(First in what may prove to be a series on the math of fantasy sports. Disclaimer: I am not a statistician, so consider this to be on the level of a "Dummies" book.)
So you've made a deposit into Fantasy Sports Live. A question that may immediately come to mind is "how many contests should I play?"
Let me answer your question with a question: "How much risk are you comfortable with?"
Assume, first of all, that you have determined the amount that you're going to put in play for the day's set of contests (1). Let's say, for example, that you've decide that you're going to play $22 worth of football contests.
In that case, your choices are one $22 contest, two $11 contests or four $5.50 contests (yes, theoretically you could play twenty-two $1 contests, but let's be real here).
Next, assume that you have an edge and that edge is consistent. You're an educated fantasy football player, which gives you an edge of 55% to win, 45% to lose in any given contest. (2)
Third, assume that you play heads up contests. (3)
If you put your entire roll on one contest, you have a 55% chance of winning $40 (plus $18 net) and a 45% chance of losing $22 (minus $22 net).
If you decide to play two contests, you have a 30.25% chance of winning $40 (plus $18 net), a 49.50% chance of "winning" $20 (minus $2 net) and a 20.25% chance of losing $22 (minus $22 net).
If you play four contests, you have a 9.15% chance of winning $40 (plus $18 net), a 29.95% chance of winning $30 (plus $8 net), a 36.75% chance of "winning" $20 (minus $2 net), a 20.05% chance of "winning" $10 (minus $12 net) and a 4.10% chance of losing $22 (minus $22 net). (4)
We can draw two obvious conclusions from this very simplistic example:
1. When you spread your bankroll over more contests, your risk of ruin (losing it all) is reduced. In this example, you've 45% likely to "go broke" on 1 contest, only 4.1% likely if you play four.
2. Conversely, the more contests you play, the less likely it is that you will make the big score -- less than a 10% chance of coming out plus $18 over four contests vs. 55% in one.
Also (but not obvious, given the simplistic example), once you get beyond one contest, the more contests played - assuming the same edge - the greater the probability that you will turn a net profit.
The takeaway? If you're trying to build a bankroll in a hurry, you'd generally be better off playing fewer, higher buy in contests (IF you can maintain the same edge). If you're more concerned with going broke, spreading your buyin over more contests is the way to go.
More thoughts on this subject to come.
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Notes:
(1) The portion of your "bankroll" that you should put into play in any given week is an entirely different subject, and one which I hope to touch on in another post.
(2) Maximizing your edge is also a subject for another post. This is groundwork right here. I realize that it's extremely simplistic to assume that your edge will always be the same - in the real world, it never is, in large part because you'll pretty much never be playing the same opponent with the same lineups.
(3) For the sake of simplicity. The math gets harder if we're talking 6 or 10 player contests.
(4) It may also be worth noting that in this example your expected value - expected return - in each case is exactly the same, $22. This is a function of both consistent assumptions and the proportionately identical 'rake' charged by the site.
So you've made a deposit into Fantasy Sports Live. A question that may immediately come to mind is "how many contests should I play?"
Let me answer your question with a question: "How much risk are you comfortable with?"
Assume, first of all, that you have determined the amount that you're going to put in play for the day's set of contests (1). Let's say, for example, that you've decide that you're going to play $22 worth of football contests.
In that case, your choices are one $22 contest, two $11 contests or four $5.50 contests (yes, theoretically you could play twenty-two $1 contests, but let's be real here).
Next, assume that you have an edge and that edge is consistent. You're an educated fantasy football player, which gives you an edge of 55% to win, 45% to lose in any given contest. (2)
Third, assume that you play heads up contests. (3)
If you put your entire roll on one contest, you have a 55% chance of winning $40 (plus $18 net) and a 45% chance of losing $22 (minus $22 net).
If you decide to play two contests, you have a 30.25% chance of winning $40 (plus $18 net), a 49.50% chance of "winning" $20 (minus $2 net) and a 20.25% chance of losing $22 (minus $22 net).
If you play four contests, you have a 9.15% chance of winning $40 (plus $18 net), a 29.95% chance of winning $30 (plus $8 net), a 36.75% chance of "winning" $20 (minus $2 net), a 20.05% chance of "winning" $10 (minus $12 net) and a 4.10% chance of losing $22 (minus $22 net). (4)
We can draw two obvious conclusions from this very simplistic example:
1. When you spread your bankroll over more contests, your risk of ruin (losing it all) is reduced. In this example, you've 45% likely to "go broke" on 1 contest, only 4.1% likely if you play four.
2. Conversely, the more contests you play, the less likely it is that you will make the big score -- less than a 10% chance of coming out plus $18 over four contests vs. 55% in one.
Also (but not obvious, given the simplistic example), once you get beyond one contest, the more contests played - assuming the same edge - the greater the probability that you will turn a net profit.
The takeaway? If you're trying to build a bankroll in a hurry, you'd generally be better off playing fewer, higher buy in contests (IF you can maintain the same edge). If you're more concerned with going broke, spreading your buyin over more contests is the way to go.
More thoughts on this subject to come.
----
Notes:
(1) The portion of your "bankroll" that you should put into play in any given week is an entirely different subject, and one which I hope to touch on in another post.
(2) Maximizing your edge is also a subject for another post. This is groundwork right here. I realize that it's extremely simplistic to assume that your edge will always be the same - in the real world, it never is, in large part because you'll pretty much never be playing the same opponent with the same lineups.
(3) For the sake of simplicity. The math gets harder if we're talking 6 or 10 player contests.
(4) It may also be worth noting that in this example your expected value - expected return - in each case is exactly the same, $22. This is a function of both consistent assumptions and the proportionately identical 'rake' charged by the site.
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