runs (a team with a low OBP or a low slugging percentage would put fewer runners in scoring position, giving some batters a disadvantage to collect very many RBI's).
Whenever a team makes an error, it should be scored on the pitcher as well as the hitter because he induced what should have been an out, and as a result had to pitch more to get out of the inning. This would basically count as an extension of innings pitched.
I think that whenever a team records a base hit, it should be scored on the nearest fielder (for example, a single up the middle would be "1B-8"). Even if the fielder doesn't make an error, this helps indicate how good his range is. If the centerfielder is playing deep and all those singles are killing you, the manager knows that he needs to make a change.
Extra bases. This is pretty important. If a runner goes from first to third on a single, or scores from first on a double, he has taken an extra base (before 1898, they were counted, but as stolen bases), which is a distinct advantage for a team's offense that sports speedy and smart baserunners. They really should be keeping track of this.
Bases covered. Another statistic that I thought up is bases covered. To figure this, you give a player four for each run he scores, three for being getting to third, two for reaching second, and one for being left on first. This is actually a helpful statistic that measures a player's ability to get on base, to get far on the bases (extra-base hits), and for baserunning.
Baserunners moved. For example, if there's a runner on second base with no out and a lefty batter at the plate, it's textbook to have the batter pull a grounder in order to get that guy into prime scoring position with one out. This maneuver can lead to scoring but it's not good for the batter's stats. It lowers his batting average without crediting him with an RBI. In order to fairly present the offensive advantage of this and similar plays, batters should be credited with how many baserunners they help move into scoring position.
Relief innings. It would be convenient to keep track of how many innings a pitcher throws in relief just to see who were the real workhorses out of the pen each season (league leaders). It would also be helpful to see how many innings a starter gets relieved of in order to see how many innings he goes per start.
A catcher's main job is defensive, to guide the pitching staff and keep everything in front of him. That said, there should be a way to estimate his impact on his pitchers. Everyone always talks about it, but does anyone really measure it? Some people keep track of catcher's ERA, which is the ERA that pitchers have with a particular catcher. I am not a huge fan of catcher's ERA for two reasons: one, it is up to the pitcher to execute a good pitch, and two, a pitcher can shake off the catcher. I would love to see stats about pitchers shaking off catchers - how many times they are shaken off, shake off percentage - and use that in conjunction with catcher's ERA to give a vague sense of a catcher's effect on pitchers. If a catcher has a solid ERA and a low shake off percentage, then that's a good sign that he's doing his job.
Catcher's interference. See my complaint in my post called Some Notes On Statistical Analysis. As of now, a catcher's interference counts as an error for the catcher and as a reach on error for the batter. The scoring should be changed, as I have already attested, and the statistic should be isolated.
Scoop percentage. It is difficult to measure the true defensive value of a first baseman (fielding percentage doesn't tell you much and range factor depends on how many ground balls the infielders get), but a very important skill to have is the ability to scoop up low throws in the dirt. While failing to do so would usually result in an error on the thrower, it should be noted in the first baseman's stat line as well.
Reach on error. It would be helpful to add in the times a hitter has reached on error and how many unearned runs he scores to more accurately see how good he was at producing runs at his own merit. A little side note - if a pitcher makes an error himself that causes runs to score, the runs should be earned because the pitcher, through his own fault, allowed extra runs to score (part of a pitcher's job is to field his position, after all). It would also be helpful to keep track of how many unearned runs score on a particular fielder's error (and those unearned runs should be added to his fielding line).
Not all errors are created equal. If a shortstop bobbles a ground ball, it usually counts for one base per runner, but if he fields it cleanly and throws it into the stands, it counts for two bases per each runner. This should be accounted for. Similarly, an outfielder dropping a fly ball usually costs his team two bases.
Inherited runners. I think that there should be statistics about how many runners a starter strands for his reliever and what a reliever does with the inherited runners, even though they are not his responsibility. Pitchers pitch differently with men on base, regardless of whose responsibility they are. It's also fair to keep track of how many earned runs a starter allows actually come home when he's on the mound as opposed to how many are let in by his reliever.
When a batter hits a fly ball that is caught, but allows runners to advance, he is credited with a sacrifice fly, which doesn't affect his batting average (since 1954), but (for whatever reason) lowers his OBP. Nobody knows whether the batter was trying to get a hit or simply to hit a fly ball in the hopes of advancing runners. Now many managers will ask certain batters for a fly ball for this purpose, but many will also ask other batters just to hit a ground ball, perhaps on the right side to get a runner on second over to third. The statkeepers seem to think that the batter was trying to get a hit, and the play, although beneficial to the batting team, lowers the both batter's average and his OBP. I think that such plays should be treated exactly as sacrifice flies are for the same reasons. EDIT: Actually, sacrifice flies are only counted when the batter drives in a runner. So hitting a fly ball is only intentional when there is a man on third base? Other fly balls that advance runners, but not score them, should also be counted the same way. I'd like to see sacrifice flies, sacrifice ground balls, and sacrifice bunts all accounted for consistently: they don't do anything to a batter's slash line.
Finally, an unassisted double play is a lot cooler than an assisted one, so it might make sense to throw that in the stat lines as well.
NOTE: This is a post that I will likely edit from time to time.