The bright side of losing Santanaby Victor Wang
January 31, 2008
In the August 2007 edition of By the Numbers, I looked at the value of top baseball prospects from 1990-1999. I determined who the top prospects were by examining Baseball America’s list of top 100 prospects. From there, I broke the top prospects into four groups: hitting prospects ranked in the top 10; pitching prospects ranked in the top 10; hitting prospects ranked from 11-25; and pitching prospects ranked from 11-25.
I then looked at the value that those prospects produced in their first six full seasons in the majors. I chose to look at the first six seasons because that is how long a Major League team has control of a player before he reaches free agency. While that player is under control, a Major League team has the ability to pay that player much less than what he would earn on the open market.
I found a prospect’s value by finding his average production in his first six years and also the monetary savings that he gave his team. To find a prospect’s production, I used Win Shares Above Bench (WSAB) and divided by three to come up with Wins Above Bench (WAB). However, all things being equal, you’d rather have an all-star season now instead of an all-star season four years in the future. To account for this, I used an 8% discount rate and converted a prospect’s average WAB into a discounted WAB (DWAB). The 8% discount rate has been used in past articles for valuing minor leaguers.
From there, I broke the prospects in each group into four subgroups based on their Major League performance: bust (averaged 0 or less WAB per year), contributor (averaged 0-2 WAB), everyday player (averaged 2-4 WAB) and star (averaged over 4 WAB per year). For pitchers, I used these same four subgroups with one exception: I lowered the threshold for a star to 3 WAB/year. I did this because pitchers tend to average less WAB over a period of time when compared to hitters. In fact, no pitcher in the study averaged over 4 WAB/year. A player was put into a subgroup based on his unadjusted WAB, not his DWAB.
To estimate a prospect’s monetary savings to his team, I estimated what a prospect makes in his first six years before free agency versus what a team would need to spend to acquire the prospect’s production on the free-agent market. The cost for 1 WAB in the free-agent market for the 2007 offseason was estimated to be $4.88 million, using 10% annual inflation applied to financial data from the 2006 offseason taken from Dave Studeman’s Win Shares article from the Hardball Times Baseball Annual 2007. I converted the savings a team gets over a prospect’s first six years into a present-value figure, divided that present-value sum by $4.88 million to convert the savings into WAB, and then added the prospect's DWAB to his WAB earned from savings to come up with his total value.
Here were the results I found:
Hitters Ranked in Top 10
Bust Contributor Everyday Star Total Players AVG WAB/yr 5 24 12 7 48 1.82 10.40% 50% 25% 14.60%
That table should be pretty easy to read. The first four columns show the number of prospects in each subgroup and the percent chance they had of occurring. "AVG WAB/yr" shows how many WAB/year the average hitter in the top 10 produced over his first six years (this is unadjusted WAB/year, not DWAB).
Bust Contributor Everyday Star WAB/Year -0.093 0.875 2.81 4.72 Chance of Occurring 10.40% 50% 25% 14.60% PV Savings/Year (in millions) -0.46 2.64 8.83 14.95 PV WS/Year -0.047 1.32 2.21 2.18
In this table, the first row shows the average WAB/year of each subgroup. The second row shows the chances of each subgroup occurring. The third row shows the total savings each subgroup averaged, converted to present value and divided by six. The fourth row is the present-value savings per year for each subgroup multiplied by the chance of the subgroup occurring (it is equal to the second row multiplied by the third row).
WAB 10.9 DWAB 8.41 PV Savings 33.96 PV FA WAB 6.96 Breakeven WAB 15.37
Here, "WAB" is the total WAB that a top 10 hitting prospect produced on average over his first six years. "DWAB" is just WAB using the 8% discount rate mentioned before. "PV Savings" are the total present-value savings for a top 10 hitting prospect. The fourth row shows how many WAB a team could buy with the present-value savings in the free-agent market (PV Savings divided by 4.88). "Breakeven WAB" is the sum of the second and fourth rows and is the value that the average top 10 hitting prospect gave a team based on his performance and savings.
The last row is also equivalent to the value that a team would need to receive in return to trade a top 10 hitting prospect. For those unfamiliar with WSAB and WAB, Alex Rodriguez led MLB last year with 26 WSAB; that is equivalent to 8.7 WAB. C.C. Sabathia and Jake Peavy led all pitchers with 18 WSAB, which is equal to 6 WAB. Breakeven WAB can be used to measure trades if the WAB received in return from the other team is fairly priced. If the player traded for is being under- or overpaid, the savings or costs need to be factored into the player’s value.
The following tables show the results for all other prospects in the top 100. I broke down the remaining hitters and pitchers into four groups: those ranked from 11-25; those ranked from 26-50; those ranked from 51-75; and those ranked from 76-100.
