how to calculate obp?

Good ol' Batting Average and its problems.  We all grew up knowing that a player who hit .300 was a good hitter.  So what's wrong with using batting average to evaluate a hitter?  The problem is that batting average misses two key things.  First, it only covers hits.  There are other important ways to get on base too, like Walks.  Second, it equates all hits.  A single is not as valuable as a double or home run.

Partial solutions: OBP, SLG and OPS.  So one can turn to two other stats which include hits, but fill in the gaps that batting average leaves.  On Base Percentage (OBP) [sometimes referred to as On Base Average or OBA] describes how often a batter reached base.  It is calculated by adding hits, walks and hit by pitches and dividing that by total plate appearances (not just at bats).  Slugging Percentage (SLG) attempts to measure the relative value of a player's hits by dividing Total Bases (4 for a home run, 3 for a triple, etc.)  by at bats.  Adding those two together gives you On Base Plus Slugging Percentage(OPS) which is a handy, but clumsy single hitting stat.

So what's wrong with OPS?  The main problem is that it equates OBP and SLG when they aren't equal.  First, they are on different scales: .000-1.000 for OBP and .000-4.000 for SLG.  Second, and more importantly, OBP and SLG don't equally contribute to run scoring.  In short, a raft of studies have found that OBP is much more important.

Problem solved: wOBA.  Preeminent sabermetrician Tom Tango created a stat called Weighted On Base Average (wOBA) to appropriately account for the value of getting on base, hitting for power and pretty much all other outcomes from a plate appearance.  This metric uses a system called linear weights to determine the run value of the various outcomes of a plate appearance.  Without going to into too much detail, this is an empirical approach which looks at how various events (like a double, a walk or a stolen base) have affected run scoring over multiple years of data.  [If you'd like a more detailed, math-heavy explanation of linear weights, click here.]  Calculating wOBA is a bit complicated, so I let others do it, but it basically involves multiplying the run value coefficient of each event (like a double) by the number of times the player did that (how many doubles he hit), adding up all of those results for all events and dividing it by total plate appearances.

What does this number mean?  This stat is scaled to OBP, so if you know what an average or good OBP is, then you know what an average or good wOBA is.  As Dave Cameron at Fangraphs put it:

What doesn't wOBA include?  It isn't currently park normalized.  It's like standard, raw rate stats in that guys in hitter's parks are going to do better and players at pitcher's parks are going to do worse.  Also it doesn't attempt to equalize players at different positions.  There are metrics which recognize the different real world hitting standards for a shortstop as compared to a first baseman, but wOBA isn't one of them.  But they exist.  We'll save that for another post in this series.

So how does this apply to the Royals?  Here is the Royals 2008 wOBA leader board (min. 100 PA):

Mike Aviles .360

If you are interested in learning more about wOBA and some other advanced hitting metrics, I would suggest the following sources, many of which I used to put this together:

On Base Percentage (OBP) is the percentage of times a batter gets on base to the number of times they have been at the plate.

A higher OBP is a sign of a hitter that is more likely to advance bases.

It is an alternative to batting average. Compared with BA, OBP includes the number of times they have been walked or hit by a pitch, which are not normally  included in statistics that rely only on upon “at bats.”

On Base Percentage (OBP) = (hits + walks + hit by pitch) ÷ (at-bats + walks + hit by pitch + sacrifice flies)

It is the number of times the batter advances to the number of times they have a chance to advance.

If a batter has been at bat 127 times and in that time has made: 32 hits, 7 walks, been hit by a pitch 2 times, and 3 sacrifice flies, then:

32 hits + 7 walks + 2 hit by a pitch = 41

127 at-bats + 7 walks + 2 hit by a pitch + 3 sacrifice flies = 139

41 ÷ 139 = 0.295

Therefore, the batter’s on-base percentage is 0.295.

In baseball statistics, on-base percentage (OBP) measures how frequently a batter reaches base. An official Major League Baseball (MLB) statistic since 1984, it is sometimes referred to as on-base average (OBA),[a] as it is rarely presented as a true percentage.

Generally defined as "how frequently a batter reaches base per plate appearance",[1] OBP is specifically calculated as the ratio of a batter's times on base (the sum of hits, bases on balls, and times hit by pitch) to the sum of at bats, bases on balls, hit by pitch, and sacrifice flies.[1] OBP does not credit the batter for reaching base on fielding errors, fielder's choice, uncaught third strikes, fielder's obstruction, or catcher's interference.

OBP is added to slugging average (SLG) to determine on-base plus slugging (OPS).

The OBP of all batters faced by one pitcher or team is referred to as "on-base against".

On-base percentage is calculable for professional teams dating back to the first year of National Association of Professional Base Ball Players competition in 1871,[2] because the component values of its formula have been recorded in box scores ever since.

The statistic was invented in the late 1940s by Brooklyn Dodgers statistician Allan Roth with then-Dodgers general manager Branch Rickey.[3][4] In 1954, Rickey, who was then the general manager of the Pittsburgh Pirates, was featured in a Life Magazine graphic in which the formula for on-base percentage was shown as the first component of an all-encompassing "offense" equation.[5] However, it was not named as on-base percentage, and there is little evidence that Roth's statistic was taken seriously at the time by the baseball community at large.[6]

On-base percentage became an official MLB statistic in 1984. Its perceived importance jumped after the influential 2003 book Moneyball highlighted Oakland Athletics general manager Billy Beane's focus on the statistic.[7] Many baseball observers, particularly those influenced by the field of sabermetrics, now consider on-base percentage superior to the statistic traditionally used to measure offensive skill, batting average,[8][9] which accounts for hits but ignores other ways a batter can reach base.[10]

Traditionally, players with the best on-base percentages bat as leadoff hitter, unless they are power hitters, who traditionally bat slightly lower in the batting order. The league average for on-base percentage in Major League Baseball has varied considerably over time; at its peak in the late 1990s, it was around .340, whereas it was typically .300 during the dead-ball era. On-base percentage can also vary quite considerably from player to player. The highest career OBP of a batter with more than 3,000 plate appearances is .482 by Ted Williams. The lowest is by Bill Bergen, who had an OBP of .194.

On-base percentage is calculated using this formula:[11][12][13]

where

In certain unofficial calculations, the denominator is simplified and replaced by Plate Appearance (PA); however, the calculation PAs includes certain infrequent events that will slightly lower the calculated OBP (i.e. catcher's interference, and sacrifice bunts).[13] Sacrifice bunts are excluded from consideration on the basis that they are usually imposed by the manager with the expectation that the batter will not reach base, and thus do not accurately reflect the batter's ability to reach base when attempting to do so. This is in contrast with the sacrifice fly, which is generally unintentional; the batter was trying for a hit.[1]

On Base Percentage (aka OBP, On Base Average, OBA) is a measure of how often a batter reaches base. It is approximately equal to Times on Base/Plate appearances. The full formula is OBP = (Hits + Walks + Hit by Pitch) / (At Bats + Walks + Hit by Pitch + Sacrifice Flies).