## Baseball Math

### Baseball Math

Baseball is a game that generates an incredible amount of statistics. Fans use them to measure the performance of their favorite teams and players. Managers use them to evaluate players and to make situational decisions. Since so much emphasis is placed on statistical analysis of the game, it might be helpful if you learn how these numbers are arrived at. On this page, you will find formulas for computing the most basic baseball statistics. For those up to the challenge, I have also included sample problems and a quiz.

### Batting Stats

Batting Average (BA) - Probably the most referred to stat for batters, the batting average expresses in decimal form the comparison of Hits to At Bats. The formula is as follows:

BA = Hits/At Bats

For example, in 1954, a young Henry Aaron produced 131 hits in 468 official At Bats. Plugging those numbers into our formula, we come up with

BA = 131/468

Dividing 131 by 468, and computing the quotient to four decimal places, we arrive at .2799. Rounding off to three digits, we find that Mr. Aaron batted .280 in 1954. (As an average, that figure implies that he had 28 hits for every 100 at bats, or 280 for every thousand.) Speaking of Hank Aaron, his autobiography, I Had a Hammer: The Hank Aaron Story, is one of the best baseball biographies I ever read.

Example 1. In 1959, Hammering Hank had 629 official AB's with 223 Hits. What was his batting average for 1959?

Example 2. In 1941, Ted Williams, The Splendid Splinter, hit safely 185 times out of 456 official times at bat. Figure his batting average, and commit it to memory.

Total Bases (TB) - Before we move on to Slugging Percentage and OPS (On Base Plus Slugging), let's have a quick look at Total Bases.

The formula for computing Total Bases is TB = a(1) + b(2) + c(3) + d(4), where "a" represents the number of singles, "b" the number of doubles, "c" the number of triples and "d" the number of home runs. A batter's stat line doesn't usually include singles. Just remember that you can determine how many singles a player has hit by subtracting his or her total of extra-base hits from their total number of hits.

For example, we know that in 1954 Hank Aaron banged out 131 hits. Of those 131, 27 were doubles, 6 were triples, and 13 were home runs. Adding 27 + 6 + 13, we come up with 46 extra-base hits. Subtracting 46 from 131, we find that Mr. Aaron stroked 85 singles that year. Using the same variables as we used for computing Total Bases, we can make a formula for arriving at a player's singles total: Singles = Total Hits - b - c - d.

Example 3. Of the 185 hits Ted Williams had in 1939 44 were doubles, 11 were triples, and 31 were home runs. How many total bases did he accumulate?

Slugging Percentage (SLG) - A common criticism of the Batting Average is the fact that it doesn't differentiate between singles and home runs and therefore isn't a true measure of a batter's performance. Slugging Percentage (which normally isn't presented as a percentage) may give us a clearer picture of a batter's effectiveness. Slugging Percentage is equal to Total Bases divided by At Bats. The formula is SLG = TB/AB.

In 1957, St. Louis Cardinals great Stan Musial batted .357 with 176 hits (38 doubles, 3 triples, and 29 home runs) in 502 At Bats. Let's figure out his SLG. First, let's compute his total bases. Subtracting his 70 extra-base hits from his hit total we arrive at 106 singles. Plugging the numbers into the formula (see above), we arrive at this:

TB = 1(106) + 2(38) + 3(3) + 29(4) = 106 + 76 + 9 + 116 = 307

Now, we're ready to compute his SLG.

SLG = TB/AB = 307/502 = .6115 = .612

Example 4. In 1920, Babe Ruth had a pretty good year batting .376 with 54 home runs. That year marked the first time he or anyone had hit 30, 40 or 50 home runs in a season. In fact, he hit more home runs that year than 14 of the other 15 teams. His output was as follows: 458 At Bats, 172 hits, 36 doubles, 9 triples, and 54 homers. What was the Babe's slugging percentage?

On Base Percentage (OBP) - Introduced by Sports Illustrated in 1956, the OBP, which indicates how often a player does not make an out, is thought by many to be an even better gauge of a batters performance. In the formula below H represents hits, BB bases on balls, HBP number of times hit by a pitch, and PA, plate appearances.

OBP = [H + BB + HBP]/PA

To determine the total amount of Plate Appearances you must add AB's to those appearances that don't normally count as an official time at bat, times when a player walks, is hit by a pitch, or sacrifices. Plug the numbers into this formula: PA = AB + BB + HBP + SF.

In 1949, Ted Williams posted these numbers: 566 At Bats, 194 Hits, 162 walks, 0 sacrifices, and 2 hit-by-pitches. First, lets compute Plate Appearances.

PA = AB + BB + HBP + SF = 566 + 162 + 2 + 0 = 730

Now, we're ready to figure out Ted's OBP.

OBP = [H + BB + HBP]/PA = [194 + 162 + 2]/730 = 358/730 = .4904 = .490

To express as a percentage, move the decimal two places to the right. In 1949, Ted Williams reached base 49% of the time.

Example 5. What was Stan "the Man" Musial's OBP for the 1949 season. Here are his numbers: 612 At Bats, 207 hits, 107 walks, 2 HBP's, and 0 sacrifices.

Before moving on, I'd like to mention a stat known as OBP + SLG. It is what it says - compute it by adding OBP and SLG. Be sure to keep your decimal points lined up.

Runs Created (RC) - A Stat To Play With. Discovered by stats maven Bill James, Runs Created is a remarkable predictor of how many a runs a team will score in a season. Since more runs scored usually translates into more wins, this formula can be a valuable tool. By now, you should be able to compute this on your own. Here's the formula:

RC = [(H + BB) x (Total bases)]/[AB + BB]

Example 6. Here are Babe Ruth's 1920 stats again: 458 At Bats, 172 hits, 150 base on balls, 36 doubles, 9 triples, and 54 homers. Compute his RC.

### Final Exam

These are Henry Aaron's numbers for the 1959 season: 154 Games, 629 At Bats, 223 Hits, 46 Doubles, 7 Triples, 39 Home Runs, 51 Bases on Balls, 9 Sacrifices, 4 HBP's. Compute the following: Batting Average, Total Bases, Slugging Percentage and OBP. Compare his numbers with those of his fellow Hall of Famers.

### Pitching Stats

Pitching stats are relatively easy to figure out. I will list here some basic formulas:

Won Lost Percentage (WLP) = Total Wins/Total Decisions
Earned Run Average (ERA) = (Earned Runs Given Up/Innings Pitched) X 9
WHIP = (Hits Allowed + Walks Allowed) / Total Innings Pitched
Strike outs per one hundred innings - Total K's /Total Innings Pitched
Strike out to Walk ratio - K 's/BB's

Examples: 1. .355, 2. .406, 3. 344, 4. .847, 5. .438, 6. 205.5
Final Exam: BA .355, Total Bases 400, Slugging Percentage .636, OBP .401

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