Pitchers Ranked in Top 10
Bust Contributor Everyday Star Total Players AVG WAB/yr 8 16 1 1 26 0.71 30.80% 61.50% 3.80% 3.80%
Bust Contributor Everyday Star WAB/Year -0.03 0.8 2.33 3.67 Chance of Occurring 30.80% 61.50% 3.80% 3.80% PS Savings/Year (in millions) -0.255 2.4 7.3 11.59 PV WS/Year -0.079 1.476 0.277 0.44
WAB 4.26 DWAB 3.28 PV Savings 12.72 PV FA WAB 2.61 Breakeven WAB 5.89
Hitters Ranked from 11-25
Bust Contributor Everyday Star Total Players AVG WAB/yr 15 35 14 6 70 1.32 21.40% 50% 20% 8.60%
Bust Contributor Everyday Star WAB/Year -0.38 0.81 2.75 4.68 Chance of Occurring 21.40% 50% 20% 8.60% PS Savings/Year (in millions) -1.38 2.43 8.64 14.82 PV WS/Year -0.295 1.215 1.728 1.275
WAB 7.92 DWAB 6.1 PV Savings 23.52 PV FA WAB 4.82 Breakeven WAB 10.92
Pitchers Ranked from 11-25
Bust Contributor Everyday Star Total Players AVG WAB/yr 19 31 7 2 59 0.74 32.20% 52.50% 11.90% 3.40%
Bust Contributor Everyday Star WAB/Year -0.03 0.65 2.44 3.56 Chance of Occurring 32.20% 52.50% 11.90% 3.40% PS Savings/Year (in millions) -0.255 1.92 7.65 11.23 PV WS/Year -0.08 1.01 0.91 0.38
WAB 4.44 DWAB 3.42 PV Savings 13.32 PV FA WAB 2.73 Breakeven WAB 6.15
Hitters Ranked From 26-50
Bust Contributor Everyday Star Total Players AVG WAB/yr 46 58 16 10 130 1.07 35.40% 44.60% 12.30% 7.70%
Bust Contributor Everyday Star WAB/Year -0.14 0.83 2.83 5.18 Chance of Occurring 35.40% 44.60% 12.30% 7.70% PS Savings/Year (in millions) -0.61 2.5 8.9 16.42 PV WS/Year -0.216 1.12 1.10 1.26
WAB 6.42 DWAB 4.95 PV Savings 19.56 PV FA WAB 4.01 Breakeven WAB 8.96
Pitchers Ranked From 26-50
Bust Contributor Everyday Star Total Players AVG WAB/yr 26 41 11 2 80 0.74 32.50% 51.30% 13.80% 2.50%
Bust Contributor Everyday Star WAB/Year -0.02 0.65 2.43 3.11 Chance of Occurring 32.50% 51.30% 13.80% 2.50% PS Savings/Year (in millions) -0.22 1.92 7.62 9.79 PV WS/Year -0.0715 0.985 1.05 0.245
WAB 4.44 DWAB 3.42 PV Savings 13.26 PV FA WAB 2.72 Breakeven WAB 6.14
Hitters Ranked From 51-75
Bust Contributor Everyday Star Total Players AVG WAB/yr 53 44 17 3 117 0.744 45.20% 37.60% 14.50% 2.60%
Bust Contributor Everyday Star WAB/Year -0.15 0.69 3.02 4.5 Chance of Occurring 45.20% 37.60% 14.50% 2.60% PS Savings/Year (in millions) -0.64 2.05 9.51 14.24 PV WS/Year -0.289 0.771 1.38 0.370
WAB 4.46 DWAB 3.44 PV Savings 13.38 PV FA WAB 2.74 Breakeven WAB 6.18
Pitchers Ranked From 51-75
Bust Contributor Everyday Star Total Players AVG WAB/yr 39 54 6 2 101 0.57 38.60% 53.50% 6% 2%
Bust Contributor Everyday Star WAB/Year -0.03 0.69 2.42 3.5 Chance of Occurring 38.60% 53.50% 6% 2% PS Savings/Year (in millions) -0.26 2.05 7.59 11.04 PV WS/Year -0.100 1.10 0.455 0.221
WAB 3.42 DWAB 2.64 PV Savings 10.02 PV FA WAB 2.05 Breakeven WAB 4.69
Hitters Ranked from 76-100
Bust Contributor Everyday Star Total Players Avg WAR/yr 49 51 11 3 114 0.67 43.00% 44.70% 9.60% 2.60%
Bust Contributor Everyday Star WAB/Year -0.1 0.72 2.73 4.74 Chance of Occurring 43.00% 44.70% 9.60% 2.60% PV Savings/Year -0.48 2.15 8.58 15.01 PV WS/Year -0.206 0.961 0.824 0.390
WAB 4.02 PV WAB 3.08 PV Savings 11.82 PV FA WAB 2.42 Breakeven WAB 5.5
Pitchers Ranked From 76-100
Bust Contributor Everyday Star Total Players Avg WAR/yr 46 53 5 2 106 0.48 43.40% 50% 4.70% 1.90%
Bust Contributor Everyday Star WAB/Year -0.03 0.63 2.34 3.36 Chance of Occurring 43.40% 50% 4.70% 1.90% PV Savings/Year -0.26 1.86 7.33 10.59 PV WS/Year -0.113 0.93 0.345 0.201
WAB 2.88 PV WAB 2.22 PV Savings 8.16 PV FA WAB 1.67 Breakeven WAB 3.89
Now, we can use these values to evaluate the Johan Santana trade. Over the last three years, Johan Santana has produced 4 WAB in 2007, 6.33 WAB in 2006, and 5 WAB in 2005. Using a weighting of 4/2/1, Santana is projected to have a value in 2008 of 4.2 WAB. On the free-agent market, 4.2 WAB would cost $20.5 million (4.2 WAB * $4.88 million/WAB). However, Santana will make only $13.25 million in 2008. That is a net surplus of $7.25 million, which is worth another 1.5 WAB. This puts Santana’s total projected value for 2008 at 5.7 WAB.
