PLB Formula FAQ

# PLB Formula FAQ

Published on May 31st, 2005

The P5s Leaderboard Formula:Points = (PrizePool1/2) / (PlaceFinished3/5)

The PocketFives.com Leaderboard Formula is a fraction consisting of two main parts: 1) the numerator, or upper portion, which corresponds to the amount of money put into the tournament and 2) the denominator, or lower portion, which corresponds to the place a particular player finished.

You can think of the numerator as an indicator of how "big" the tournament is (i.e., how many total points the tournament is worth), while the denominator represents the way in which those total points will be distributed to each competing player.

There are three main reasons why PocketFives.com uses this formula as opposed to a formula that is strictly based on amount won or ROI:

* We want a standardized formula that correlates all online tournaments without being bound to the arbitrary payout structure that a given site decides use. In particular, we do not believe that a player should receive more points for finishing 3rd on Party than a player who finishes 3rd in an otherwise identical tournament on Stars, just because Party decides to pay a higher percentage to 3rd place.

* We believe that for tournaments of similar prize pools, place finished is a better indicator of skill than amount won, and we do not wish to reward players for "sneaking" into the next money level. Players who outlast an opponent, even if only by a few seats, should be granted increasingly more points, even if a particular site decides to pay the two spots the same.

* We do not want to discourage people from continuing to play. In a system that solely rewards ROI (even with a set minimum number of tournaments) there are advantages to abstaining from play after producing large scores. In addition, we wish to promote wins (in the spirit of celebrating online talent) as opposed to focusing on how much players are spending to get there. While this line of thought does reward players who participate in more tournaments and allows some competitors to focus on quantity over quality, PocketFives.com believes that this ideology continues to exalt the best players, while still promoting the industry as a whole.

A Standardized Formula that Correlates All Online Tournaments:

When reviewing prize money awarded for similar tournaments across different sites, there are major differences in payouts compared to respective prize pools. In addition, even tournaments on the same site vary in prize pool distribution based on number of entrants. Shown below are three charts that demonstrate these differences.

 PLACE FINISHED STARS 101-200 ENTRANTS DISE 101-200 ENTRANTS 1 30.00% 27.50% 2 20.00% 17.00% 3 11.90% 11.50% 4 8.00% 8.50% 5 6.50% 7.25% 6 5.00% 5.75% 7 3.50% 4.50% 8 2.60% 3.00% 9 1.70% 2.00% 10 1.20% 1.50% ~10-20 1.20% 1.15% PLACE FINISHED STARS 1001-1200 ENTRANTS TILT 1297-1395 ENTRANTS 1 25.00% 22.00% 2 14.00% 14.00% 3 9.00% 10.25% 4 6.50% 8.13% 5 5.30% 6.25% 6 4.30% 4.50% 7 3.30% 2.90% 8 2.30% 2.10% 9 1.50% 1.54% 10 0.90% 0.87% ~10-20 0.45% 0.64% ~20-30 0.35% 0.31% ~30-40 0.30% 0.27% ~40-50 0.25% 0.24% ~50-60 0.25% 0.21% ~60-70 0.20% 0.19% ~70-80 0.20% 0.17% ~80-90 0.15% 0.16% ~90-100 0.15% 0.15% PLACE FINISHED STARS 4001-? ENTRANTS PARTY SUNDAY MILLION 1 20.00% 15.50% 2 11.95% 8.46% 3 7.45% 5.25% 4 5.75% 4.25% 5 4.45% 3.50% 6 3.45% 2.75% 7 2.60% 2.00% 8 1.80% 1.50% 9 1.60% 1.00% 10 0.65% 0.50% ~10-20 0.30% 0.25% ~20-30 0.22% 0.19% ~30-40 0.18% 0.18% ~40-60 0.14% 0.17% ~60-80 0.11% 0.16% ~80-100 0.09% 0.15% ~100-150 0.08% 0.13% ~150-200 0.07% 0.12% ~200-250 0.06% 0.08% ~250-300 0.05% 0.07% ~300-400 0.04% 0.06% ~400-500 0.03% 0.03%

As you can see (even from the small sample set of tournaments analyzed) there is a wide range of payout percentages as related to place finished.

The prize for first place, for example, spans from 30% to 15.5% of the entire prize pool, depending on the size of the tournament or the site on which it is played. Similar gaps in payout percentages are seen across all payout spots.

Note also that approximations had to be used for "grouped" payout spots because different sites almost never cull payouts into similar groups. (Place 11-20 may pay the same amount on Party, whereas on Stars, the relative range spans from 10-18, and Paradise splits the relative range into two groups, with an 11-15 and a separate 16-20.)

Because PocketFives.com believes that the skill required to place in a given tournament does not depend on the arbitrary payout structure that a particular online site decides to use, we created our own standardized curve to reflect the value of first place as compared to all other cashes.

