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### BSAT: The Baseball Statistical Aptitude Test

Think you know baseball stats? Then take your chances at pitching a perfect quiz. And just like pitching a perfect game, mowing down opponents becomes increasingly difficult the deeper into the game you go. You won't need a calculator, but you will need your best stuff to go the distance.

FIRST INNING

1. Runs are:

A. The number of times a player steps on the plate at any point

B. The number of times a player's spikes tear up his socks

C. The number of times a player or team scores

2. LOB stands for:

A. Left on base

B. Loss of batters

C. Lumps on brain

D. Number of hanging curveballs thrown

3. If a pitcher has won 20 games, lost five and had nine no-decisions, what would be his winning percentage?

A. .690

B. .800

C. .588

D. 20

SECOND INNING

4. If a player has come up to the plate 12 times, with three hits, two walks, four strikeouts and three groundouts, what would be his batting average?

A. .300

B. .250

C. .375

D. 755

5. What is a pitcher's ERA if he works 20 innings and allows 25 hits, 16 runs and 10 earned runs?

A. 0.50

B. 4.50

C. 7.20

D. 4,256

6. Slugging percentage measures:

A. The ratio of total bases to at-bats

B. The ratio of extra-base hits to at-bats

C. The number of power hits per game

D. Manny Trillo on a really good day

THIRD INNING

(Not even a close call yet, huh?)

7. WHIP stands for:

A. Wins and Holds gained by Inside Pitching

B. Walks and Hits per Inning Pitched

C. Walks and Hits in all Innings Played

D. Keith Hernandez's middle names

8. Blown saves happen when:

A. A pitcher enters in a save situation but loses the lead

B. A hitter batting against a reliever blows up a save chance

C. A pitcher enters in a save situation, but does not finish the game

D. Mariano Rivera can't play

9. On-base percentage is:

A. The percentage of times a batter reaches base without making an out

B. The percentage of a game that a batter is on the bases

C. A percentage of how many bases are occupied by a team during a game

D. The amount of time the first baseman spends with at least one foot on the base

FOURTH INNING

(OK, these guys have seen you once already.)

10. BABIP is:

A. Batters' Average Bunts that turn Into Pop-ups

B. Batting Average after being Brought Into Play

C. Batting Average on Balls put Into Play

D. Something a toddler might say

11. Runs created measures:

A. How many runs have scored based on what an offensive player has done

B. The number of potential runs a team is likely to score based on its off-season moves

C. How many runs a pitcher has allowed based on how well he can keep runners from advancing on the bases

D. An unfortunate result of too much ballpark food

12. OPS stands for:

A. Overall Power Score

B. On-base percentage Plus Slugging percentage

C. On-base Percentage minus Strikeouts

D. On-board Personal Satellite

FIFTH INNING

(Your fielders are on their game, too.)

13. Fielding percentage measures:

A. How much efffort a player gives to get a batted ball, compared to the league average

B. How many errors a player makes per game

C. How many error-free plays a fielder makes out of his total chances

D. Sam Horn's ability to miss grounders

14. Range factor measures:

A. A player's overall fielding ability

B. The distance an average outfielder covers on a given play

C. How far a pitcher's arm and hips rotate

D. The percentage of total cattle rounded up in a given amount of time.

15. DER stands for:

A. Defensive Error Rate

B. Defensive Efficiency Record

C. Defensive Equalized Runs

D. Record on Even Dates (European naming convention)

SIXTH INNING

(The line drive and dying quail last inning were close.)

16. ISO stands for:

A. Isolated runs allowed

B. Infielders' Saved Outs

C. Isolated power

D. Intentional strikeouts

17. Speed score is:

A. A player's time running from first to third base

B. A measure of how much a player's speed will help a team

C. The number of times a player's speed helps a team win

D. A measure of Mo Vaughn - with a sundial

18. Run support measures:

A. The average number of runs a pitcher's team scored while the pitcher was in the game.

B. The average number of runs gained by putting a particular hitter behind another in the lineup

C. The average number of runs scored by a particular pitcher at the plate when he was in the game

D. How much weight a player can carry while rounding the bases

SEVENTH INNING

(No stretching here - the bullpen's on empty. You're going all nine.)