Now we need to evaluate the prospects that the Twins got in return. Last year, Carlos Gomez was rated as the #60 prospect in baseball by Baseball America. His stock has not changed much, but to be conservative I think it is fair to evaluate him as a 76-100 hitter. The second prospect the Twins received, Deolis Guerra, was rated one spot above Gomez in the Mets top 10 prospect list for this year. Since we rated Gomez as a 76-100 hitter, I think it would be fair to rate Guerra as a 76-100 pitcher. Again, I am trying to stay conservative.
Kevin Mulvey, the third prospect the Twins received, was rated one spot below Gomez. However, he does not appear to be a consensus top 100 prospect. I feel that it’s fair to knock Mulvey down from the overall 76-100 pitching prospect value of 3.9 WAB to only 2.5 WAB. Finally, Phillip Humber last year was the 73rd-best rated prospect in all of baseball. However, his stock has fallen, and he was rated as only the Mets’ #7 prospect before the trade. If we give Mulvey a value of 2.5 WAB, I feel comfortable giving Humber a value of 1.5 WAB.
When we add it all up, we get this:
Johan Santana, 5.7 WAB
Carlos Gomez, 5.5 WAB
Deolis Guerra, 3.9 WAB
Kevin Mulvey, 2.5 WAB
Phillip Humber, 1.5 WAB
Total: 13.4 WAB
And there you have it: Bill Smith is the new Branch Rickey. Not so fast, though—there are a few factors we should account for before we make conclusions about the value exchanged in this trade:
- Prospect risk premium: Although the prospect values that I have presented above represent the expected value of prospect performance, they likely overestimate the trade value of prospects. Due to the risk involved with prospects, there is probably a risk premium when it comes to trading prospects.
- Position on the win curve: These breakeven numbers that I have formed do not reflect a team’s position on the win curve. It may be beneficial for a team to give up future value if they are “one player away.” For the Mets, Johan Santana will likely be replacing starting pitchers who would be bench-caliber or replacement-level pitchers. Moreover, given that the Mets barely finished behind the Phillies last year, and that the prospects traded by the Mets would probably not have made much of a contribution to the Mets in 2008, the Mets likely have vaulted themselves to frontrunners in the NL East.
- Better offers for the Twins: Philip Hughes. Ian Kennedy. Jacoby Ellsbury. Jon Lester. These were names that were rumored to be heading to the Twins for Johan Santana. In fact, I bet that most, if not all, people would take the rumored Yankee or Red Sox offers before the Mets offer. Basically, many believe that Bill Smith did not maximize what he received in return for the best pitcher in the game. However, we do not really know what was offered to Bill Smith; in fact, the Mets offer may have been his best offer.
- Mets sign Johan to below-market deal: Note that I did not account for the Mets' getting the rights to negotiate a contract extension with Johan. I did not do this because I am assuming that the Mets will sign Johan for around the same price that they would have spent if Johan was a free agent. However, if the Mets are able to sign Johan to a below-market deal, the savings they get from that need to be factored into the trade.
In conclusion, the Twins were not ripped off as many claim. However, I would not say that the Twins won the deal outright, as the raw prospect value numbers show. When we include the four factors mentioned above into our evaluation, I would say that the Mets come out as slight winners; the extent of their edge depends on what happens with the contract negotiations with Santana.
If I were a Twins fan, I would be slightly disappointed by the fact that the rumors of the Boston and New York proposals did not come true. Still, the Twins did come away with good value in this trade.
Victor Wang's work on OPS has been featured in SABR's By the Numbers magazine, and was the 2007 recipient of SABR's Jack Kavanagh Memorial Youth Baseball Research Award. He can be reached via email here.