[This analysis is also featured in our emerging blog www.theimperfectgame.com]

With less than one month to go, the American League MVP race is very close. While usually nothing is set on stone in early September, during the last few years the AL MVP has been a two-man race (Mike Trout with either Josh Donaldson or Miguel Cabrera). This year, however, features five remarkable candidates: Mookie Betts, David Ortiz, Jose Altuve, Mike Trout and Josh Donaldson. Yes, I expect a few other to grab a few top-five votes (e.g. Cano, Cabrera, Lindor and Machado) but I don’t anticipate the award to fall outside those five players.

Let’s look at the classic, old-school numbers first, which not only are sometimes referenced in casual conversations at local bars and pubs but also frequently (and occasionally unfortunately) followed by voters. I’ve plotted R, RBI, HR, OBP, SLG and SB as percentiles of the entire population. Let’s take a quick look.

If you like well-rounded players, probably this year you’re excited with Altuve, Trout and Betts, who dominate across the board. In an era where stolen bases keep declining, 20+ SB will get you to the 90th percentile. On the other hand, if you’re into true sluggers, then the show Ortiz has put this season should be one to remember. However, then again, these metrics paint only part of the picture — they don’t take into account when or where each event happened nor they include defense or base running on its most complete form.

Let’s take a deeper look at WAR and a quick indicator for each batting, fielding and base-running performance.

Obviously when we move away from batting, David Ortiz loses ground — he only contributes in one aspect of the game, and while he has been outstanding in the batter’s box, likely it will not be enough for him to win. When we adjust by park and league, we realize the Trout – Betts race for the best OF is not as close as I initially thought. Trout has quietly put a(nother) great season on an awful team (again) — he’s already at 8.1 WAR and a 175 wRC+, with both easily leading the league. His defense is slightly below average at best but he compensates by running extremely well. Altuve and Donaldson have had similar seasons offensively. However, Altuve is having a down season in both defense and base-running (remarkably low on Ultimate Base Running (UBR), which measures how frequently and effectively a runner takes an extra base via running). Betts drives his value largely from his defense, where he’s settled in nicely as one of the best OF this year.

One of the metrics I tend to assess when I look at awards is how performance was spread the entire season. I want an MVP to be someone that I rely throughout the year, not only during a hot stretch. Additionally, having a big month can really uplift the numbers and build up a misleading argument in favor of someone. Let’s understand how wRC+ is split by month.

This picture to me is interesting for a couple of reasons. First, part of the argument on Betts’ candidacy is that he’s getting better, and delivering when it matters the most — in the middle of a pennant race. After a below-average March/April, Betts has been a beast since July, when Ortiz cooled off a bit. Now, then again, Mike Trout has also followed an upward-trending curve — peaking at 206 in August — and his lowest point is at 144, which is the highest of all lowest points in the sample. From my perspective, if everything else is equal, I’d rather have a Trout-esque curve than Donaldson’s one, who has the highest single-month wRC+ (213 in June) but also with the largest swing (118 difference between May and June). And then you have remarkably constant Altuve — with the narrowest gap between highest and lowest points throughout the season and at least 140 wRC+ in any given month.

Now, most of what we have shown up to now is context-neutral. An argument could be made that every single game is worth the same, regardless of whether it’s in April or July — what’s really important is to deliver in key, high-leverage situations. There is where true MVPs show their full potential to influence a team and define its fate. As they say, a home run against a non-contender team when you are losing by five runs is not as valuable as a game-winning double against our wild-card-rival’s closer in the 9th inning. I’ll admit neither OPS in high-leverage situation or Win Probability Added (WPA) is the perfect metric to evaluate this, but they provide a very good proxy to how well they have fared in tough, game-changing situations. If you are not familiar with WPA, please click here.

Again we see the usual suspect — Mike ‘King’ Trout — leading not only this graph but the MLB with his 5.66 WPA, closely followed by Josh Donaldson, and they’re the only two players from this sample to have a higher OPS in high-leverage situations than in low-leverage ones. Interestingly, Boston’s Betts and Ortiz’s OPS go down 9% and 15% respectively when the stakes are high. I definitely don’t want to say that Altuve’s 0.841 OPS in high leverage is bad, but I certainly want to recognize Donaldson’s and Trout’s clutchier performance.

