Home > MLB, NFL > Sept. 8 – Simpson’s Paradox, Week 1 Picks (Part 3)

Sept. 8 – Simpson’s Paradox, Week 1 Picks (Part 3)

Well, Aryeh got it right – the answer is that C is not necessarily true – and particularly in this case – it’s not. This particular example is brought up by Ken Ross in his book A Mathematician at the Ballpark (I own it and recommend it). Player A is Derek Jeter. Player B is David Justice.  Let’s look at the numbers a little more closely:

  1995 1996 1997 Combined
Derek Jeter 12/48 (.250) 183/582 (.314) 190/654 (.291) 385/1284 (.300)
David Justice 104/411 (.253) 45/140 (.321) 163/495 (.329) 312/1046 (.298)

When looking at stats, it’s always important to remember the importance of your sample size. Jeter’s .250 year was only in 48 AB. Justice’s .321 year was only in 140 AB – and even though he hit .329 the following year in a significant number of AB, overall he still didn’t make up the difference of hitting .253 in 411 AB in 1995.

 There’s a mathematical classification for this type of occurrence. It’s called Simpson’s Paradox. It’s defined as the apparent paradox that occurs when a trend present in several groups (in our example – years) is reversed when the groups are combined together. There are many different fields where statistics is utilized where this paradox can occur – clinical trials, scientific studies, and sports stats to name a few. So keep an eye on the sample size!

 Here are picks 5 to 1:

Kyle Orton - courtesy broncosbanter.com

5) Denver at Jacksonville (Line : JAX – 2.5, O/U : 39.5) The Jags finished last season pretty poorly. Should be some interesting battles: MJD vs. a fair Denver D-Line – and Orton vs. a weak Jags secondary. The model gives the advantage to the road Broncos in a mild upset:  Broncos 29 Jaguars 23

4) Cleveland at Tampa Bay (Line : TAM – 3, O/U : 37)An opening battle of two teams that struggled mightily last year. However, both teams managed to come on stronger at the end of the year with big wins. Still, the model doesn’t like many points here, and gives the edge to the Browns:  Browns 21 Buccaneers 15.

3) Arizona at St. Louis (Line : ARZ – 4, O/U : 39) Sam Bradford will be thrown into the fire right away, while the Cards try to move on in the post-Warner era. This might be a prime “Week 1 is hard to predict” example- the Cards scored 68 points in their last 2 games of 2009. Even with Anderson plugged in instead of Warner, the model heavily favors Arizona:  Cardinals 34 Rams 19.

 2) San Francisco at Seattle (Line : SFO – 3, O/U : 37.5) Pete Carroll starts the season at home against a hungry Niners team, which now looks like the favorite in their weak division. Hasselbeck and company will look to open it up against a stingy 49ers D, while Frank Gore will try to carve up a weak Seattle D-Line. The model likes San Francisco – Big:  49ers 30 Seahawks 13.

 1) Carolina at N.Y. Giants (Line : NYG – 7, O/U : 41) This is another case of what the model does not know. The model is using last year’s results, where the Giants gave up points to anyone who came calling. In fact, one of those games was a 41-9 whipping by these same Panthers. The model does not know about the new stadium, nor the defensive additions. Even so, 7 seems like it may be a lot of points for a team that went 8-8 last year. It’s definitely an unusual 24 points off of the line, but the model likes Carolina to win big:  Best bet – Panthers 34 Giants 17.

 I will not be posting until early next week due to the Jewish New Year. Then I will post reviews of the games, and how the model did overall.

To all of my Jewish friends and followers, – a happy, healthy, and prosperous New Year.

Categories: MLB, NFL
  1. mike smith
    September 11, 2010 at 12:55 PM

    hey, great article, i just subscribed…if you get a chance, check out my blog and let me know what u think… http://footballguru92.blogspot.com/

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