Homework Assignments

Due Monday, August 26 : Define OPS and discuss briefly its importance. Next, find (1) top 10 players per league sorted by highest OPS (with a reasonable number of plate appearances), (2) top 10 OPS players career, and (3) top 10 OPS single seasons by a player.

Due Monday, September 9 : Define Runs Created, RC/27, and EQA. Find the top 10 players in each league in each of these categories. In brief, why are each of these stats better measures of offensive performance than OPS?

For the presenter: study 3 players of your choice, as long as one of them is Ichiro, and explain why their OPS is different than their {RC, RC/27, EQA}.

Due: Monday, September 16 : Read pages 455-459. For the whole class: assuming the average OPS for an outfielder is .820, determine the OPS the Red Sox replacements for Manny Ramirez (in 2002) must have to make that position league average. Assume that the average player gets 650 plate appearances in a year. (Assume Ramirez gets injured today, ending his season.) Then, determine the OPS at that position if his replacement makes an out every time. Finally, determine the OPS at that position if a replacement level player at the outfield position has, on average, a .680 OPS.

Next, determine the OPS of the Braves' first base position in 2002. Also, find the combined salary at that position.

For the presenter: given a replacement level average for center fielders of an OPS of .600, what was the CF OPS for the Mariners in 1995? Assume 650 plate appearances and that Griffey was the only CF until his injury.

Due Monday, September 23 : Define MLE's. Compute MLE's for the following two Minor league players (assume both players are in AAA, so the expected decrease in offense would be 18%):

Name	AB	R	H	2B	3B	HR	RBI	BB	K
PlayerA:	483	91	156	33	5	20	76	53	107
PlayerB:	562	103	160	28	1	27	100	40	130

Assume player A plays in a park that increases offense (all kinds) by 10%. Assume player B plays in a park that decreases offense by 5%. Which player had the better season (by OPS)?
Repeat, reversing the home park factors. Now which player had the better season?

Would either of these players have done better in the Majors than the following player (assume neutral park):

Name	AB	R	H	2B	3B	HR	RBI	BB	K
JoeCool	575	102	120	15	0	16	55	60	50

Due Monday, September 30 : Offensive Strategy

First, read this article. Suppose that you are the manager and you have a runner on first, with no one out. You want to know whether you should sacrifice or perhaps steal.

Some data:

• The probability of the bunt advancing the runner to second, with the batter making out is 70%.
• The probability of the bunt resulting in a double play is 10%.
• The probability of the bunt resulting in 1st and 2nd is 10%.
• The probability of the bunt resulting in an out, with no advance, is 10%.

• From the table, write down the expected runs per inning of each of the following scenarios: man on 2nd, 1 out; no one on, 2 outs; 1st and 2nd, 0 outs, and man on 1st, 1 out.
• Compute expected runs per inning if you bunt. Is this better or worse than not bunting, based on number of expected runs scored?
• Suppose that there are only 2 possible outcomes: man on 2nd, 1 out, and 1st and 2nd, 0 out. What percent of the time must the bunt result in 1st and 2nd to make the expected number of runs scored identical to not bunting?
• What is the break-even point of stealing 2nd, with 0 outs, if we assume that either the runner is out or makes second (i.e., no errors are possible).

Next, consider the table of probabilities of scoring at least one run. Answer the following:

• Is it better to bunt a runner to 2nd with 0 outs than to not bunt, if you want to maximize the chance of scoring at least one run? Why or why not?
• Is it better to bunt a runner to 3rd with 0 outs than to not bunt, if you want to maximize the chance of scoring at least one run? Why or why not?
• Is it better to bunt a runner to 3rd with 0 outs than to not bunt, if you want to maximize the chance of scoring as many total runs in a game as possible? Why or why not?

Note: many of you may be unfamiliar with probabilities. A probability is simply the likelihood that an event occurs. In particular, the probability of a coin coming up heads is 1/2. An expected value is just an average. So, the expected number of heads over 10 coin flips is 5. That doesn't mean that there will be exactly 5 heads, but that is what we expect.

For this assignment, you will be using weighted averages to compute expected values. This sounds horrible, but isn't. For example, suppose that a hitter either homers or strikes out, with probability 1/2 for each. Then, the expected number of bases that the hitter gets in a given at bat is 2. We get that as follows: (1/2) * 4 + (1/2) * 0 = 2. In other words, half the time he gets 4 bases, and half the time he gets 0 bases. If instead the probability of a homer is 3/4 and the probability of a strikeout is 1/4, the expected number of bases in an at bat is (3/4) * 4 + (1/4) * 0 = 3.

Due Monday, October 15 : Find the top 10 all time leaders in the following categories:

• Runs Created (career)
• Runs Created/ 27 outs (career)
• EQA (career)
• EQA (single season)
• OPS+ (career)
• OPS+ (single season)

Due Monday, October 22 : Briefly, define support neutral wins and mention why they are interesting. Find the top 10 MLB pitchers in support neutral wins. Also, find the 10 pitchers most damaged by their bullpen in terms of support neutral wins.

Due Monday, October 29 : Briefly, define zone rating. Why might it be important? Find the top player in zone rating at each position in the National League.

Due Monday, November 11 : Explain define "adjusted runs prevented". In addition, explain how this uses material we have already covered this semester (be specific). Then, list the top 10 relievers in ARP in the major leagues.

Due Monday, November 18 : Briefly describe the Bill James Hall of Fame Monitor. Using that (or other material from this semester), make a Hall of Fame case for an active player. This player should be eligible for the Hall of Fame if he retires this offseason. Please try to choose someone interesting (i.e. not Bonds or Maddux).

Due Monday, December 2 Read the series of articles by Doug Pappas entitled analysis of MLB's finances on Baseball Prospectus site.