[Ganchrow]

For updated data please see my Half-Point Calculator.

Spread	N	Freq.
0	248	0.00%
1	657	1.22%
2	801	1.87%
3	989	6.67%
4	1,038	2.99%
5	1,108	2.08%
6	1,015	2.76%
7	955	5.45%
8	960	1.98%
9	870	1.26%
10	693	3.17%
11	668	2.10%
12	684	1.61%
13	624	0.48%
14	585	4.44%
15	995	1.01%
16	957	1.67%
17	912	5.04%
18	837	2.99%
19	736	2.04%
20	713	2.81%
21	684	4.68%
22	624	1.28%
23	575	2.09%
24	568	4.40%
25	515	2.52%
26	453	1.55%
27	422	2.84%
28	389	3.60%
29	337	1.48%
30	306	2.29%
31	281	4.27%
32	240	2.92%
33	207	0.00%
34	180	3.33%
35	156	1.92%
36	128	2.34%
37	112	1.79%
38	97	8.25%
39	76	1.32%
40	64	1.56%
41	56	3.57%
42	46	2.17%

---

Methodology:

• All NCAA Football available regular season final scores and closing points spreads (from http://winningpoints.com/) with from the 2000 season through September 30^th of the 2006 season were analyzed (4,054 games in total) for various favorite margins of victory.
• The push frequency for a given point spread was determined by the percentage of games with a closing spread within 4 points (2 points for spreads of 14 or less) of the spread in question ending with a favorite margin of victory equal to that spread. For example, the push frequency of a spread of 17 was determined from all games with a closing spread between 13 and 21.
• This is based on Stanford Wong's methodology as described in Sharp Sports Betting.

[Ganchrow]

For updated data please see my Half-Point Calculator.

Total	N	Std. Err.	Freq.
33	65	2.64%	4.62%
34	114	1.51%	2.63%
35	178	0.79%	1.12%
36	259	0.77%	1.54%
37	353	0.97%	3.40%
38	474	0.69%	2.32%
39	615	0.46%	1.30%
40	747	0.58%	2.54%
41	886	0.63%	3.61%
42	1,058	0.46%	2.27%
43	1,213	0.38%	1.81%
44	1,380	0.41%	2.32%
45	1,502	0.47%	3.40%
46	1,587	0.33%	1.76%
47	1,677	0.38%	2.50%
48	1,718	0.38%	2.56%
49	1,723	0.37%	2.44%
50	1,702	0.35%	2.17%
51	1,682	0.43%	3.27%
52	1,609	0.40%	2.67%
53	1,548	0.38%	2.26%
54	1,456	0.37%	1.99%
55	1,346	0.42%	2.45%
56	1,208	0.38%	1.74%
57	1,084	0.36%	1.38%
58	913	0.56%	2.96%
59	792	0.76%	4.80%
60	651	0.55%	2.00%
61	556	0.69%	2.70%
62	452	0.54%	1.33%
63	378	0.83%	2.65%
64	316	0.63%	1.27%
65	265	0.92%	2.26%
66	211	0.94%	1.90%
67	172	0.82%	1.16%
68	140	1.01%	1.43%
69	113	1.95%	4.42%

---

Methodology:

• All NCAA Football available regular season final scores and closing points spreads (from http://www.covers.com/) from the 1990 season through the 2006 season were analyzed (4,924 games in total) for the frequency of various totals.
• The push frequency for a given point spread was determined by the percentage of games with a closing spread within 3 points of the over/under in question ending with a total equal to that over/unders. For example, the push frequency of an over/under of 42 was determined from all games with a closing over/under between 39 and 45.
• This is based on Stanford Wong's methodology as described in Sharp Sports Betting.

[Dark Horse]

Great stuff, Ganch.

Just checking if 38 with a percentage of 8.25 is correct.

So, if I understand correctly, that means that of the 97 games within 4 pts of 38 (i.e. spreads 34-42), 8.25 percent ended on 38.

[darkghost]

That is an unusually high percentage for such a high spread but then again the sample size is still too small.

[Ganchrow]

Originally Posted by Dark Horse

Great stuff, Ganch.

