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Morning Line

A morning line is someone’s estimate of what each horse’s closing odds will be. It also could be someone’s opinion of what they think each horse’s chances should be. I’m never quite sure which one the author of a morning line is trying to convey. I do know that many morning lines are mathematically incorrect. There is a correct way to make a morning line and hopefully this will help in making a more mathematically correct morning line.

The first thing to do is take the number 100 and add to it the track takeout for win. If the track takeout were 18% our starting number would be 100 + 18 = 118 or 118%. The odds assigned each horse, when converted to a % and added up must = 118%. I don’t believe being a point or two off is the end of the world, but being 5 or more points off is a disservice to the racetrack patron who looks at a morning line for guidance.

To convert odds to percentages you add the divisor to the dividend and divide that number into the divisor. Example: (dividend/divisor) say the odds of a horse are 3/1. Add the 1 (the divisor) to the 3 (the dividend) = 4 and then divide 4 into 1 = .25%. When someone makes a horse 3/1 they are saying that the horse has a 25/118 or will win once every 4.72 attempts. If there were zero takeout, then the horse would win (25/100 = 4) once in every 4 attempts if this line were accurate.

Listed below are the correct percentages when converting odds to percentages.

Tote Odds Formula
Percent Tote Odds Formula
Percent
1/9* 1+10 = 11 10/11 .909 7/1 7+1 = 8 1/8 .125
1/5 1+5 = 6 5/6 .833 8/1 8+1 = 9 1/9 .111
2/5 2+5 = 7 5/7 .714 9/1 9+1 = 10 1/10 .100
½ 1+2 = 3 2/3 .667 10/1 10+1 = 11 1/11 .091
3/5 3+5 = 8 5/8 .625 11/1 11+1 = 12 1/12 .083
4/5 4+5 = 9 5/9 .556 12/1 12+1 = 13 1/13 .077
1 1+1 = 2 ½ .500 13/1 13+1 = 14 1/14 .071
6/5 6+5 = 11 5/11 .455 14/1 14+1 = 15 1/15 .067
7/5 7+5 = 12 5/12 .417 15/1 15+1 = 16 1/16 .063
3/2 3+2 = 5 2/5 .400 20/1 20+1 = 21 1/21 .048
8/5 8+5 = 13 5/13 .385 25/1 25+1 = 26 1/26 .038
9/5 9+5 = 14 5/14 .357 30/1 30+1 = 31 1/31 .032
2/1 2+1 = 3 1/3 .333 35/1 35+1 = 36 1/36 .028
5/2 5+2 = 7 2/7 .286 40/1 40+1 = 41 1/41 .024
3/1 3+1 = 4 ¼ .250 45/1 45+1 = 46 1/46 .022
7/2 7+2 = 9 2/9 .222 50/1 50+1 = 51 1/51 .020
4/1 4+1 = 5 1/5 .200 60/1 60+1 = 61 1/61 .016
9/2 9+2 = 11 2/11 .182 70/1 70+1 = 71 1/71 .014
5/1 5+1 = 6 1/6 .167 80/1 80+1 = 81 1/81 .012
6/1 6+1 = 7 1/7 .143 90/1 90+1 = 91 1/91 .011

* The tote board will display odds of 1/9 but it should correctly be displayed at 1/10.

How I make a morning line is give every horse a % chance of winning and list it in decimal form. The chances of every horse must add up to 1 or 100% (.55 is the same as 55%). Once I have my “chance of winning” I need to multiply by (the takeout + 1). If the takeout is 14% or .14 then the multiplier is 1.14. Looking at row #1 the true “chance of winning” for horse #1 is .55556. If the takeout is 14% then .55556 x 1.14 = .633338

Now that we know how to convert odds to percentages we can construct a morning line that is mathematically correct. An example of making a morning line is listed below.

Horse # Chance of Winning 14% Takeout 24% Takeout




1 .55556 .633338 .688894
2 .22222 .253331 .275553
3 .11111 .126665 .137776
4 .04762 .054287 .059049
5 .03030 .034542 .037572
6 .02299 .026209 .028508
7 .01020 .011628 .012648




Total 1.0000 1.140000 1.240000