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Fantasy Strategy Ideas from the Guru
Optimal Smallworld Rosters
July 4, 1999
I calculated the optimal rosters for rosters varying from $50 million to $120 million based on SWP production (SWP/EG) at the end of June. The tables at the bottom of the page show the optimal rosters in $5 million increments. This data can be used to answer three pressing questions:
1) What is the value of 1 million additional SW dollars?
Previously on this site, the Guru has noted that the slope of the "efficient frontier" on a graph of SWP/EG vs. $ was approximately equal to 2 SWP/EG / $1 million. However, at the "cutting edge" of the frontier, when applied to fully optimized rosters, the marginal point gain per $1 million is not quite that high. This does not necessarily mean that your expected point gains should be less, however, since it is rare that any team's roster would continually trade along that optimal edge. Nevertheless, maintenance of efficiency is the basis for this discussion.
What happens as one's income continues to expands, while maintaining an optimal roster? As we can see, it is optimal from the beginning to lock in a #1 starter. As your roster gains value, each additional player, although more productive in terms of SWP / EG, is actually LESS productive in terms of SWP / EG / $. This should be fairly intuitive. When you have very little money, SWP / EG / $ is a very critical factor. As the quantity of money you have increases, the less important efficient use of that cash is, meaning that you become increasingly desirous of high SWP / EG players (and you don't quite care as much about the '/$' part). I will refer to this phenomenon as an "income effect" -- the higher your level of income, the less you care about SWP / EG / $ and the more you care solely about SWP / EG.
How big is this "income effect"? Consider the accompanying tables of optimal roster SWP / EG for various roster values from $50 million to $120 million. The last line on each table represents the average value of an extra $1 million for a roster in that value range. As you can see, the additional SWP / EG you can get from an extra $1 million falls from a high of 1.5 extra SWP / EG (for rosters valued between $50 and $55 million) to a value basically 2/3 of that total, about 0.92 SWP / EG. Practically, what does this mean? Well, if you have a high roster value and there are 80 games left, a free $1 million is going to be worth 0.92 * 80 points to you, or 74 SWP. If your roster value is just $50 million, that same additional $1 million is going to be worth 1.5*80 points, or 120 SWP.
So let's say that you have one trade left on Tuesday evening, and you can spend it either on a player you think will go up by $1 million, or a player that will give you one extra start for that single trade (see Guru's "Pitching Rotation" for a more thorough discussion of how to get the most starts per trade). Do you make this trade? The easy answer would be that, yes, you would make the trade for the $1 million gainer if you think that the starter will score fewer than 74 points (in the previous example). However, this is only part of the story. Once you get that $1 million in additional cash, you still have to convert that higher roster value into higher production. This will take trades. When you are trading for money, you need to think very carefully about how you can convert that extra value to cash and then to better players. The optimal rosters contained in the tables below spend a lot of trades to get a very few extra SWP / EG.
On a more positive note, the computer is also starting with an already optimized roster; we humans are definitely not. Therefore, each situation has to be evaluated independently. It is possible that an extra $1 million in cash could be converted into more than 1.0 SWP / EG. However be mindful that on average if you are playing very wisely, this shouldn't happen too often (barring injuries and cold streaks of course), and that sometimes converting that extra $1 million in cash into SWP will require waiting to accumulate even more cash, or making a large number of trades. Both of these are hidden costs.
2) How should you lock down players?
Each one of us actually knows who should be on our fantasy team if we didn't have a money limitation -- simply choose the highest point producers at each position. As each of us accumulates more cash, our rosters will gradually look like that ideal team, but how do we get there?
The computer gives us a clue as to what the optimal rosters should look like as our income expands. The exact specifics will change each year based on individual players, but the principles will largely be the same. Let's look at how the computer "locked down" All-Star calibre players at various positions.
First, the computer chose with the initial draft roster value of $50 million to buy Pedro Martinez (note: the player prices are current prices, but once again, this exercise is illustrative). The idea behind this pick was fairly obvious. Pedro has produced a tremendously high number points. By purchasing lower priced players who are very effective for the money, this leaves a large amount of cash that can be spent on a high point producer like Pedro. Therefore, we get a high rate of points per dollar with all our cheap picks, but we also produce a fair number of total points when we add Pedro's numbers.