Just checking if 38 with a percentage of 8.25 is correct.

So, if I understand correctly, that means that of the 97 games within 4 pts of 38 (i.e. spreads 34-42), 8.25 percent ended on 38.

Yes that is correct.

But just remember that the sample size for that spread is only 95.

[LVHerbie]

How can you use this data to see the value of buying (or maybe selling, if one is using pinnacle) a half point or more at certain numbers? I'm assuming that this type of data is what sites use to decide what buying and selling of points is worth and I've also assumed that they obviously charge more (or pay less) then the true value... Thanks for good info ganchrow....

[Ganchrow]

Originally Posted by LVHerbie

How can use this data to see the value of buying (or maybe selling, if one is using pinnacle) a half point or more at certain numbers?

The results will be slightly different whether you're moving on to or off of an integer line.

Let's assume you're moving on to an integer line that occurs with probability p, and further assume that you're buying a half point, and that the theoretical hold on the unadorned line is given by H.

If the probability of the buy team winning the bet before the half point was purchased is given by b, then the win probability post-purchase would still be b, the push prob would be p, and the loss prob would be 1-p-b. Hence the relative win prob would be given by b/(1-p), and the fair decimal odds, figuring in a theoretical hold of H, would just be:

(1 - H) × (1 - p)
----------------   (buying a half point on to an integer)
           b

And using similar logic, in the case of selling a half point on to an integer spread (relative win prob post-purchase of [b-p]/[1-p]), fair decimal odds would be given by:

(1 - H) × (1 -p)
----------------   (selling a half point on to an integer)
        b - p

---

Using a specific example:

Purdue -7½ -102
Northwestern +7½ -108

This implies a Purdue ATS win prob of 49.30%, a Northwestern ATS win probability of 50.70%, and a theoretical hold, H, of 2.36%.

So let's first consider buying a half point on Purdue (b=49.30%). From the chart above we see that the spread 7 has an associated probability, p, of 5.45%. Using the buy-on-to-an-integer-formula we find that fair decimal odds (assuming zero book profit other than the original hold) for the purchase of the half point should be: (1-2.36%)*(1-5.45%) / 49.30% ≈ 1.8726, corresponding to US-style odds of about -114.60. Pinnacle is offering the line at -117, implying (if you trust the predictive power of the push frequencies above) that it's charging a player an extra 0.93% worth of hold make the half point purchase.

In the case of the sale of a half point on Northwestern (b = 50.70%) fair decimal odds would be given by (1-2.36%)*(1-5.45%) / (50.70% - 5.45%) ≈ 2.0402, or US-style odds of +104.02. Compare this to Pinnacle's line of +103 on the offered half-point, and you see that you're giving up an extra 0.49% worth of hold to make the sale.

---

Anyway, the logic is nearly identical in the case of buying or selling off of an integer spread and I leave the following as an exercise for the interested reader:

Assuming no change in theoretical hold, and taking the push probabilities above as given, what money line should be associated with a side of Fave -6½ given a market of:

NCAA FB Fave -7 -102
NCAA FB Dog +7 -108

[Ganchrow]

A number of people have recently been asking me about how to calculate the fair price of buying or selling a half point when moving off an integer spread (the above post only illustrates how to perform the calculation when moving on to an integer spread.) So I thought I'd just fill in the two remaining buy and sell scenarios.

Let's assume you're moving off of an integer line that occurs with probability p, and further assume that you're buying a half point, and that the theoretical hold on the unadorned line is given by H.

If the relative probability of the buy team winning the bet before the half point was purchased is given by b then the absolute win probability^* would be b x (1-p), and the win probability post-purchase would be b x (1-p) + p, the push prob would be 0, and the loss prob would be 1 - b x (1-p) + p. This means that the fair decimal odds, figuring in a theoretical hold of H, would just be:

    (1 - H)
---------------   (buying a half point off an integer)
 b x (1-p) + p

Similarly, in the case of selling a half point off of an integer, the win probability post-purchase would be b x (1-p) with a push prob of zero. This means that the fair decimal odds, figuring in a theoretical hold of H, would just be:

    (1 - H)
---------------   (selling a half point off an integer)
   b x (1-p)

(Note that if we were going to express these two formulas in terms of pre-purchase absolute win probability, b', then the two formulas above would simplify to (1-H) / (b'+p) for buying and (1-H) / b' for selling.)

