# Better to Sign out of HS or College? Part 2

I*f you haven’t read part one of the study, you can get caught up here.*

If you have, you’ll remember that the previous analysis suggests that, for almost every round in the draft, the mean bonus a player receives after going to college is greater than what they were offered out of high school. At first glance, this finding may seem to suggest that players are better off financially by going to college. But there is more to consider than just the signing bonus a player receives.

Players who sign out of high school get to the majors at a younger age than players who go to college, and, as a result, players who sign out of high school reach arbitration and free agency at younger ages. This part of the analysis is key, because free agency is where the lion’s share of the money is.

To come up with a more comprehensive quantification of whether going to college or singing out of high school is a better financial decision we need to know three things: 1) how many extra free agent seasons does signing out of HS give you? (how much younger are HS players when they reach the major leagues than players who sign out of college), 2) how much are the extra free-agent seasons worth? and 3) what is the likelihood that a player becomes good enough that his free-agent seasons are valuable?

Luckily, some research has been done on these topics.

A study by three economists at Loyola College in Maryland examining the draft found that players drafted out of high school do reach the major leagues at younger ages.

Examining first-round picks taken in the 1990-1997 drafts, the researchers found that it took high school players who ultimately became ‘stars’ 2.44 years from the time they were drafted to reach the major leagues; it took college players who became stars 1.97 years to reach the majors. It took HS draftees who became ‘good’ players 3.56 years, while only 1.84 for college players who became good big leaguers. High School players who became ‘regular’ big leaguers took 4.31 years to reach the bigs compared to 2.25 years for college draftees who became regulars to reach the majors.

It’s important to note that the economists based their research on first-round picks only. It’s possible- maybe even likely- that first-round players who become star/good/regular players reach the majors faster than players drafted in the later rounds who also become star/good/regular level players. Maybe part of the reason players were drafted in the first round to begin with was the fact that teams viewed them as more ‘major-league ready’, or maybe players drafted in the later rounds who become productive major-league players simply take longer to develop. As I said earlier, there are a lot of assumptions that have to be made to carry out this analysis. Assuming different level players all reach the majors at the same time irrespective of the round they were selected is a simplifying assumption I’ve made to ease the analysis.

In the sample I collected, high school players were drafted an average of 2.43 years after they were drafted out of high school. Adding 2.43 years to the length of time it takes each level of college player to reach the majors and then subtracting how long it takes HS players of that same level to reach the majors gives us an estimate of how many extra free-agent seasons signing out of HS gives players of each skill level.

Star players gain two years of free agency by signing out of high school, good players get a .71 year jump on free agency, and regular players get only an additional .37 years.

The next question we need to answer is how much are free-agent seasons worth for each type of player. Unfortunately, the researchers based their classification system on BP’s old WARP, which from what I understand is not an appropriate way to value players. Using a rough estimate, I valued a year of free agency for a star player at $16 million per year, $10 million for a good player, and $5 million for a regular player. I used this off-season’s signings as a guide, but I tried to stay conservative in my estimate for star players.

To put a dollar figure on the extra free-agent seasons a player gets by signing out of HS, we need to know the percent chance that a player from each round stands of becoming a star, good, or regular player. Using the same 1990-1997 time frame, Jim Callis analyzed how many players from each round became stars, regulars, and good players (link). Because the researchers from Loyola referenced Callis’ data in their analysis, I believed both used the same system to classify players.

To estimate the chance high school players from each round became star, good, or regular major leaguers, I put a logarithmic trendline through Callis’ data for each type of player. More work still needed to be done, because a logarithim function can return negative values. Obviously it’s impossible that the chance a tenth-round pick becomes a good major leaguer is negative. To overcome this problem I looked at a study done by Baseball Time in Arlington that calculated the percentage of draftees who reached the majors in each round of the draft.

I used the same distribution from the percent of players who reached the major leagues when the logarithmic trendline began to break down by getting too close to zero (usually around the 8th round). What I mean by copying the distribution is that I looked at what percent each subsequent total was of the preceding round. For example, in the 6th round 16.4 percent of draftees reach the majors. In the 7th round only 14.4 percent do. Fouteen point four is 87.6 percent of 16.4, so moving from the 6th to the 7th round we should expect the 7th round total to be 87.6 percent of the 6th round’s total. I did this for each round, and then copied it to the star, good and regular player distributions. So when the trendline began to return unrealistic numbers, I just had the next round be 87.6 percent (or whatever to change between the two corresponding rounds) of the preceding total.

Obviously, there are some problems that arise from using this system. For one, the percentage of players reaching the major leagues from each round was calculated using a sample of both HS and college players. My guess would be that in the early rounds college players make the majors at a a higher rate, while high school players catch up in the later rounds. Furthermore, there is no reason to suspect that the distribution of players reaching the majors is the same as players the distribution of players who become stars, good players or regulars.

Again, these simplifying assumptions cloud the ultimate findings. Keeping the shortcomings in mind, here are the distributions I came up with (click for a clear version):

Once we have calculated how many extra years of free agency high school players of each skill level gain by singing out of high school, how much free-agent seasons are worth, and the percent chance that a player, based on the round he was drafted, has of becoming a star, regularĀ or good player, we can come up with an estimate of how much extra money a player stands to make by signing out of high school relatively simply.

* For star players the value of signing out of high school is (% chance of becoming a star*(2 extra years of free agency at $16 million a year);

* For good players (% chance of becoming a ‘good’ player*(.71 of an extra years of free agency at $10 million per year);

* For regular players (% chance of becoming a ‘regular’ player*(.37 of a free agent season at $5 million a season).

In the table below are the probabilities, by round, that a player performs at a certain level, and based on those percentages how much a player drafted in each round stands to make by signing out of high school and getting to free agency quicker (click for a clearer view).

Monday, we’ll delve deeper into the calculations and see what advice the findings hold for today’s high school players.

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