Another way of looking at the MVP is to ask yourself: Where would that team be if that player wouldn’t have been part of it? While in essence it is impossible to know for sure the answer, a nice proxy is to measure what percentage of position-player WAR is that player responsible for, i.e. what percentage share does this player represent.

Well, this is another way to see Mike Trout’s leadership on the field. Almost half of the Angels’ WAR have Trout’s name attached to it, which is amazing. (For reference, the leaders in this table are Khris Davis and Marcus Semien with 122% (2.2 WAR each out of 1.6 Athletics total WAR). Now, Donaldson and Altuve have, too, a remarkable 33% and 35% of their total, but probably Betts falls short again with his 23%.

At the end, when all is said and done, it looks like numbers indicate it should go down to a Donaldson vs. Trout race, just as it was in 2015. Ortiz has had an amazing season but his base-running and defense (or lack thereof) limit his overall impact on his team. Betts is definitely an exciting, five-tool player, but his performance hasn’t been as good as Donaldson’s or as consistent as Trout’s. Additionally, Boston’s talent-loaded team reduces his value (this is the opposite of the Trout-Angels argument – how valuable can you be when your team would perform well, even if you’re not there?). His future is extremely bright though. Finally you have Altuve, who may have a legitimate case but falls (a bit) short on overall performance to Donaldson and Trout. Houston has under-performed and arguably that’s a worse outcome than Trout’s, because we knew the Angels were going to be bad, but we thought the Astros would be better.

Last year, Donaldson built his case with a magnificent August, when he posted a 1.132 OPS and Toronto got to first place in the AL East. This year it was Trout who had a torrid August, but the Angels are not in the wild card race. It surely seems to me as if we are measuring the MVP as a team award. Though I understand the rationale of having an MVP on a winning team, there is more to it. If I had a vote, and still being a few games away from the end of the season, I’d support Trout in his quest for his second MVP (as of today), but it looks like momentum and narrative are gaining traction around Donaldson — who has posted much better numbers than in his MVP season — Altuve — who brings new blood to the MVP discussion and might get an extra push if Houston makes it to the playoffs — and Betts — who is clearly the face of Boston’s extremely talented young generation. They, though, despite great Septembers, will post worse numbers than Trout. Yes, the Angels are a bad team — but to what extend is that Trout’s fault? What else could he have done? When did ‘valuable’ translate into ‘winning by himself beyond reasonable expectations’? When did we change this award to ‘best player on the best team’? In 2012 it was Cabrera’s Triple Crown and in 2015 it was Donaldson’s ‘ability’ to get Toronto to the postseason for the first time in many years. In 2016, Trout has been comprehensively better, avoided any deep slumps during the season, and performed very well under pressure and shown that you can put counting stats up on a bad team. We are running out of excuses this year.

The MLB draft has passed but its impact will last. Some selections will go down as busts (e.g. Matt Anderson by the Tigers in 1997). Others will be real bargains such as Carlos Beltran with the 49^th pick in 1995. I decided to look at the numbers in an attempt to answer the following questions I read over the last few weeks:

1. How many Round 1 picks do end up in the big leagues? What’s the average impact of a Round 1 pick? How does that compare to Round 2? Are there differences between pitcher and batters?
2. What has been the best draft class for the 1993-2008 period? (per three first rounds)
3. What teams have done a better job?
4. What is the best round (top 10 overall picks)?

As I usually do, let’s define the data sources and assumptions. First, my data source is Baseball-Reference. There are many assumptions and disclaimers in this process, but the most important ones are:

1. I am using data from 1993 to 2008 to give ample time for players to reach MLB. As I am using career WAR, I don’t want to over-penalize players that have been selected in the recent years and therefore have not accumulated MLB service time.
2. Organizations change and so do their ways of conducting business, which evidently includes draft strategy. We are looking at teams rather than specific front offices or general managers.
3. WAR refers to Baseball-Reference WAR (i.e. bWAR).
4. Teams may have more than one pick per round due to compensation and supplemental picks.
5. This methodology does not take into account the overall quality of the draft pool i.e. total WAR per draft year is not constant.
6. All WAR is allocated to the team that drafts the player. Understandably, that is not true but let’s toy with the idea through this post.