19. Holds are:

A. The number of times a pitcher does not allow a run in a relief appearance

B. A measure of how well a pitcher holds a runner on first

C. The number of times a reliever enters a game in a save situation, gets one out and leaves with the lead

D. Places underneath a stadium where rowdy fans are taken

20. Leverage is:

A. A measure of the relative importance of two hitters, based on their position in the lineup

B. A measure of the importance of situations in which a reliever has been used

C: The probability that one team will be able to beat another in a season series

D. Kent Hrbek, especially with regard to Ron Gant in a 1991 World Series game

21. PAP stands for:

A. Probability of Accumulated Power.

B. Pitcher Abuse Points.

C. Pitcher Accuracy Percentage.

D. A mispronunciation of David Ortiz's nickname.

EIGHTH INNING

(Good luck finding anyone willing to sit within 10 feet of you in the dugout.)

22. WXRL stands for:

A. Winners' expected runs in late innings

B. Walks that lead to runs in late-game situations

C. Expected wins added over a replacement-level pitcher

D. The call letters to a radio station whose programming motto is: All Bud Selig, all the time

23. EqA is:

A. Equivalent average

B. Equivalent runs allowed

C. Equalized arm rating

D. The amp rating of an equalizer used in the clubhouse

24. FRAR stands for:

A. Fielding runs above replacement

B. Fielding rating adjusted for running speed

C. Fielding range affected by runner position

D. Forecasted runs adjusted for rivalries

NINTH INNING

(Three more batters left. Don't trip.)

25. Win shares measure:

A. How much a player should get paid after winning a playoff series

B. A player's total value to a team

C. How much a pitcher's teammates have contributed to his win-loss record

D. How much good feeling fans get when their teams win

26. A Markov calculation, applied to baseball, is used to:

A. Estimate how many victories a pitcher will earn based on his team's starting hitters

B. Estimate how many runs a given batting order will average

C. Estimate the number of wins a given batting order will produce in a season with an average pitching staff and defense

D. Determine the total effect on a team or league of any players who have lived in or visited Russia.

27. VORP stands for:

A. Value of outs recorded by pitchers

B. Value over other right-handed pitchers

C. Value over replacement player

D. A strange planet only statisticians know

1. Runs

The correct answer: (C) The number of times a player or team scores. Why it's important: It's the object of the game. Score more runs, you win. How it's figured: Simple counting.

2. Batting average

Why it's important: It shows a batter's ability to get hits. How it's figured: Divide the number of hits into total at-bats. (Consult the official scoring rules as to what constitues an official at-bat. Walks don't count.)

3. Winning percentage

Why it's important: Winning is paramount. To use a line from NFL coach Herm Edwards, "You play . . . to win the game."

How it's figured: Divide the number of wins into total decisions (wins plus losses).

4. LOB

The correct answer: (A) Left on base. Why it's important: High numbers generally show wasted opportunities, and the need for a lineup change. How it's figured: For teams, count the number of runners left on base at the end of an inning. For batters, count the number of runners left on base after an at-bat.

5. ERA

Why it's important: It gives an indication of how many runs allowed per game for which a pitcher is responsible. How it's figured: Multiply the number of earned runs by 9 and divide that figure by innings pitched. In this instance, 10 earned runs times 9 is 90. Divide 90 into 20 to get 4.50.

6. Slugging percentage

The correct answer: (A) The ratio of total bases to total at-bats. Why it's important: It gives a decent indication of a batter's power or ability to create runs. How it's figured: Divide a batter's total bases (from hits only) into at-bats. A figure above .400 is good; above .600 often will lead the league.

7. WHIP

The correct answer: (B) Walks and Hits per Inning Pitched

Why it's important: It gives an indication of a pitcher's effectiveness at keeping runners off base. How it's figured: Divide hits and walks allowed by innings pitched. A number below 1.25 is good; below 1 often will lead the league.

8. Fielding percentage

The correct answer: (C) How many error-free plays a fielder makes out of his total chances

Why it's important: It's one way to judge a fielder's performance. How it's figured: Divide putouts plus assists into total chances (putouts + assists + errors).

9. OPS

The correct answer: (B) On-base percentage Plus Slugging percentage

Why it's important: It's a version of runs created that isn't nearly as accurate, but is much easier for fans to compute and use. How it's figured: Add on-base percentage to slugging percentage.

