Because we like baseball, we like statistics. Baseball statistics, that is. You can thoroughly enjoy baseball without paying any attention to its statistics, of course, but to really understand the game deeply, you’ve got to dive in.
Following is a definition of most of the stats we use. For more information, be sure to check out Fangraphs’ Sabermetric Library. By the way, when you see a writer refer to a batter’s performance in this way—.275/.338/.425 (insert your own numbers)—he’s referring to the batter’s BA/OBP/SLG. If you’re not sure what those are, read on.
The stat then looks at each individual play and divides the player’s WPA in that specific play by the LI of that specific play. It then sums up all the plays in the year. Finally, it subtracts this figure (the sum of each specific WPA/specific LI) from the first figure (overall WPA/overall LI). The result is an index of whether the player did better or worse in “clutch” situations. Zero is neutral, a positive number is “clutch” and a negative number isn’t.
You can read more about Leverage Index in Tango’s three-part series on THT: (Part One, Part Two, and Part Three).
You can improve the accuracy of the Pythagorean formula by using a different exponent (the 2 in the formula). In particular, a sabermetrician named US Patriot discovered that the best exponent can be calculated this way: (RS/G+RA/G)^.287, where RS/G is Runs Scored per game and RA/G is Runs Allowed per game. This is called the PythagoPat formula.
As an example, a standard linear weight for a home run is 1.4. This means that, on average, all home runs add 1.4 runs to a team’s runs scored when factoring in the difference between run expectancies before and after the home run. In RE24, however, a home run with the bases empty will count as only one run (because a bases empty situation with the same number of outs has the same run expectancy). RE24 will then count a home run with the bases loaded and two outs as 3.2 runs, since the team was expected to score about 0.8 runs, on average, in that situation. So exactly *when* the batter hits each kind of hit is taken into account.
Note that RE24 doesn’t take the inning or score into account. This is done in WPA
And that creates a problem. Comparisons to average means that a player who plays just one game and is average in that game is just as valuable as the player who played an entire average season. Doesn’t make sense. So we compare players to replacement level instead. Replacement level is usually thought of as the level at which a player can be easily replaced by a bench player, a freely available free agent or someone else. Replacement levels are also useful for salary analysis in which it is assumed that a player who performs at a replacement level should receive a minimum salary.
There are a lot of ways to calculate replacement levels. Here is one, presented by our own Sean Smith. There are several legitimate approaches. A key thing to remember is that replacement levels will differ by position, because it is harder to find a good-hitting catcher than a good-hitting first baseman (for example).
UZR is adjusted in many ways and includes other fielding metrics. It gets complicated very quickly. But the bottom line is that a player with zero UZR is an average fielder at his position. A positive number indicates he was an above-average fielder, and a negative number indicates that he was below average.
wOBA uses a “linear weights” approach in that it assigns a coefficient to every contribution made by a batter (technically, wOBA uses a linear weight and then adds the value of an out) and then divides by his plate appearances. A season-specific “wOBA Scale” is then applied to make the average wOBA equal average OBP. You can read more about wOBA in this THT article. You can also alter the coefficients based on the batter’s run environment.