Let’s get to it.

Question 1 – How many Round 1 picks do end up in the big league? What’s the average impact of a Round 1 compare to a Round 2 pick? Are there differences between pitcher and batters?

The table below outlines how many players have been/were called up to the majors and how many actually have had a positive career WAR i.e. over 0.0. I have also added the average career WAR per player and I have broken down the data by round and by position (pitcher and batter) to grasp the differences easily. Just take a moment with this table:

Three things come to my mind:

First, this provides some empirical validation of what we intuitively thought: First-round picks produce greater WAR values than the others. While I only have data for the first three rounds, it’s worth noting that the gap between Round 1 to Round 2 (10%) is smaller than from Round 2 to Round 3 (41%).

Second, I actually found surprising that 67% of first-rounders reached MLB at some point. That is two players out of three and it’s a testament to how important raw skills are when it comes to moving up through the minors.

Lastly, the answer to the question of whether t draft pitchers or batters looks like an easy one. Batters not only reached MLB at a higher pace but delivered better results as a group and as individuals. While these results are not statistically significant, they provide a pragmatic answer to the question and suggest a sound strategy might be to draft batters and trade for pitchers later down the road.

Question 2 – What has been the best draft class for the 1993-2008 period?

This table should provide guidance on how to answer this question but does not fully explain it. If we think of it as the number of players that got to MLB, then 2008 is the best year. That year highlights Eric Hosmer, Buster Posey, Brett Lawrie, Craig Kimbrel and Gerrit Cole as the most prominent stars, but offers a very low career total WAR as most of its players are still playing – they’re the youngest generation of my sample. In this class, 27 out of the top 30 picks have reached MLB, though a few for a very short stint e.g. Kyle Skipworth or Ethan Martin.

If we think of the highest total career WAR, then the winner is 2002. This class is led by two of the best picks on the sample (Zack Greinke and Joey Votto) but also features Prince Fielder, Jon Lester and Curtis Granderson. If we think of highest concentration of skills, then the 1995 class has to be the first one with an average of 11.8 WAR per MLB player. On the other hand, only 41 players got the MLB call, the lowest among the sample. While Carlos Beltran and Roy Halladay are the most notable names in that draft, player such as Darin Erstad, Kerry Wood, Randy Winn and Bronson Arroyo enjoyed nice peaks.

Question 3 – What teams have done a better job?

Evidently, not every team has selected in the same combination of draft slots e.g. some teams have had the opportunity to choose top picks (Rays, for example), while other have frequently picked from mid-bottom draft slots (Yankees).  It would not be fair to compare total career WAR for players the Yankees has selected against those that the Rays has because the latter had more options and access to a different pool of players than that the Yankees had. How to fix that? I am comparing what each team did on the overall pick they were slotted. If we use 2016 as an example, I would be comparing how good Philadelphia was in choosing Mickey Moniak as pick 1 against the average of all other first picks in the timeframe (1993-2008). Once I know the WAR gap between a particular team and the average WAR per pick, I need to standardize that number by the standard deviation i.e. calculating Z scores. In simple terms, this is understanding how good or bad a pick was in relation to the entire distribution of a particular draft slot. The Z-score number allows us to compare how good a 14th pick was in relation to a third pick, for example. Finally, to identify which teams have fared better, I am calculating the average of Z-scores for all picks.

Again, there are many caveats here, but this should give us a ballpark estimate on how well teams have drafted from 1993-2008. Keep in mind, this methodology does not produce a linear WAR per draft slot. That would mean, for example, that overall pick 4 will produce greater WAR than pick 5. On average, the 4^th pick has produced 6.2 WAR on average, while the 5^th one has produced 14.3. While this might be counter-intuitive (it is at least for me), the empirical evidence of this sample size shows that.