To determine what formula should be used for this standardized curve, PocketFives.com analyzed the average payout structure across all major online sites. Below is the average payout curve for most online tournaments:

Notice the right angle bend very early in the curve. This angle represents the top-heavy payout structure for multi-table tournaments; most of the prize pool is given to the final table. Once we hit this angle, we stair-step down to 0, a graphical representation of "grouping" payouts, the technique that all sites use to simplify prize pool distribution.

The weight formula used by PocketFives.com to approximate the above prize pool graph is shown below. Again, this prize pool weight corresponds to the denominator (or lower portion) of the P5s Leaderboard Formula (weight = 1/(PlaceFinished3/5)).

You will notice that the above graph closely resembles the average payout graph discussed in the last paragraph with a few key exceptions. The weight graph is much smoother, and you no longer notice the sharp right angle or the stair-step descent to 0 (except perhaps as a result of pixelization). The smoothness of this graph provides a great benefit: while still granting the largest percentage of weight to the final table, the distribution is no longer chopped into unequal proportions in relation to how far away someone placed compared to each of his opponents. In addition, this curve creates a standardized payout weight that can apply across all sites.

Below is a final chart comparing two 50-place-payout tournaments with the PocketFives weight distribution (multiplied by 25%, the approximate payout to first for tournaments of comparable size).

 PLACE FINISHED STARS 501-600 ENTRANTS TILT 496-594 ENTRANTS P5S WEIGHT FORMULA * .25 1 25.00% 25.00% 25.00 2 15.00% 15.50% 16.49 3 9.55% 11.25% 12.93 4 7.00% 8.75% 10.88 5 5.50% 6.50% 9.52 6 4.50% 4.75% 8.53 7 3.50% 3.10% 7.78 8 2.60% 2.50% 7.18 9 1.70% 1.95% 6.69 10 1.10% 1.10% 6.28 11 1.10% 1.10% 5.93 12 1.10% 1.10% 5.63 13 1.10% 0.85% 5.37 14 1.10% 0.85% 5.13 15 1.10% 0.85% 4.92 16 1.10% 0.60% 4.74 17 1.10% 0.60% 4.57 18 1.10% 0.60% 4.41 19 0.60% 0.45% 4.27 20 0.60% 0.45% 4.14 21 0.60% 0.45% 4.02 22 0.60% 0.45% 3.91 23 0.60% 0.45% 3.81 24 0.60% 0.45% 3.71 25 0.60% 0.45% 3.62 26 0.60% 0.45% 3.54 27 0.60% 0.45% 3.46 28 0.45% 0.38% 3.39 29 0.45% 0.38% 3.32 30 0.45% 0.38% 3.25 31 0.45% 0.38% 3.19 32 0.45% 0.38% 3.13 33 0.45% 0.38% 3.07 34 0.45% 0.38% 3.01 35 0.45% 0.38% 2.96 36 0.45% 0.38% 2.91 37 0.35% 0.33% 2.86 38 0.35% 0.33% 2.82 39 0.35% 0.33% 2.78 40 0.35% 0.33% 2.73 41 0.35% 0.33% 2.69 42 0.35% 0.33% 2.65 43 0.35% 0.33% 2.62 44 0.35% 0.33% 2.58 45 0.35% 0.33% 2.55 46 0.35% 0.30% 2.51 47 0.35% 0.30% 2.48 48 0.35% 0.30% 2.45 49 0.35% 0.30% 2.42 50 0.35% 0.30% 2.39

You may notice that the gap between the P5s-weight-value and the site-payout-percentage expands as place finished increases. There are two reasons for this:

1) The weight formula is not burdened with a "limited" prize pool and is free to award points independently of the amount of money put into the tournament. Keep in mind, however, that although the size of the prize pool is not a consideration for the P5s weight curve, it is the sole contributor to the numerator (or upper portion) of the P5s Leaderboard Formula.

2) The weight formula doesn't abruptly stop at the last payout position. Although such scores don't count towards leaderboard races, non-cashing finishes still have a relative score, all the way down to last place.

A Formula That Rewards High Finishes in Large Prize Pool Events:

In addition to considering how well a player finishes compared to his opponents, a good rankings formula must consider the size of the prize pool for the tournament in question. While the denominator of the PocketFives Leaderboard Formula weighs players against their competitors, the numerator balances larger prize pool events against their smaller counterparts.

Cashes in larger prizepool events should be valued higher than those with smaller buy-ins or those with fewer participants, but point values should not increase linearly as prizepools increase. As an example, winning first place in a 50K prizepool tournament should not be worth twice as much as winning first place in a 25K prizepool tournament. Not only does first place in the larger tournament generally not award double the payout (see the payout charts for different sites at the top of this article), but also it is not an indicator of twice the skill. The competition may be tougher, but certainly not "twice as tough." More specifically, the change in "toughness" between tournaments does not increase by the same factor as the difference in amount of money put into the tournament.

As such, in the nominator of the Pocketfives.com leaderboard formula, the spectrum of online tournaments yields another standardized curve. Higher prize-pool events make up the top end and lower prize-pool events make up the bottom end. The result is a three-dimensional curve, gradually rising as tournament prize pools increase and peaking on each slice at first place: