[Editor's Note: Welcome new contributor Cody Callahan, part of the ASU team at this year's Diamond Dollars competition! While Cody wrote up much of this article, credit should be shared to his entire team. We're delighted to post the case here at BtBS.]
Baseball analytics guru Vince Gennaro, author of Diamond Dollars: The Economics of Winning in Baseball, consultant to Major League Baseball teams, a regular on MLB Network's analytics show Clubhouse Confidential and president of SABR, also is the creator of the first national competition based on baseball operations issues.
Earlier this month, 21 teams from universities around the country gathered in Phoenix to compete in Gennaro’s fourth annual Diamond Dollars Case Competition at SABR’s annual analytics conference. Our team from Arizona State University’s W.P. Carey School of Business – Sean Aronson, Emerson Frostad, David Bocchino, Reid Smith and I – won this year’s graduate school contest, competing against outstanding teams from Stanford University, the University of Chicago and other top graduate business schools. The 12 judges were executives in baseball operations departments of seven MLB teams.
This year’s case, designed by Gennaro, was straightforward: find the best two trades involving Philadelphia Phillies pitcher Cole Hamels. In this case, best trades were defined as the trades that provide each team with maximum value. Additionally, each proposed trade with the Phillies was required to have a unique trade partner. Once each team defined two mutually beneficial trades, they proceeded to declare a best trade and second-best trade. The teams were given one week to design a winning trade strategy.
Here is how our ASU team looked at the problem and developed the solutions:
Ideally, a trade sends an equal amount of wins to each party involved. However, this gets tricky when a team is trading for future wins. A win today is more valuable than a win next year. To account for this, future wins need to be discounted to their present value (NPV). For our purposes, we elected to use a discount rate of 35%, a value derived from Gennaro’s research.
An equitable exchange of NPV wins was our standard for evaluating a fair trade. With that established, we needed to quantify the amount of wins Hamels will contribute over the length of his contract and determine the value a team will gain by acquiring the Phillies pitcher. Once we knew the teams that have the greatest need for Hamels, we looked at the pool of prospects those teams have to offer. We then projected each prospect’s production in future seasons and discounted it to present value. When the cumulative NPV of wins that Hamels will contribute was equal to the cumulative NPV of wins of the prospects, we would conclude the trade is fair.
Valuating Cole Hamels
To determine the wins Hamels will contribute over the life of his contract, we first needed a set of similar pitchers. We used a K Nearest Neighbors model to find the 30 pitchers who are most similar to Hamels at this juncture in his career. Our model evaluates all pitchers from 1969-2014. The model accounts for 13 different variables at each age 28, 29 and 30. Additionally, the model accounts for each pitchers cumulative innings pitched at age 30, as well as his height and weight. The model uses Euclidean distance to determine the 30 most similar pitchers to Cole Hamels.
Below is a Tableau visualization, developed by David Bocchino, of our 30 most similar pitchers. Increased hue and size indicates Euclidean proximity to Hamels.
Once we identified the 30 nearest neighbors, we used their production to simulate Hamels’ WARP each year from age 31 to 35. We then ran simulations on each age specific histogram. Each histogram contains six bins, with bin sizes dependent on the WARP of our nearest neighbors at that age. In each simulation, bins were selected through random number generation. Because WARP is uniformly distributed within bins, we randomly selected the projected WARP within the selected bin. If a player had not reached the necessary age for a specific histogram, (e.g. Jon Lester) he was not considered in that histogram. Pitchers who retired were given a WARP of zero because they were replaced.
After we ran 10,000 simulations, we received the following WARP projections for Hamels. Sean Aronson executed our WARP simulations.
We included 4-year and 5-year totals because Hamels’ has a vesting option in year 5 of his contract. Because the vesting option is triggered if Hamels reaches certain innings pitched thresholds (400 IP in 2018-2019 and 200 IP in 2019), we used the same process to simulate innings pitched. Emerson Frostad executed our innings pitched simulations.
Our simulations indicated that there is a 20.3% change that Hamels will reach 200 IP at age 34. This led us to believe it is somewhat unlikely Hamels will activate his vesting option in 2019. In spite of our uncertainty about Hamels reaching the necessary innings pitched thresholds at age 34, we do project his performance will be strong enough to motivate his team to pick up his option at a relative discount in 2019, particularly if they plan on contending that season. Going forward, we operated with the assumption that the team acquiring Hamels will retain him in 2019.