Perhaps surprisingly, the Phillies come at the top of the list. The Phillies advantage came in three picks: First, Chase Utley was drafted in 2000 with the high 15th pick and has had a great career that is up to 63.4 WAR. Second, in 1993, the Phillies chose Scott Rolen (70 career WAR) with the 46th overall pick – which seems like a bargain now. Finally, Randy Wolf in 1997 was selected in the 54^th position and went on to have a 23.1 career WAR. The Nationals have had very much success on their first few years as a franchise with both Jordan Zimmermann and Ryan Zimmerman. The sample size does not include Bryce Harper or Stephen Strasburg, which may push the Nats to the top of the list in the near future.

Astros, Expos, Yankees, Cubs and Indians are the bottom five teams. Coincidentally or not, these teams have long droughts (Yankees exempted). Interesting to see if there is a relationship between draft performance and wins but I guess that’s is another post.

We could go and dig deeper for each team into what they’ve done well and not so much but that would not make sense. Teams make mistakes and it looks like the draft selection is pretty damn hard with an extremely high WAR standard deviation (11.6 WAR through the first 30 picks).

Question 4 – What is the best round (top 10 overall picks)?

This question is about finding the best selection on each of the first 10 picks. I’ve used the Z-score which pick was really ahead of the curve.

Well, this is quite a nice group of players. A-Rod is the WAR leader of our sample. Even as a first pick, which on average has yielded the highest WAR, he manages to be three standards deviations above the mean. Five other players are active and two of them (Greinke and Kershaw) still are among the best starting pitchers in the game. They will continue to cement their position as great draft picks for the Royals and Dodgers. Interestingly enough, Barry Zito and Eric Chavez were part of the A’s Moneyball team that frequently over-performed a few years ago — a reminder of how important it is to build a strong core of players.

As a bonus question – these are the top 10 picks, according to this methodology:

As always, feel free to share your thoughts and comments in the section below or through our twitter account @imperfectgameb.

Note: This analysis is also featured in our emerging blog www.theimperfectgame.com

[Part I was published here and here]

In the previous post we discussed essentially two questions: First, whether there is a relationship between team payroll and wins. Second, has this relationship changed in time? If so, where are the peaks? Where are we now? Let’s continue digging this topic up.

Question 3: Will money buy you a ring or a post-season ticket? If so, how much should we spend?

Let’s start by saying that nothing will buy you a championship ring. But money can and will improve your odds! I’d say it can get your foot in the door.

The following graph shows the probability of reaching the playoffs, winning the American or National League or winning the World Series at the beginning of each season (BoS). I have split teams into three tiers depending on their payroll total each year. The low tier refers to the bottom 33% payroll total of all teams in a season, medium tier goes from 33% to 66% and top tier is the top 34%. Keep in mind I am analyzing data from 1976 to 2015, excluding 1994 due to the strike. I have also added to the graph below the expected probability for each event e.g. playoff appearance, league win and World Series win. The expected probability is the natural probability each team has at the beginning of the season; for example, each team has 1/30, or ~3.3%, chance of winning the World Series. In the long run, in a very competitive and balanced league, the numbers should be closer to the expected rates, however they are not.

Did you see that? Let’s state the obvious first: Large-payroll teams had done better than the rest of the teams, i.e. got to the playoffs as well as reached and won the World Series more frequently than low and medium tiers. Let’s digest that again: top-tier teams are almost four times more likely to reach the playoffs than low-tier teams. As we move along in the postseason, as expected, high-budget teams win more often. While the rich teams got to the playoffs at a ~80% better rate than expected, they won the World Series at a ~106% better rate than expected.

Let’s look at the tiny 0.3% of low-tier teams that won the Series. I should say team. I am talking about the Miami Marlins in 2003. They are the only low-tier team that has won the Series, since 1976. Amusingly, they beat the Yankees.

Now, these numbers do not show the full picture because I am compounding the effect of being eliminated in the previous step of the event I am measuring. For example, you can’t win the World Series if you did not win your league. You can’t win the league if you did not make it to the playoffs. Let’s dial back and think of the probability of winning the World Series once you are in the World Series. The same situation happens with the league championship probability. Let’s calculate out of the teams that are already in the playoffs. The graph below shows the probability of winning at the beginning of each event (BoE). Does that make sense? I hope it does.