So now we can answer the question from above:

Originally Posted by Ganchrow

Assuming no change in theoretical hold, and taking the push probabilities above as given, what money line should be associated with a side of Fave -6½ given a market of:

NCAA FB Fave -7 -102
NCAA FB Dog +7 -108

This is a case of buying a half point off an integer. Based on a market of -7 -102/+7 -108, then as in the previous post above the relative win prob of the favorite, b, would be 49.30% with a theoretical hold, H, of 2.36%. From the chart above we see that the spread 7 has an associated push probability, p, of 5.45%.

Hence, the fair decimal odds after buying a half point from -7 to -6½ would be (1-2.36%) / [49.30% x (1-5.45%) + 5.45%] ≈ 1.8754, or US-style odds of -114.23.

---

^*The relative probability of a bet winning refers to the percentage of non-push outcomes where the bet wins. The absolute probability of a bet winning refers to the percentage of all outcomes (including pushes) where the bet wins. (Hence, it should be apparent that in the case of a non-integer spread (where there's no probability of a push) the relative and absolute win probabilities will be equivalent.) This means that for any relative win prob b, and any push prob, p, the absolute win prob is given by b x (1-p).

To give an example:

Team A line +100
Team B line +100
Push Probability 20%

The relative win probability of both Teams A and B would then be 50% and the absolute win probability would be 50% (1-20%) = 40%. In other words, the probability of A winning, conditioned on A & B not pushing, is 50%, while the unconditional probability of A winning is 40%.

[cincy_1]

This is a GREAT thread. Thanks for posting it.

[linebacker]

cool

[strictlywinners]

i absolutely love this thread. Im am a math and probablilty junkie.

[idontlikerocks]

can u get a larger sample? perhaps from prior year scores.. and can u post the same information on half-time lines please?

[Ganchrow]

Originally Posted by idontlikerocks

can u get a larger sample? perhaps from prior year scores.. and can u post the same information on half-time lines please?

My half-point calculator uses data going back to 1994.

As far as half-time data goes, that may be available in a future version depending upon data availability.

[louis]

This is great stuff. I want to thank Ganchrow for this information. I wonder how much the frequency of the spread varies with the total. For example, with a lower total, taking a middle of the "3" becomes more valuable, especially near the end of the season when the lines are sharp.

[Debbie3]

This is really great stuff. Love math and do enjoy this thread

___
http://www.kansascitychiefsfans.com/

[Richkas]

This stuff only matters if your betting everygame.

[LINE-crush-ER]

I am with you ,
I am glad we have someone to do this for us .
when would have time to call in our bets
what I get out of ths is , the cappers are suppose to push every game ,
they dont , so this is how close they are to being physics , this is how close they are to being near
so basically guys someones going to win the game , just be on the right side
but still glad i dont have to do this

[clowncar]

I have been sports betting for a long time and I also make my rounds at most of the handicapping sites on the internet.

This is one of the best threads that I have ever seen. The lazy will just disregard it but those interested in actually making money should take notice.

Truly appreciate this.....

[dabruinwarrior]

Hello,

This is the first time I'm posting. I had a question. For both NCAA and NFL, I am playing at a local book that fixes their lines from wed/thurs, however the vig is 20%. Sometimes there is 4.5 to 6.5 pts gaps on both o/u's and pointspreads(difference from a current line to the fixed line). For example, last week on one line I had North Texas at +22.5. On another I had North Texas+17.5 I was looking at the push chart for both NCAA and NFL on both O/U and sports and I was confused on the frequency percentage because the bottom notes that the percentage is taken from a range of 2 or 3 pts. I was wondering if anyone out there knew when it is mathematically feasible to middle between a fixed line with 20% vig and moving (current line like pinnacle) with a vig of 5%.

Thank you.

[notset]

Ganch thx for this theard, will be bookmark it...