Now let’s return to our WARP projections for Hamels. We needed to discount Hamels’ cumulative WARP value to its present value. Below, we present the cumulative range of simulated WARP values over the duration of Hamels’ contract, discounted to NPV.
WARP projections are all well and good, but how well will Hamels pitch in the future, relative to all pitchers? If we rank each pitcher by his WARP value each season, we find that the WARP value at each percentile is relatively consistent year to year. We used this theory to estimate where Hamels will rank among all pitchers in each future season until age 35.
We found the WARP value at each integer percentile, 1-99, for each of the past six seasons. We then took the average of the six WARP values at each integer percentile. We then inserted Hamels’ mean projected WARP to determine which percentile he will occupy. Reid Smith calculated our mean percentile values. The results are below.
Our WARP simulations and projected ranking among starting pitchers indicated that Hamels should be near the top 10% of all pitchers in his next two seasons, while still maintaining value as a starting pitcher in the subsequent three seasons.
Potential Trade Partners
To quantify the value Hamels will add to each MLB team we developed an index, which we labeled Needy Team Index (NTI). NTI evaluates each team on three criteria: proximity to playoff contention, ability to take on Hamels’ contract and starting pitching need.
1) Teams Near Contention
To evaluate teams near contention, we first projected each team’s win total next season. We used the PECOTA projected standings for these values, which are available at Baseball Prospectus. Then, we needed to establish a win threshold for winning each division and for earning a wildcard in each league. For division thresholds, we averaged the PECOTA projections with the average wins it required to win each division over the past six seasons. We choose to use the past six seasons to capture recent trends within the division. The same process is used to develop wildcard thresholds, except we only used two years of historical data to account for the new wildcard rules.
If you don’t enjoy reading about formulas, here’s a cleaner explanation for reference.
Division Threshold = (0.5* historical division champion wins) + (0.5 * PECOTA division champion wins 2015)
Wildcard Threshold = (0.5 * historical wildcard champion wins) + (0.5 PECOTA wildcard champion wins 2015)
After we established a threshold for each division and wildcard spot, we determined what the "Sweet Spot" is for each division and each league’s wildcard. The Sweet Spot is two wins below its respective threshold. We used two wins because we project that Hamels will contribute two wins next season. If a team is currently projected to finish directly at the divisional Sweet Spot, they have the highest amount of value added. Each win away from the Sweet Spot becomes progressively less valuable. Once we found each team’s distance from their respective divisional and wildcard Sweet Spots, we standardized those distances.
The charts below give us the standardized value added with respect to division and wildcard Sweet Spots.
The National League chart above gives us a great opportunity to explain when a team will have a high level of standardized value added. The Nationals and Cardinals are projected to finish relatively close to the divisional Sweet Spot, which is why they have high standardized value added scores. However, the Dodgers are projected to win the NL West by a wide margin, which is why their standardized value added is significantly lower.
2) Starting Pitching Need
We used a similar process and the same data to evaluate each team’s starting pitching need. The only difference is we look at cumulative starting pitching WARP instead of wins. Threshold equations are below:
Division Threshold = (0.5* historical division champion WARP) + (0.5*PECOTA division champion WARP 2015)
Wildcard Threshold = (0.5*historical wildcard champion WARP) + (0.5*PECOTA wildcard champion WARP 2015)
The Sweet Spot remains two wins below the threshold because Hamels is projected to have a WARP of about two next season. The charts below show the amount of value each staff has to gain by adding Hamels.
3) Teams with Financial Flexibility
Without consulting with each team, it is impossible to know exactly how much a team is willing to spend. However, we were able to come to a logical estimate of each team’s maximum budget. Using the past six seasons of payroll information, we determined the payroll for each season, relative to the current level of league spending. To find these values, we applied the league growth rate to determine what each season’s payroll would be at the current level of league spending. We used this calculated maximum budget as each team’s potential budget.
The chart created by David Bocchino illustrates the concept of league growth rate and applies the growth rate to determine maximum budgets of the New York Mets and Los Angeles Dodgers.
The chart below illustrates the teams that are able to pay Hamels’ contract in full next season. The available budget is in red and the current payroll is in gray. Tableau visualizations are generated by David Bocchino.
This chart shows us the teams that are only able to afford half of Hamels’ contract in 2015.