Let’s go over each event, from left to right: First, playoff appearance probability remains the same as before. Mid- and low-tier budget teams reached the playoffs with a lower probability than you would expect. The second bucket is related to winning the league (read: reaching the World Series) once you are in the playoffs. For example in 2015 there were 10 teams in the playoffs (five teams per league). The expected probability of those teams to reach the World Series is 20%. With the inclusion of the Wild Card and then the second Wild Card, that number has decreased but historically sits at 31%. While top and mid-tier payroll teams have reached the World Series more frequently than the benchmark would suggest the difference is small and, interestingly, higher for mid-tier teams. It is important to notice that poor teams have a little more than half the expected chances of reaching the World Series, once they get to the playoffs. So even if you assume low-tiers teams at this stage are good (they are in the playoffs after all), they have performed considerably worse than the rest. This is a finding in itself.

If we move to World Series, the situation gets even tougher for low-budget teams. Similarly to the league-win breakdown, rich and mid-tier teams have performed better than the average, but in this case, rich ones have done slightly better than mid-tiers. If we think about this, we would expect this result because two very good teams are facing each other — no matter how much they are playing their players. On the other hand, low-tiers ball clubs have fared badly in this situation, accomplishing only one World Series win (the aforementioned Marlins in 2003) in seven attempts. It looks that their chances are reduced by ~71%. Again, remember we are talking about good/great teams playing the World Series, but again and again they have failed to deliver.

So I would like to highlight the findings so far in this question:

1. Payroll matters in relation to reaching the playoffs as rich teams get there with approximately twice the frequency of mid-tiers and four times more than low-budget teams. Therefore money seems to be an important element at the beginning of the season.
2. Once the postseason starts, though, rich and average teams perform similarly both in the path to the World Series and in the Series itself.
3. Low-tier teams perform worse than expected as the season goes on, even under the assumption that they are good teams. Their probabilities of success go down from half what’s expected during the season (11% vs 23%) and in the first rounds of the playoffs (17% vs 31%) to one-third (14% vs 50%) in the World Series.
4. Therefore it looks like money matters when the postseason starts because top and mid-tier teams have done ‘equally’ well, but much better than low-tier teams. While further study needs to be undertaken, my hypothesis is that investing more than what would be needed to be in the top 34% of all teams (i.e. be a top-tier team) would not drive better results than mid-tier teams once in the postseason. Therefore any extra dollar spent beyond what it would take to be a top-tier team is not a dollar (arguably) efficiently spent.

Question 4: Are there big spenders? If so, who are they? Have they changed over the years?

If you are still reading, I have reached my objective.

To answer this question I have plotted the average versus the standard deviation of the z-score for each team.  I have also bucketed teams into four types of spenders e.g. high, mid-high, mid-low and low. The table below shows the number of seasons per team with their payroll labelled as high, medium and low tier. Please take a look at those:

Please remember low tier refers to the bottom 33% payroll total of all teams in a season, medium tier goes from 33% to 66% and top tier is the top 34%. The answer to our first sub-question seems relatively straightforward. As you can see, there are three teams (NYY, BOS and LAD) who have been significantly above the pack, in terms of average payroll. The Yankees have been a high-tier payroll team in 39 out of 40 seasons. The Red Sox and Dodgers have been in the top tier 33 and 28 times out of 40, respectively. These teams have big payrolls consistently and therefore are the truly big-market teams. You may argue that the Mets or Angels are big-market teams and you would not be entirely wrong. They are definitely wealthy but payroll comparison shows they have not been in the league’s top 34% payroll on at least 40% of the last 40 seasons.

I have also, of course, included the teams that I have classified as low spenders. These are the Pirates, Marlins, Twins, Rays and Nationals. The Rays have never been in the top tier, which is the lowest spender in the league followed by the Marlins — what is going on in Florida? You may argue that the Padres and/or the Expos are (were) low spenders and I would not try to persuade you to think otherwise. The line is thin but had to be drawn somewhere.