10. BABIP

The correct answer: (C) Batting Average on Balls put Into Play

Why it's important: It's a good way to determine how much of a pitcher's success is due to defense or luck. How it's figured: For a pitcher, divide the number of hits minus home runs into at-bats, without counting home runs or strikeouts. An average BABIP will be around .290. Because the number doesn't depend on the pitcher's skill, pitchers who have unusually high or low numbers generally regress toward the middle the next season. That can project changes in ERA and other stats.

11. On-base percentage

The correct answer: (A) The percentage of times a batter reaches base without making an out. Why it's important: It shows how effective a batter is at getting on base, which statisticians have shown to be far and away the biggest factor in a team scoring runs. How it's figured: Divide times on base (H + HBP + BB + times reached on interefence) by plate appearances (AB + SF + BB + HBP + times reached on interference). A figure of .370 or above is excellent; above .430 often leads the league.

12. Blown saves

The correct answer: (A) A pitcher enters in a save situation but loses the lead

Why it's important: It helps give a better indication of a reliever's performance than ERA. How it's figured: A pitcher is charged with a blown save if he enters the game in a save situation and loses the lead, or if runners he put on base score, resulting in a lost lead.

13. Run support

The correct answer: (A) The average number of runs a pitcher's team scored while the pitcher was in the game. Why it's important: It helps show how much the hitters on a pitcher's team has helped or hurt the pitcher's record. How it's figured: The statistic nearly is always shown as an average of run support per nine innings, and is not calculated for relievers. Take the number of runs scored by a pitcher's team while he is in the game, multiply by 9, then divide by innings pitched. For a season, most pitchers' figures will range between 2.8 to 6.5.

14. Range factor

The correct answer: (A) A player's overall fielding ability

Why it's important: When combined with a player's fielding percentage, this helps show how many balls a player reaches. It's not meaningful for first basemen, catchers or pitchers. How it's figured: Add putouts and assists. Multiply by 9 and then divide by innings played on defense. The number is only meaningful for a large number of games. Normal range factors vary considerably by position, from 6 for a good second baseman to 1.5 for a marginal left or right fielder.

15. ISO

The correct answer: (C) Isolated power

Why it's important: It's a way to measure a hitter's ability to hit for extra bases and create runs without depending strictly on home runs. How it's figured: Subtract a batter's batting average from his slugging percentage. A figure below .085 shows a player who has very little power, anything above .200 is a bona fide power hitter, and .400 or above is the stuff of legends.

16. DER

The correct answer: (B) Defensive Efficiency Record

Why it's important: Created by Bill James, this is a good measure of how effective a defense is at converting balls in play into outs. How it's figured: First, find total plays made. It's calculated by taking the average of two estimates, which follow. The first is putouts minus outfield assists, double plays and opponents' strikeouts and times caught stealing. The second is the sum of a team's opponents' at-bats and sacrifices minus oppoents' hits, opponents' strikeouts and a factor of 0.71 times the team's errors. Average the two estimates to reach plays made.

Then use following formula to find DER: Take errors multiplied by 0.71, add that to plays made and opponents' hits, then subtract opponents' homers. Now divide plays made into that number and you have DER. Big-league teams average around .695.

17. Speed score

The correct answer: (B) A measure of how much a player's speed will help a team

Why it's important: It's a measure, though crude, showing how much a fast, or smart, runner can help a team's production. How it's figured: The speed score developed by James takes five factors - stolen-base percentage, number of stolen-base opportunities resulting in steals, triples, percentage of double-play opportunities resulting in times grounded into a double play, and percentage of times on base ending in a run. The overall score generally is expressed on a scale from 0 to 10, with higher numbers showing players whose better running skills helped more. Most players fall between 3 and 7.

18. Runs created

The correct answer: (A) How many runs have scored based on what an offensive player has done

Why it's important: Created by Bill James, it attempts to show how many runs directly result from a player's actions, both at the plate and on the bases. How it's figured: A fairly accurate calculation of runs created that can be done with easily available stats follows. First, you need to determine a number for three factors. For factor A, use: H + BB + HBP - CS - GIDP. For factor B: TB + (.24 * (BB - IBB + HBP)) + (.62 * SB) + (.5 * (SH + SF)) - (.03 * K). For factor C: AB + BB + HBP + SF + SH. Then: (2.4 * C) + A and (3 * C) + B. Multiply the two figures. With that number, which we'll call "D," use: (D / (9 * C)) - (0.9 * C) = runs created.

