Participants of daily GPP tournaments often get into a sticky situation when their team is successful, all risks are calculated, but the winning goes to other players. It may occur on a regular basis and irritate “outsiders” or even result in unwillingness to continue an interesting game.

Reasons for loss

It stems from mathematical phenomenon called “dispersion”. The term was borrowed from Einstein's theory of probability. It is a mathematic indicator of deviation from the expected event probability ratio.

For better understanding the phenomenon, let’s consider an example. A player spins a perfect coin without scuffs and notches. According to the theory of probability, twice tossed coin would result in one head side and one tail side. In reality, the result may be different, because of the dispersion.

Dispersion factors

In GPP tournaments with a significant number of participants, dispersion may occur because of specific reasons. The main problem is the disposition of the prize fund among a limited number of participants. To get to the winning places is difficult even forthose well-versed in fantasy sports.

## Dispersion vs.the number of tournaments

Dispersion index depends on the number of tournaments: the more often a player participates in the competition, the greater winning probability is.

Reducing of the mathematical deviation can be clearly illustrated by an example. Let us assume that GPP tournament involves 25 people who contributed \$10 each. The prize fund of the tournament is \$225. The fund is distributed amongfive winners in percentage terms.

An experienced player with a long-term ROI amounting to 19% takes part in the tournament. The percentage corresponds to the average level of the best players in the daily fantasy sports in the United States, and also raises the probability of receiving a prize in amount of 26%. ROI is an economic term, indicating investment-profit relationship.

To calculate the impact of dispersion on the probability of receiving a prize you can use network calculator. Let us assume that the player will participate in 10 tournaments. In such a case, the profitgraph is as following (Fig.1).

The yellow curve indicates that under favorable results, the winning will be \$160, which is unlikely, taking into account the total amount of prize money of the tournament.

The green curve indicates that the player can win 2 out of 10 games at best. The probability of loss is 45%.

The situation will change for the better if the player participates in 100 tournaments. The graph looks differently (Fig. 2), and the probability of loss is reduced to 21%. Dispersion is reduced.

The last calculation is made for 1 000 tournaments. Dispersion rate approaches zero, a larger number of calculated options is at the top of the graph (Fig. 3) and promises profit, with the number of losses reduces greatly.

Experiment result

The illustrative example shows that in the longer term player will get winning places more often, since the impact of dispersion on winning probability approaches zero.

Experienced player will lose in a short period of time, but it should not spark panic – it is a natural process based on mathematical model of the theory of probability.

Tips for dispersion reduction

To reduce dispersion and increase profitability is possible in the following way:

• participate in the GPPtournaments with a limited number of winners more rarely
• register several teams for the same tournament (some team members should be the same)
• control bankroll
• abandon GPPtournaments in favor of other formats (e.g.: H2H or 50/50).

Successful participation in fantasy games depends greatlyon the intelligence of players. The concept of dispersion allows you to better understand the probability of winning/loss as for fantasy sports professionals.