Two human examples

1
Two human examples

• Madden, Peden Yamaguchi, 2002
• Reed, Reed and Marten, 2006

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Madden, Peden, and Yamaguchi (2002)

• Introduction to study is all about optimal
  foraging
• reviews the premises
• N1/N2 A1/A2
• habitat matching
• Because foragers in resource site must share
  resources available in that site
• deviations from matching mean individuals in 1
  group obtain more resources than another
• e.g. 50 units of food available
• 40 animals in site 1
• 60 in site 2
• Site 1 animals 1.25 units/animal
• Site 2 animals 0.83 units/animal
• Model states that therefore some animals from
  site 2 move to site 1 to even out and equalize
  ratios
• Notes that this is simply the matching law
• ideal matching
• bias

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Human discrete trial procedure

• Group of humans
• choose 1 of 2 resource sites
• show red or green cards
• can move freely
• Gound that data supported matching
• Problem real life foraging NOT a discrete trial
• so purpose of experiment is to examine humans
• but in free foraging situation

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Experiment 1

• 12 college students
• Could earn 30 and 10 for earning points
• Seated in desks in a circle
• Two cards red and blue
• Score sheets
• Earn as many point as possible
• Allocated different amounts of points to each
  card
• But have to share them among people who show same
  cardSo if red 100 and 10 people choose red
  only get 10 points
• Varied ratio of red to blue points
• At choose now showed card, could keep changing
• When no switching for 5 secs, recorded answer
• Counted red/blue cards, divided and recorded
  points
• Put cards face down again, and did again
• About 20 trials per condition

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Results

• Good interobserver agreement (.98 to 1.0)
• Compared predicted and obtained matching ratios
• intial decision
• final decision
• Initial selection a .4, r2 0.55
• Final selection a .92, r2 .99
• No bias
• BUT initial selection much different than final
  selection- they balanced themselves out to get
  most points!
• Why?
• More knowledge of others actions counted and
  observed others
• Shows this foraging is fluid- as predicted

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Experiment 2

• No talking or switching!
• Same set up
• Only initial card selection counted
• Continued trials in a condition until selection
  was stable (stability criterion)
• Results
• Good IOA 0.97 to 1.0
• Now found better matching a 0.82, r2 0.98
• Why?
• Initial selection now more important
• No more socialization to determine choice
• Chose according to odds, improved with trials
• Responding to ratio of reinforcement, not social
  cues

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Experiment 3

• Now used conc VI VI schedules rather than
  discrete trials
• Tables at each end of classroom where go to earn
  points
• Red paper zone
• Blue paper zone
• Must move to enter a zone (note- no chairs in
  room, subjects did sit on table or near a zone,
  though!)
• Observers recorded placement of participants time
  in reinforcer zones
• Had to be in a zone when points awarded according
  to VI schedule

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Results

• IOA results good again 0.98-0.99
• Movement of participants tended to stabilize
  after initial movement period of about 20 minutes
• a 0.71, r2 0.99
• Not as good as cards, but not bad matching
• Group was sensitive to changes in conditions
• Less sensitive to reinforcement- why? (was
  harder)
• Interesting that initial movement, then ratios of
  individuals in each zone settled down
• Also if more sensitive to reinforcer magnitude
  (absolute amount of points) rather than ratio,
  follow dispersement of points, even when at lean
  side

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Conclusions

• Humans match!
• Are sensitive to group dynamics
• Baum and Kraft found
• Individuals do not match time or response
  allocation to distribution of reinforcers
  obtained by group
• No regular patterns of switching across sessions
• No regularities or preferences for one resource
  site over another across sessions or conditions
• No tendency for human participants to be
  consistently higher point earners across sessions
• BUT looked at MOLAR level
• Madden, et al
• Looked at more molecular level
• Did find shifts in switching WITHIN a session
• Showed melioration moving to the better source
• Suggests are both molar and molecular changes
  that lead to matching!

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Reed, Critchfield and Martens (2006)

• Football and matching
• Again, note that matching law can be broadly
  applied
• widely used in animal research
• optimal foraging
• human research
• employee absenteeism
• teen pregnancy
• classroom behavior

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Why football?

• Want to know if it affects sports behavior
• (why? Because it is there!)
• sites several studies
• Vollmer and Bourret (2000)
• Matching and basketball
• Choosing 2 point vs 3 point shots
• Matching law described decision making for taking
  a shot
• Bias towards making 3pt shots (why?)
• a about 1.0

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why choose football?

• Play calling individual behavior
• Quarterback
• Offensive coordinator and head coach
• Highly skilled
• When calling play, consider success/failure of
  previous attempt in decision for next play
• Individual differences in play-calling patterns
  (throwing vs passing teams)
• Focus at team level

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Method

• Data obtained from NFL
• Primary data
• number of passing/rushing plays
• net yards gained
• Several characteristics
• plays categorized as rushing or passing based on
  what occurred rather than what was called (no way
  of knowing that)
• sacks failed rush play
• yards gained completion even if fumble after
  catch
• Fit data to matching equation
• Ratio of yards gained through passing vs. rushing
  used as predictor of ratio of pass plays/rush
  plays called

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Results

• Season aggregate league outcome
• a 0.725,
• r2 75.7
• b -0.129 (favor of rushing)
• Historical comparisons
• 1975-2005
• 2004 fell out of typical range
• R2 decreases about 4/year across years,
  suggesting more variability in play calling
• Why?
• Shift in rules designed to favor passing
• Free-agency rules
• Salary caps

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Comparison with other leagues

• Top four leagues
• NFL Europe 0.619. 82.1
• CFL a .544, r2 .567
• Arena Football a .56, r2.784
• United Indoor Football League a 61.3, r2 59.8
• Others
• National Womens football association a .55,
  r2 .709
• College teams
• NCAA Atlantic Coast a 0.63, r2.809
• NCAA Western a .868, r2.946
• NCAA Mid-America a 0.509, r2634
• overall college was R2 .57-.95
• Generally good fits
• 6 of 9 leagues favored passing rather than
  rushing
• CLF rushing rather than passing (turnover risk?)

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Special Circumstances

• Examined specific circumstances
• examined down number (1,2,3)
• how does matching change?
• a decreasing with down
• less likely to pass with increased down
• Is this surprising?
• Examined by type of game
• Regular season games
• Preseason fits relatively poor a .43
• Later in season better fits a .58
• Post season slightly better a .59
• Why

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Game by game individual team outcomes

• Does matching fit predict team success?
• Teams show some variability in fit to equation
  (see pg. 290)
• Interesting no relationship with lay
  descriptions of teams
• Colts known as passing team, but showed more
  rushing bias than Atlanta, which was a rushing
  team
• Has to do with ratio of called plays to success
• Bias avoidance of risk of turnover
• Many influences on play calling
• Coach vs. quarterback
• Team structure may differ

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Team by Team analysis

• Better (more successful) teams showed steeper
  matching functions
• If matched better, were better team
• Suggests that matching impacts winning!
• This was significant! R -.579, p.0007
• Why negative?
• Correlation between between matching and LOSSES

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Cause and Effect Questions

• Play calling influences yardage gained
• But yardage gained influences play calling!
• Real world influences
• Many unaccounted for factors
• What is contingency here?
• Matching law assumes a contingency
• What is the contingency for players/coaches, etc?
• Data suggest that better sensitivity to reward
  better success
• How else can use matching law in real world?