As our income grows, we will gradually "upgrade" different positions. The logic behind each upgrade is related to the amount of extra SWP / EG we will get. Even though the players are more expensive, we will choose to buy their higher SWP / EG since we can now afford them. Here is a rough run down of the suggested "income expansion" rosters of the computer's optimized picks:
Initial draft: Lock #1 starter
Lock in other players as cash becomes available. Now, obviously, the exact timing of each of these "lock-downs" is a matter for debate, and there are many other factors involved. There are two main principles that cannot be understated, however. First, the computer seems to pick a strong mix of cheap, value picks with All-Stars. Second, certain positions should be upgraded first. The basic principle behind the order of upgrades is largely one of relative dominance. This relative dominance is the productivity of the top player versus the VALUE pick that is the real second or third best alternative. Therefore, at SS, for example, there are multiple great players this season. However, it is one of the first positions to be locked as income expands because there is a relative lack of decent VALUE picks. The reason why catcher is locked down relatively late for position players is likely the presence of Mirabelli, who, at $500K, is an extremely productive player for the money. 3B never really got locked down, since the computer kept oscillating between Matt Williams for points and F. Tatis for SWP / EG / $. Thus, the "value" pick was also an exceptionally good point producer, meaning that the computer was relatively happy with either of them.
3) How do you win this game -- pitching rotations from the beginning or roster value buildup and then rotations? If the answer is the latter, when do you stop trading for gains and start trading for points?
We can use the above tools to give us some hints as to the optimal strategy overall in this game. Let us assume that if you use all 5 trades for cash that you can earn $5 million per week. Further, let us assume that it is costless to move from the optimal roster composed of just $50 million to the optimal roster of $55 million. Furthermore, let us assume that you could simply use the $50 million optimized roster, and use all trades for starts. Trading at peak efficiency, you can rotate Pedro's spot to obtain four additional starters by using five trades. This means that the value of any single trade is equal to, .8*(average per start of the 2nd through 5th best pitchers) = .8*140 = 112 points per trade (roughly). There are 162 games in the season, and the season lasts for roughly 25 weeks. This means that a pitcher rotation strategy could net you 25*5*112 points above the optimized $50 million roster. This is equal to 14,000 points.
If you trade for cash under the above assumptions, how many points could you produce? Let us say that there are 6.5 games per week, and that those games are evenly distributed throughout the season (let's pretend). Over the course of 15 weeks, let us assume you accumulate a roster value of $120 million. The increased roster value will net you 9045 SWP (you gain 7.5 points per game for the $5 million from week one gains, an additional 7.2 points per game for the $5 million gain after week 2, etc.; after week 15, you will earn a steady 77 points per game more than someone with a $50 million roster value). Now, you can rotate trades for the remaining 10 weeks, so that gives you 50 trades, worth about .8*130 each (at a $120 million roster value, you will likely already have two, if not three of the top starters, thereby reducing the SWP / G you can get from your rotated pitchers). Therefore, you will have 9045 SWP above the $50 million roster production (from your increased roster value), PLUS 5200 more SWP from the rotated pitchers, for a grand total of 14,200 points. This means that a team of pure roster rotations can expect to stay close to a roster of money accumulation up until the last week of the season!
This is an extremely well balanced game! Should you go for more than $120 million in roster value? I doubt it, and here's why. There is a way to determine when you should stop trading for cash and start trading for gains. For simplicity, let's assume that each $5 million in gains is equal to 30 points per week (this roughly corresponds to the information in the table). By trading for gains again this week, you will get those 30 extra points per week for each of the remaining weeks. With 10 weeks remaining, for example, you could expect that $5 million to earn you 300 more points. Those five trades used for starts could earn you 4*130 = 520 points. Therefore, even with the above numbers (which are fairly generous for both start traders and money traders), waiting until 10 weeks left in the season to change strategies is not optimal. You should have been trading for starts earlier.
So how much earlier? To find out when you should quit trading for gains, calculate your estimate for how many points you could get by trading for starts. Divide that calculation (520 in the above paragraph) by the number of weeks left in the season. Then separately calculate how many millions you think you can gain by trading. Refer to the tables to figure out how much those extra millions should be worth per week (take the extra SWP / EG and multiply by 6.5 or so). See which is larger. Once the points you can get per start is larger than the value of the extra money, it is time to rotate!
I only wish I would have
known all this back in April :-). Happy trading!
Tables showing optimal rosters
in $5 million increments
RotoGuru is produced by Dave Hall (a.k.a. the Guru), an avid fantasy sports player. He is not employed by any of the fantasy sports games discussed within this site, and all opinions expressed are solely his own. Questions or comments are welcome, and should be emailed toGuru<email@example.com>.
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