Drafting: Bottom-Up Strategy
Here is a list of pitchers in the imaginary free agent market this year with some
of their 2010 statistics.
Pitcher
Team
Win
SF
16
Tim
Lincecum
LAD
13
Klayton
Kershaw
Cliff Lee SEA/TEX 12
NYY
21
C.C.
Sabathia
LAD
3
Hong-Chih
Kuo
STL
16
Chris
Carpenter
PHI
21
Roy
Halladay
TB
19
David
Price
Ted Lilly CHC/LAD 10
COL
19
Ubaldo
Jimenez
BOS
14
John
Lackey
TB
15
Matt
Garza
SEA
13
Felix
Hernandez
WAS
5
Stephen
Strasburg
ATL
16
Derek
Lowe
CHC
15
Ryan
Dempster
Lose
10
Save
0
ERA
3.43
K
231
WHIP
1.27
10
0
2.91
212
1.18
9
7
0
0
3.18
3.18
185
197
1.00
1.19
2
12
1.20
73
0.78
9
0
3.22
179
1.18
10
0
2.44
219
1.04
6
0
2.72
188
1.19
12
8
0
0
3.62
2.88
166
214
1.08
1.15
11
0
4.40
156
1.42
10
1
3.91
150
1.25
12
0
2.27
232
1.06
3
0
2.91
92
1.07
12
0
4.00
136
1.37
12
0
3.85
208
1.32
You are one of the two general managers to draft these players. The rule is
simple. You first rank all 16 pitchers you would like to pick to your team.
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Name of Player
Toss a coin to decide who gets to pick first. At each time, pick the highest-ranked
player from your rank above. Write down the draft results on the table below:
Team A
Team B
How do you feel about your drafting results? Did you get the ones you like?
Now let’s play dirty a little bit. Let’s assume that you KNOW the ranking of the
other GM. You will then work out a sequence of picking NOT following your ranks,
but to put another party’s last rank onto your last pick. After all, there is no rush
to fetch that player if you are sure that the other GM is not interested in him. Such
strategy is called bottom-up strategy, developed by mathematicians D.A. Kohler and
R. Chandrasekaran in 1969. Let’s practice it:
Team A
Team B
How does this draft look? Does this look a bit fairer than playing clean?