# More Discussion of Auction Price Inflation

How’s that for a clickbait headline? (Not so good). Yesterday’s post on the interaction between keeper values and inflation generated a lot of great discussion. If you’re interested in that sort of thing, I recommend wading into the comments.

As one commenter noted, when calculating inflation, the industry standard is to use pre-inflation price times the sum of one plus the inflation rate. Or written another way: Post-inflation price = Pre-inflation price * (1 + inflation %). Said commenter thought I preferred: Post-inflation price = Pre-inflation price ^ (1 + inflation %).

I don’t use either formula. But to be entirely honest, my math chops aren’t great. I’m sure they exceed the average American since the media kindly informs us we’re all stupidheads. I digress, the point is that I don’t agree with either method of formulating inflation. Instead, I try to walk a middle line while leaving myself free to make big changes to my draft plan mid-auction.

When a league is sufficiently competitive to merit the labor, I hand-calculate my inflation values. First you have to get an estimate of the actual inflation. I usually just do some simple spreadsheet work using the FanGraphs auction calculator. For competitive reasons, I don’t generate my personal valuations using that tool. Still, it’s good enough for making estimates. I only need a rough idea of the surplus value of all keepers.

Once I know surplus keeper value, then I know how many extra dollars are in the draft pool relative to the remaining talent. Here’s where you would apply a formula or, in my case, use arbitrary personal values. Here’s how I go about it.

First, there are certain high profile targets. Mike Trout is one of them. Maybe you’re enamored with a certain pitcher – I like Dallas Keuchel more than most. A “high profile targets” list doesn’t have to mean the top 15 players in the draft pool, but it probably should only contain high priced players. It could just be the top 15 players. I’ll go above and beyond my price estimate for guys on this list. As it turns out, many of your rivals will too. You’re unlikely to win more than a couple of them.

After addressing the most attractive talent, I have a bundle of leftover surplus value. Call it roaming cash. I’ll distribute this based on position and category scarcity as well as my roster composition. For me, they’re my reserve cavalry; I call upon them as needed. For others, they have auto-updating spreadsheets that calculate the value of each player to their current roster. I recommend going this latter route for most serious fantasy players.

Unusual Philosophy

I have an unusual philosophy when it comes to drafting – I don’t believe it matters who I pick. I mean, yes, it does matter, but our projections aren’t good enough to take a hard and fast approach to valuation. I played with value ranges this winter. If memory serves, I had Giancarlo Stanton worth between \$27 and \$54 in my home league (pre-inflation). The size of the range diminishes as the quality of player diminishes, but most players carry a very wide set of likely outcomes.

It’s common to say that the goal of a draft is to do two things: accrue the most units of production and pay the least for those units. Those phrases mean the same thing assuming everybody spends all of their money. It’s also a shortsighted mindset. Winning the draft is only half the battle.

Since we don’t know what will actually happen, I figure I need reasonable projections, roughly accurate expected dollars, and a manageable roster. Few leagues are decided on draft day. Team management, trades, and waiver moves play a huge role in deciding a winner. Picking up the next J.D. Martinez in place of Scrublord McGee can be more important than any draft pick.

I’ve played the “stick to my values” game in the past, mostly with bad results. Typically, I find I made some errant assumptions. Last year, too many people used the same projection sources (Steamer and ZiPS) which leads to overlap in valuations. Then you wind up in bidding wars for players only Steamer likes. I paid way too much for Mark Trumbo, and I’ve never even liked him (well, not since he was a waiver add).

Member
RC

While I think that the Post-inflation price = Pre-inflation price * (1 + inflation %) method is the most mathematically sound, one thing that cannot be captured in the math in human behavior. Depending on the actions of others in the league, inflation can fluctuate wildly.

Scenario 1: Everyone follows the same basic methodology, sticks to their prices, and drafts balanced teams. In this scenario the “standard” inflation is probably fine. However….

Scenario 2: 11 of 12 teams have decided they are running a “stars and scrubs” draft. You come in with your “inflated” values, but seem to be outbid on all of the top players. Even by getting an entire team of “values” in the second and third tiers, you end up with money left over. In the meantime, tier 4 has now become the \$1 tier, and the teams that “overpaid” for the stars are getting “deals” on the 4th tier players because the league supply of money is depleted and you don’t have enough roster spots to price enforce.

In most drafts, the true outcome is somewhere between Scenario 1 and Scenario 2. That’s one reason that I think Brad’s suggestion of paying close attention to league history is an important one. Knowing how the other players act and react in a draft is more important that having valuations that tie to the last dollar.

Member

I think that the Post-inflation price = Pre-inflation price * (1 + inflation %) method is the most mathematically sound

I can’t say with certainty that you’re wrong about that, but are you really sure the percentage method is more mathematically sound and not simply more familiar? I don’t know definitively if the power function (thanks Nate!) approach models high dollar players more accurately than the percentage method, as I can’t think of a great way to test that. But we do know definitively that the power function gives the correct amount of inflation for \$1 players (zero) while the percentage method always attributes some inflation to \$1 players even though \$1 players should never be affected by inflation at all. Now proponents of that method will point out that you almost never have enough of a percentage increase to prevent that number from being rounded back down to \$1 and therefore the practical result is the same, but to me it’s meaningful to know for a fact that the percentage method is doing something mathematically wrong even if that wrong largely disappears.

Member
RC

I guess I should specify that it works best when accounting for the \$1 players. Here’s another way to approach it:

Prior to inflating, subtract \$1 from each players value (and \$1 per open roster slot from the pool). Then do the 1 + inflation% method on the remaining dollars. Once it’s done, just add \$1 back to every value. Your \$1 guys will still be \$1 (since you were multiplying by 0 in the inflation step), and the allocation of inflation dollars will match the allocation of marginal dollars you had already determined to be the right match for your pool. So if the top player is worth 1.3% of the total money available, that player will still be worth 1.3% of the money available after inflation.

Member

That’s a neat trick.

Member

But you’re not applying inflation to the dollars you removed and therefore it is still mathematically incorrect.

Member
RC

You don’t need to apply inflation to the dollars your removed. They are the marginal dollars above the minimum cost. So if every team must spend \$25 on their roster at minimum (assuming 25 roster spots), then the “value” of the team isn’t the \$260 budget….it’s \$260-\$25=\$235. \$1 doesn’t really have any “value” over replacement….it’s the second dollar and up that has value, and that’s what needs to be inflated.

Member
RC

If you could draft players for \$0, then not inflating the first dollar would be a problem. But since \$1 is the minimum, it shouldn’t be included in the inflation.

Member

That’s a fair point. I hadn’t thought of this solution before but it is elegant.

Member
dangor2

Scenario 2: I ran into this last night in a 14-game mixed, non-keeper. All the studs were going for \$8-\$10 over value. I salivated and exercised excruciating patience and struck in the middle getting \$2-6 values on every player. Alas, I was kinda happy with my squad. But somehow seeing Victor Martinez and all of the cheap closers go for a dollar each not to mention players like Snell, Buchholz and Harrison also going for a buck to the people that overspent, I suddenly wanted to throw up. I had never thought through this pitfall (it probably can’t happen in a single league as you run out of talent) for shallower leagues. Lesson learned.

Member

It happens in my A.L. and N.L. leagues regularly. ~\$5 players often go for \$1 precisely because of what you mentioned regarding spending on the elites. That being said, how much players cost and what their actual value is are two different subjects, both worth discussing.