Another interesting insight is payroll variance. No team has been more consistent than the Cardinals or Rays. On the other side of the spectrum we have the Phillies and the Mariners. This is probably a reflection of how these organizations are run. Below there is a plot of accumulated payroll z-scores and win percentage (for the entire period 1976-2015). If you have been following baseball for a few years most of this resonates with you: The Cubs, Mariners, Rockies and Mets have historically been underperforming while the Cardinals, Braves, Reds and A’s usually find non-payroll-related ways to win.

With the best fit-line information (Expected W% = 0.0296*Payroll Z-score + 0.4994), I have calculated the expected winning percentage (read: what ‘should’ have happened) and compared it to what actually happened. This will quickly allow us to identify good performers over the 40-years period. In essence, in the table below I am highlighting which teams are furthest away from the dotted line in the graph above.

We have one last question to discuss in this post and it is whether deep-pocket teams have changed over time. I think by now you know the short answer to this is ‘yes, they have’ — however, the truth of the story lies in the details. I partly addressed this question with the standard deviation of the z-scores before, however I would like to share a view of how this picture has evolved by decades.

I sliced teams into four categories. First there are the downward spenders. It is interesting how some teams e.g. the Expos, Brewers, Reds and Pirates moved from mid-high payroll spenders to (very) low ones. It looks as if they re-shifted their spending priorities in the mid-80’s and have stuck with that strategy since. The second bucket (Swingers) is teams that have swung between high and low-payroll tiers, depending on how the wind blows. Teams such as the Indians, Phillies, Twins, Rockies and Tigers are here. The third group (Upward) is comprised of those teams who have progressively moved into the upper tier e.g. the Mariners and Nationals. These are big-city, relatively new franchises that have not had on-field success. Finally there is a group (Keepers) that have remained constant on payroll spending. These are the likes of the Yankees, Red Sox, Angels, Dodgers, Padres, Marlins, and Rays.

In summary, it looks like money matters since the relationship between payroll and wins is weak but statistically significant. However, the influence of payroll is not as big as we may originally have thought. Money definitely influences which teams go to the postseason i.e. postseason chances are directly proportional to payroll, but once a team is in the postseason, payroll predictive power goes down i.e. it does not pay off to over-invest in payroll (did you hear that Theo?). Thus there seems to be a diminishing returns curve during the season as the value of $1 extra in payroll changes depending on where you are in the curve. Ideally, a GM wants to spend just enough to get his/her team to the playoffs because, after that point, the field is more leveled, raising the question of whether more of those resources should be allocated to other areas e.g. manager, front office, or player development. I guess that’s part of another post.

Money in baseball has been an infinite source of criticism. In MLB, there is no salary cap as in other major sports, and luxury tax is relatively recent. Media has made us believe that the small fish (e.g. small-market teams) will always be eaten by the big one (e.g. big-market teams). The Kansas City Royals’ performance during the last couple of years, along with the tricky and often misunderstood Moneyball concept, has brought back salary to the newspaper headlines even though it is safe to say the Royals were not even a low-end payroll team. In any case, this post is an attempt to see if popular beliefs regarding money, power and on-field performance pass the numerical test.

There are many interesting questions related to this topic. However I will limit myself to the following during two posts:

1. Is there a relationship between payroll and wins? If so, how strong is it?
2. Has this relationship changed over time? If so, where are the peaks? Where are we now?
3. Will money buy you a ring or a post-season ticket? If so, how much should we spend?
4. Are there truly big spenders? If so, who are they? Have they changed over the years?

Let me start off by stating what my data sources are, and laying out my assumptions so that we are in the same page. My sources for salaries are Baseball Chronology (1976-2006), Sean Lahman database (2007-2014) and Sportrac (2015). For wins and post-season appearances, my references are MLB and the Sean Lahman database. MLB revenue data is from Forbes.

My assumptions and caveats are the following:

1. Payroll values are not adjusted for inflation. Time value of money has not been taken into account.
2. The Houston Astros are considered an American League (AL) team. The Milwaukee Brewers are considered to be a National League team.
3. 1994 strike-shortened season does not have playoff teams or a World Series champion.
4. Payroll is considered to be Opening Day payroll. Payroll is assumed to be constant throughout the season for simplicity. Arguably this may not hold true as winning/better teams will likely be buyers at the trade deadline. Losing teams will likely be sellers.
5. I have not tested for any confounding effect on the variables studied (payroll and wins).

