Billy Hamilton, 2nd Rounder

On Tuesday night, I participated in the 15-team LABR Mixed League draft (full team recap coming Monday). If you were following the draft live and/or were active on Twitter during the evening, you may very well be aware of the firestorm that erupted after my second round selection. I drew the #11 draft slot, which meant that my second round pick was the 20th. I settled on Billy Hamilton and I will explain why.

But before I successfully convince you that Hamilton was indeed worthy of being selected 20th overall, I want to mention that I was expecting Ryan Braun to make it to me. If that had happened, he would have been my pick, as I had the two equally valued. Naturally, he was selected the pick right before mine, which we affectionately like to call getting “sniped”. That’s why it’s always vital to have two potential picks in mind, so you don’t panic and try to decide on your pick before the clock runs out.

So Billy Hamilton. 20th overall. Is it crazy? Check out his current NFBC ADP:

It’s true that his ADP of about 47 suggests that this was a “reach” (a term I still haven’t fully figured out what is meant by it). However, check that Min Pick number. It’s 17. That means that at least one person in NFBC drafts felt he was worthy of the #17 pick. Does that then make it okay to take him that early or at 20? Absolutely not. I’m sharing this because frankly, I was a bit surprised by the vehemently negative reaction stirred up by my selection. You know how many players in this draft went far earlier than their Min Pick? A heck of a lot. So I personally didn’t think this was such a headscratcher, regardless of what my own values told me.

On Twitter, some reactors simply assumed my projections for Hamilton must have been much more optimistic than everyone else. That’s a normal reaction. Generally, we draft players we like more than the rest! It’s not always the case of course, but it would be unusual to draft a player who you project to perform worse than the rest of your leaguemates. So let’s compare my 5×5 projections with the rest of the systems and include his 2014 stats:

*The average of Steamer, ZiPS and Fans only

Would you look at that. My batting average projection is dead on with the average, as is both my homers and runs batted in. The stolen bases are essentially the same, and only are my runs scored a bit optimistic compared to the average of the systems. But those counting stats are brought down by Steamer’s pessimistic AB projection. Given Hamilton’s pitiful .287 wOBA last season, perhaps it’s justifiable to consider that his playing time, or at least spot atop the order, is at risk.

But there are two factors here that mitigate that risk in my mind. First, Hamilton was exceptional defensively in center field, posting a 21.7 UZR/150. Even with his poor offense, his fielding and base running were strong enough to record a 3.5 WAR. The Reds have no real candidates to replace Hamilton in center field and given his overall performance, are unlikely to be looking to replace him.

So that’s what’s keeping him in the lineup. But his place atop the order also seems safe. Because, once again, who the heck else are they going to bat at the top?! Brandon Phillips? His projected OBP is barely higher. A team that thinks outside the box might consider Joey Votto, but the Reds aren’t that team. Hamilton is going to lead off all year and stay there.

So if it’s not a matter of a difference in projections, then it must come down to valuation. Valuing players ain’t easy. But it all comes down to math. If you’re not using math to devise your rankings, you’re just making guesses at a player’s worth. I don’t like guessing.

It’s true that we have yet to develop a perfect valuation system and each of the well known ones will produce slightly different values. But they are all still fairly similar. I use a system designed by our friend Todd Zola over at Mastersball, because I’m not smart enough to come up with my own. Without getting into the boring details, the system compares a player’s 5×5 stats to a mythical replacement level player at that position. It then compares the player’s adjusted stat line to the aggregate stats of the entire population of positively valued players.

I have Hamilton as the 15th most valuable player. In my mind, I actually netted a bit of profit snagging him 20th! Let’s find out how that is possible. My spreadsheet displays exactly how much a player’s dollar value is derived from each category. His stolen base dollars earned is actually higher than his overall value. That means that his other four categories combine for negative value. Really though, his batting average is about neutral, and he’s a decent positive in runs. Not surprisingly, it’s the homers and runs batted in categories he hurts you in.

How valuable are Hamilton’s steals? The value they earn him is the most value earned in any single category by any player. Dee Gordon‘s steals are next, followed by Ben Revere’s steals. It’s because stolen bases are concentrated in a couple of the top guys and then fall off significantly. On the other hand, home runs are much more evenly distributed, so no one guy is going to earn an extreme amount from his contributions there.

Let’s dive into a bit of math. Below is a comparison of Hamilton’s stolen base contribution to Giancarlo Stanton’s home runs. Stanton’s home run contribution earned him the second most home run value, just behind Evan Gattis.

*The two columns with the asterisk account for replacement level. Basically, I calculated that a replacement level outfielder, one you could acquire freely during the season, should steal seven bases. Similarly, you could find 12 home runs floating around your waiver wire. If those stats are freely available, you shouldn’t pay for them at the draft or your auction. So we remove seven steals and 12 homers from every outfielder. That’s the second “Adjusted” column. The same process is done for every player at each position and then summed. The “Entire Pool” column listed next is the sum of those adjusted stats after replacement level production is removed from each player.

So now we could look at what percentage of the positively valued player pool does Hamilton’s steals and Stanton’s home runs represent. You learn that the share of the entire pool that Hamilton’s steals represent is more than double Stanton’s share from his homers. I then take that percentage and multiply it by the money allocated to the category. That’s simply pretending each team had a standard $260 budget, multiplying that by 15 LABR teams, assuming 69% of the budget is used for hitting, and then dividing that by five to evenly distribute the dollars to each roto category. And that’s how you get a value of $28.68 earned from Hamilton’s steals versus $11.22 from Stanton’s home runs.

If you buy into this valuation method, which I have for 10 years, then there’s no arguing Hamilton’s worth. You could absolutely disagree with the projections. You could even tell me that strategically, you avoid drafting one-category guys and prefer to go after more balanced players. That’s all cool and valid reasons for stating that you personally would not have made the pick. But the math is the math and the math says that Hamilton, given his above projected stat line, is worth a 20th overall selection.

Be aware that these valuations are strictly for the 15-team LABR Mixed league format. In a shallower league, such as a 12-teamer, Hamilton is probably worth less, perhaps significantly so. As I’ve said many times in past posts, player valuations could change drastically depending on your league format.