Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I take a look at how the numbers suggest the Jets should attack the Steelers.
Weekly Game Probabilities - Conference Championships
published on 1/20/2011
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As last week, as spreads these numbers are:
Packers -4.5
Steelers -8
My look at the bookies makes it
GB .65, CHI .35
NYJ .35, PIT .65
Pretty much bang on for the NFC. AFC it seems the money is going on the romantic choice (Jets knocking off Colts, Pats then Steelers all on the road would be an incredible story).
Larger bettors are getting on the Steelers thus far. The line opened at about -3 -110 and is now -3 -130 or so.
I've always wondered...does that mean that the smart money is on the Steelers, or the stupid money?
Tom, can you give the formula you use for converting the percentage into a spread. Thank you very much.
Tony. I have used a simulation model to produce a spread-to-percentage table starting at 0.5 points and ending at 40 points. The simulation uses the statistics of two theoretical league average teams and plays out millions of games between them. It has a configurable variable to gift one of the teams a number of points beyond what they score. It then counts how many wins and losses they have, with that advantage, and gives the probability of a team with said advantage winning.
There is no better way of creating the distribution, and too few NFL games have been played on the recent era of the game to get a true distribution from those.
I'd be happy to post up a table of the numbers if you or anybody else would like.
Inverse Pythagorean expectation converts Brian's numbers to spreads of 4.5 and 8.5 -- so theory and simulation pretty much agree.
Normal Pythagorean is used to convert scoring differentials recorded to date to estimate future win probability. I've found that doing the reverse -- taking win % records to date, calculating a win probability for one team over other by using Log5, then applying Pythagorean "backwards" to project a corresponding point differential -- produces a result that by accuracy very closely matches that of the Vegas line compared to actual game results. (Brian's number gives us the win probability straight up and so eliminates the need for the Log5 step, so there we are.)
Tom, I would love to see the conversion table if it's not a bother. I basically want to take Brian's win %age numbers and convert them into a pointspread. Thanks
Here you go tony. You will notice on this table that certain probabilities have multiple values, this is because the probability is rounded to 2dp, since to calculate all these to 3dp would take a long time, and wouldn't be particularly useful. As such, this doesn't really say that no team will ever win by 33.5 points, as we've seen is does happen, it simply means that it happens in only one of every 200 or more games.
Spread Win Probability
0 0.5
0.5 0.52
1 0.54
1.5 0.55
2 0.56
2.5 0.57
3 0.59
3.5 0.61
4 0.63
4.5 0.65
5 0.65
5.5 0.66
6 0.68
6.5 0.69
7 0.71
7.5 0.73
8 0.74
8.5 0.74
9 0.76
9.5 0.76
10 0.79
10.5 0.79
11 0.81
11.5 0.82
12 0.83
12.5 0.83
13 0.85
13.5 0.85
14 0.87
14.5 0.87
15 0.88
15.5 0.88
16 0.89
16.5 0.89
17 0.91
17.5 0.91
18 0.93
18.5 0.93
19 0.93
19.5 0.93
20 0.94
20.5 0.94
21 0.95
21.5 0.95
22 0.96
22.5 0.96
23 0.96
23.5 0.96
24 0.97
24.5 0.97
25 0.98
25.5 0.98
26 0.98
26.5 0.98
27 0.98
27.5 0.98
28 0.99
28.5 0.99
29 0.99
29.5 0.99
30 0.99
30.5 0.99
31 0.99
31.5 0.99
32 0.99
32.5 0.99
33 0.99
33.5 1
Ok, that has posted horribly, hopefully you can ake use of it. Each probability (except for the last, which is simply '1') starts with '0.' so hopefully with that in mind it is readable.
Thank you very much, Tom