The base statistic is a total, so for a big-league season, a number more than 100 is good; more than 125 is stellar.

19. Holds

The correct answer: (C) The number of times a reliever enters a game in a save situation, gets one out and leaves with the lead

Why it's important: It gives some idea of a middle reliever's effectiveness, since ERA for most relievers basically is useless. How it's figured: A hold is credited any time a reliever enters a game in a save situation, records at least one out, and leaves the game never losing the lead. More than one pitcher can be credited with a hold in a game, but a pitcher can't get a hold and a save in the same game.

20. Leverage

The correct answer: (B) A measure of the importance of situations in which a reliever has been used

Why it's important: It helps differentiate with more precision the effectiveness of a relief pitcher. How it's figured: We don't have the space to go through it all. Baseball Prospectus defines leverage as the change in probability of winning the game from scoring or allowing an additional run in the current game situation divided by the probability change from scoring or allowing one run at the start of the game.

21. PAP

The correct answer: (B) Pitcher Abuse Points

Why it's important: It helps show how many high-pitch outings a starter has thrown. How it's figured: Baseball Prospectus created this statistic, which a considerable number of other baseball statsiticians have said may not mean much. BP assigns zero points to any start in which a pitcher throws 100 or fewer pitches. For other starts, it takes the number of pitches thrown over 100 and multiplies that to the third power to determine points.

22. WXRL

Why it's important: It helps show how much more effective a reliever is against the average hitter, when compared to a typical replacement. How it's figured: The actual name of the stat is expected wins added over a replacement-level pitcher, adjusted for level of opposing hitters. The stat takes at least a half-dozen factors into consideration, including a pitcher's beverage of choice on off-days. Wait, that last part isn't part of the formula. We think.

23. EqA

The correct answer: (A) Equivalent average

Why it's important: It's a measure of total offensive value - including skill on the basepaths - per out, if a player was in an average league, home park and faced average pitching. How it's figured: The scale is set to be about equal to batting average for ease of interpretation, so the league average EqA is always .260. First, you have to find raw EqA, which is roughly close to OPS. The raw figure is then normalized to account for league difficulty and scale to create EqA, but there's no need to go into that here. You'll thank us.

24. FRAR

The correct answer: (A) Fielding Runs Above Replacement

Why it's important: It shows the effectiveness of a player's fielding ability when compared to an average replacement player. How it's figured: It might be easier to locate the Loch Ness Monster - or a healthy Larry Walker - than it is to find an easy way to calculate this statistic. The stat normalizes a player's fielding ability based on how many plays most players make at a given position. For a full big-league season, the number of runs an average player would save over the average replacement ranges from 10 for a first baseman to 39 for a catcher.

25. Win shares

The correct answer: (B) A player's total value to a team

Why it's important: It's a way to put into numerical value how important a player is to a team. The statistic credits individual players with the number of wins he contributes to a team, based on almost everything he does on the field: batting, pitching, fielding and even some running. How it's figured: Let's put it this way: For James to fully explain how he calculated the statistic, he needed about 100 pages, or about the average length of a big-league game for most people to read and digest. Play ball!

26. Markov calculation

The correct answer: (B) Estimate how many runs a given batting order will average

Why it's important: It can help a team determine the most productive batting order, as well as how a replacement player would help or hinder the lineup in various spots. How it's figured: Though the statistic has taken criticism because it often strays from the traditional lineup structure. If you have on hand the probabilities of scoring from every runner and out situation, can handle matrix algebra and have a good spreadsheet, the calculations aren't a big problem. But if you think we're going to actually tell how to figure a Markov lineup calcuation, you're crazy.

27. VORP

The correct answer: (C) Value Over Replacement Player

Why it's important: It can help show how much value a given player has to a team, and can help show if an excellent but often-injured player is worth keeping. How it's figured: This is the double-black-diamond slopes of baseball statistics. Unless you can rattle off the definition and uses for "replacement-level delta," have a spreadsheet, and plenty of time, patience, mathematical skill, food, water, and some bread crumbs to find your way back, you will get hurt. We are not kidding. Leave this kind of thing to the trained professionals and just enjoy the result from afar. It's better for everyone this way.

How'd you do?

Give yourself one point for every correct answer. First, though, if you answered "D" to four or more questions, you score a zero for the entire test.