Hitting: average, on-base and slugging
Batting average is the proportion of at-bats that produce a hit. It dominated the sport's conversation for a century and has two serious flaws: it ignores walks entirely, and it treats a single and a home run as identical events.
On-base percentage fixes the first problem by counting every way a batter reaches base. Slugging percentage fixes the second by weighting hits according to how many bases they produce. Added together they form OPS, which is crude — it adds two numbers with different denominators — but tracks run scoring remarkably well for something so simple.
The more careful versions weight each outcome by how many runs it is actually worth and then adjust for the ballpark and the run environment of the era, producing a single number where average is set at one hundred. That adjustment is what makes it possible to compare a hitter from a low-scoring era with one from a high-scoring one without arguing in circles.
Pitching and the fielders behind it
Earned run average measures runs allowed per nine innings, excluding those attributed to fielding errors. It is intuitive and imperfect, because the distinction between an error and a ball a better fielder would have reached is a scorer's judgement.
The deeper issue is that a pitcher does not control what happens once the ball is in play. Two pitchers with identical skill will post different ERAs behind different defences. Measures built only on the outcomes a pitcher controls directly — strikeouts, walks and home runs allowed — are more stable and predict future performance better.
WHIP, which counts walks and hits allowed per inning, sits between the two: simple, widely quoted, and still partly a description of the defence. Wins as a pitching statistic have been quietly abandoned by everyone who thinks about the sport seriously, because they mostly measure run support.
Value measures and their caveats
All-in-one value statistics attempt to express a player's total contribution — hitting, fielding, baserunning and position — as a single figure representing how much better he is than a freely available replacement. They are the most useful tool available for comparing dissimilar players.
They are also models, and the fielding component in particular carries real uncertainty. Different providers publish different figures for the same player, sometimes by a wide margin, because they weigh defence differently. Treating a small gap between two players as meaningful is a misuse of the number.
Baseball has the deepest statistical record of any team sport, which is a gift and a trap. The numbers are excellent at describing what happened and much weaker at explaining why, and the answer to a surprising figure is usually another question rather than a conclusion.