SubscribeThis is the fourth and final post in a series describing the methodology the Price Guide uses to come up with dollar values for players. The principal explanation can be found in the previous sections: Part I (standard scores), Part II (positional adjustments), and Part III (dollar values).
In Part I on this series, I explained how the first step of creating fantasy baseball values was finding standard scores based on the top 108 players (for our example 12 team league with 9 hitters per team). I also hinted how this presents a bit of a catch-22: We need to know who the top players are before we can rank them. But we need to rank them before we can determine the top players.
The Price Guide’s solution is to perform the valuations iteratively. Each time it processes, it feeds the top players from the previous iteration into the current one. It keeps going through that process until the results from a previous run are identical to the current run. At that point it has found the optimal player pool.
That means that the first time it runs, it assumes that the first 108 players it comes across must be the top players, regardless of how the list is initially sorted. If the list of players is in alphabetical order, the Price Guide will plug in guys like Reggie Abercrombie and (the humorously named) Andy Abad to come up with standard scores.
Even using these guys, the cream rises quickly to the top. Think of it this way: If you’re in a league where Andy Abad gets drafted in the first round, it still makes tons of sense for you to grab Pujols. In fact, Pujols looks even more valuable in this league, because the competition is even further below him than usual.
So after one iteration, the rankings already look decent. The first round players are mostly ranked somewhere in the first round, although at prices that are too high. Things start to drift a little bit after that, but we are definitely a lot closer than at the start.
The second time through, the extreme values it gave to the top tier players are toned down a bit, and the rankings look like something you could bring to a draft without embarrassment. Each successive valuation after that is really just tweaking the draft pool–moving guys up or down a couple of slots, balancing speed and power, switching around some of the bottom of the barrel players. Within 3 to 10 iterations, it has settled on the optimal draft pool.
Anyway, that pretty well sums up the methodology I’m using to come up with fantasy dollar values. Looking back at the posts, I realize that this isn’t the most interesting subject to discuss. However, my purpose for this series is to provide some reference material–not necessarily enjoyable reading. So consider this series as Appendix A sitting somewhere near the back of the Last Player Picked site.
Of course, if you managed to wade through all four parts of this explanation and have any questions or comments, feel free to let me know.
Related posts:
I personally find these parts the most interesting, the Iterations part is especially intriguing, lol i doubt my excel program could handle that. I just use a simple formula for each position that’s pretty rough and then do standard scores. This site makes it even easier, although I wish I could upload my own projections w/o manually changing each one.
@confused:
iterations are pretty easy to do in excel… i did the same type of thing w/ my homemade college football & NFL rankings. all you have to do, once you have the original set of values and have run a single iteration, is record a simple macro that cuts that set and pastes (values, not formula) over the original ones. then run that macro several times (or program a LOOP if you know VBA) and you’ll start to see them even out.
@mays,
just came across this site (thanks to our mutual love of AJ Mass’s “math” skills) and i love it. i’ve been doing the same type of thing as your price guide (without the auction prices) with almost identical results… and might just abandon it for yours, seeing as you have much more customizable rankings and better projections. keep up the good work!
Just finished reading these four articles on how the price guide works. It’s all easy enough to follow, so kudos for simplifying this process.
I have a couple questions though, which seem not to have been addressed in these articles.
First, you didn’t quite specify what you did about the bench. I’m assuming you ignored it, but please correct me if I”m wrong.
Second, and this might just show my lack of statistical knowledge, why do you divide the difference of the players stats in a category and the average players stats in that category by the standard deviation? It seems as though the higher the standard deviation of a category, the more that category would be sought after; yet, in your system, you seemingly punish categories with higher standard deviations. I understand that by dividing, you accomplish normalizing these categories; however, if there is some other method of normalizing that doesn’t make it harder to value categories with higher standard deviations, it seems as though that might be preferable.
Now, I’m trying to implement a method similar to yours to rank and value fantasy football players for an auction draft. Am I correct in skipping the normalizing step and simply using the points I project the players minus the average points of all of the starters; then, taking the lowest valued player at each position and subtracting their value from each player of their position; finally, dividing the players value by the total draftable value and multiplying that by the total marginal dollars and adding one? This approach seems sensible, but it appears to be pumping out somewhat low dollar values for even the top players from last season.
Regardless of whether you choose to respond to this, I would like to thank you for sharing your methodology of pricing players.
EDIT to above post!: When making my spreadsheet for fantasy football, I made a mistake. The numbers are not low anymore; instead, the numbers at the top are kind of high. However, that is probably to be expected, as Chris Johnson had a remarkable season. Anyways, my spreadsheet is working now, so you can ignore my questions about fantasy football implementation.
@Nate:
No, the higher the standard deviation, the less valuable that category becomes. Standard deviation is basically the average distance from the average, so if it is high, there are a wide range of values for that category. If it is low, then most values in the category fall pretty close to the average, making the outliers much more valuable. If nearly everyone in the league hits between 15 and 25 homers with an average of 20, then a player who hits 50 becomes much more valuable because the standard deviation for that category is low. Alternatively, if there were a bunch of players who stole very few bases and a bunch who stole over 50, with an average around 15, then stealing 60 bases is less valuable than the homers because it is not as uncommon to steal that many bases, hence the standard deviation is higher. Hope that clears it up a little.
@Matt:
Thanks a lot. That certainly clears things up!
I really appreciate your blogs. I have been doing a similar set of valuations, but do them with some manual sorting due to the idiosyncrasies of our league (points) :
Taking all Hitters, sorting them by position, ranking by points at a position, assessing how many players at each position would get drafted, then figuring out how much better at a position is a player than a reference player, and using this for valuations.
Your thought process really is helpful. Thanks.
Instead of average player, I was using the last expected player drafted at a position’s value to set positional value. Example:
If I thought 20 2B were going to be taken (in a 12 team league, 12 + 8 MI…yeah, I know cruder than your method), I would take the points associated with the 20th player and divide that into each 2B points to get a “positional ratio.” This told me how much better than replacement level a player was. Doing this for all players and positions (a couple players I had to decide upon for which position), I would use this factor times their expected points to calculate a value I would use for valuation :
If Ian Kinsler was worth 100 points, but was 20% better than a replacement 2B, he would be 100*1.20 = 120 points for valuation.
So, Am I over / undervaluing players by using the last player taken value for scarcity instead of average player taken?
Great series. This StdDev based system of valuing players makes a lot more sense that SGPs, I’m sold.
I have one question on player pool and average values. The purpose of the player pool is to determine what the average category values (and StdDevs) will be for players in your league in the coming season. But since you and your leaguemates are not clairvoyant, you will not select the best 108 players for your league in your auction (or indeed during subsequent free agent pick-ups). Instead, the expected production of some players will not materialize and leave them out of the top 108. Therefore, doesn’t it make more sense to determine league average values not by looking at the top 108 players in last season’s stats (or this year’s projections) and instead add another 20-30 players to the list to account for inherent inefficiency in player selection?
I’m planning to predict the average values by a) determining the number of hitters on rosters in my league (active and bench players) and then b) adding 20% to that number. This will lower the average values to account for sub-optimal player selection that will naturally occur.