Applying Weights to Each Criterion
To get team team’s Needy Team Index value, we applied a weight to each criterion and multiplied the weight by the standardized value added, with respect to each Sweet Spot. For financial flexibility, we applied binary values in lieu of standardized value added. A team received a value of 1 if they were able to afford Hamels’ contract in full and a zero otherwise. The same method is applied for teams that can afford half of Hamels’ contract in 2015.
Needy Team Index = W1*(Value Added to Win Division) +W2*(Value Added to Win Wildcard) +W3*(Pay 50% Hamels Contract) +W4*(Pay 100% Hamels Contract) +W5*(Value Added to SPWARP Division) +W6*(Value Added to SPWARP Wildcard)
We provided two different sets of weights. The first option operates under the assumption that a division title is twice as valuable a wildcard birth. The second option values standardized value added the same for both division and wildcard titles. We tend to favor the former option because a division title ensures more playoff games and a stronger probability of a deep playoff run in October. We included the top 10 teams by NTI, using both weighting options, below. Reid Smith developed the different weight options.
Weights (W1, W2, W3, W4, W5, W6) = (0.266, 0.134, 0.1, 0.1, 0.266, 0.134)
Weights (W1, W2, W3, W4, W5, W6) = (0.2, 0.2, 0.1, 0.1, 0.2, 0.2)
While the order of the teams varies between the two options, the same 10 teams are in both top 10 lists.
Evaluating Prospect Packages
Using these 10 teams with the highest NTI values, we evaluated the top prospects on each team using the Baseball Prospectus Top 101 and the Baseball America Top 10 prospects per organization to determine the best prospects. We eliminated teams that do not have the quantity of prospects necessary to make this trade work. At this stage, we took a closer look at the prospects on the Toronto Blue Jays, Chicago Cubs, Seattle Mariners and Boston Red Sox.
We then created a system to project future WARP through age 28 of all top prospects on each of these teams. First, we established Future Value scores, which are available at FanGraphs, as our prospect projection. The Future Value scale ranges from 20-80 with a mean of 50 and a standard deviation of 10. We used this scale to map out Future Values onto a WARP scale.
To do this, we looked at each players WARP through age 28 between the years 1969 and 2014. We then took the mean and standard deviation of those cumulative WARPs, which can be seen in the chart below. With this knowledge, we were able to map Future Value scores to the WARP scale and have an estimate of cumulative WARP through age 28.
Sean Aronson developed the charts below.
Once we had cumulative WARP values through age 28, we used scouting reports to determine when a player would break into the Major Leagues. We then distributed WARP evenly through his age 28 season and discount each season’s WARP to the NPV. The cumulative WARP of prospects, discounted to NPV, allows us to find a trade that will give the Phillies enough NPV WARP to deal Hamels.
Proposed Trade #2 – Chicago Cubs
Our second-best trade has the Cubs sending Kyle Schwarber (C/OF), Pierce Johnson (RHP) and Duane Underwood (RHP) to the Phillies in exchange for Hamels. As evidenced in the chart below, the mean NPV WARP that is being exchanged is about equal. The Phillies would benefit immensely by adding two Baseball Prospectus Top 101 prospects. The Cubs were a top-10 NTI team, which means they stand to benefit a great deal by adding Hamels to their starting pitching staff.
There are a few additional qualitative reasons we selected this trade. The Cubs have a deep farm system, and none of the prospects we have in our proposal are the top players that are expected to get their cup of coffee this season. Essentially, the Cubs will still have a great crop of young talent even if they part with these three prospects.
The Cubs youth also indicates they will be a team that will contend well into the future. The five years of team control the Cubs would have with Cole Hamels would certainly not be wasted by a narrow window of contention.
Proposed Trade #1 – Boston Red Sox
Our most optimal trade partner for Hamels is the Boston Red Sox. The proposed trade sends Hamels to the Red Sox in exchange for Henry Owens (LHP), Manuel Margot (OF) and Eduardo Rodriquez (LHP).
The trade makes sense from the Phillies perspective. They add two quality arms and a promising outfielder, all of which are Baseball Prospectus Top 101 prospects. In this trade, the Phillies are actually receiving a larger quantity of mean NPV WARP than they would in the proposed Cubs deal.
However, the most significant reason we chose this trade is because of the value it will bring the Red Sox. The Red Sox had the highest NTI, in both weight iterations, by a considerable amount. This shows us that the Red Sox have the most to gain by adding Hamels.
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Cody Callahan is a contributor to Beyond the Box Score.