Without further talk, I will get to it.

Question 1: Is there a relationship between payroll and wins? If so, how strong is it?

To answer this question, I found the correlation between yearly payroll and winning percentage for every individual season played from 1976 to 2015. Because payroll values have changed so much in 40 years, I used z-scores or standard scores, which allows us to compare different seasons, regardless of payroll differences.  A payroll number on its own does not mean much and should be compared to the pool of teams on a yearly basis i.e. it is the distribution of payroll in the league that matters. Here’s a link in case you are not familiar with the concept of z-scores; please keep in mind that correlation does not imply causation. Check out the correlation here.

A couple of interesting insights can be drawn from this graph. The first one, quite obvious, is there’s a positive slope there, implying that more money affects wins positively. The second point, though, is that payroll alone does not wholly explain the total number of wins. We inherently knew that. In 40 years, we are able to find teams that satisfied each situation: low-payroll teams that were awful (Houston 2013), low-payroll teams that played over a .600 win percentage (Oakland 2001 and 2002), high-payroll teams that unperformed (Boston 2012) and high-payroll teams that exceeded expectations and went on to win 114 games (NYY 1998). There is a mid-tier team that did extremely well (SEA 2001). These are all outliers, though people can (will?) use every one of these cases to support a preconceived idea e.g. “baseball is a sport and it is attitude and effort that matters,” “money will buy you handshakes at the end of each game,” “big-money teams won’t win because they lack camaraderie,” etc. Therefore, let’s focus on the big picture.

The third point I’d like to highlight is the R-square. The R-square measures how successful the fit line is in explaining the variation of the overall data on a 0-to-1 spectrum. In this case R-square is 0.1905 so it looks like ~19% of the total variation in wins can be explained by the linear relationship between payroll and wins. Also, the slope of the best fit line is 0.0302. This means for a one-unit increment in Z-scores, there is a 0.0303 win-percentage increment. Remember z-score increments are not linear e.g. going from -0.5 to 1.5 requires a different amount than moving from 2 to 3.

However, the potential drivers behind the total number of wins are complex (injuries, roster construction, plain luck, etc.) and the R-square, along with the F-test and P-value, shows that money matters but seems to be overrated. Again, remember that correlation does not imply causation.

Question 2: Has this relationship changed over time? If so, where are the peaks? Where are we now?

We have established that team payroll can predict win percentage with a low confidence level. However, has that always been the case? Was money more important in the 80s than now? The following graph shows the R-square value for every two-year period from 1976 to 2015. It is important to keep in mind that the higher the R-square value, the stronger the relationship between payroll and winning percentage.Check out the R-square of payroll and winning percentage for every 2-year period.

The answer to our question of whether the relationship has changed over time is definitely yes. There are noticeable peaks and valleys. There have been two periods (which I highlighted in green) when money was a better predictor of winning percentage: from 1976 to 1979 and from 1996 to 1999. The first period corresponds to the first four years of free agency. Team owners flooded the league with new money as they went after key players e.g. Mike Schmidt or Reggie Jackson, and payroll increased drastically (60% in 1977, 34% in 1978), as shown below. These have been largely documented (here, here and here). Click here for the payroll growth trend since 1976.

The second period (1996 – 1999) is linked to the Yankees, Orioles (though they dramatically underperformed in 1998), Indians and Braves’ successful expenditure (read: lot of won games) and to the lack of Cinderella stories (perhaps only Houston in 1998 and Cincinnati in 1999). This period was also characterized by, firstly, a league expansion sequel: Tampa Bay and Arizona joined the league in 1998 and, understandably, underperformed. Secondly, MLB revenues year-to-year growth averaged 17% from 1996 to 1999 (not adjusted), so probably teams redirected that surplus to the salary pool. Lastly, in the late 90s, MLB was increasingly becoming a rich-team game. The graph below will show the payroll coefficient of variation for the 1976 – 2015 timeframe. This number, which I will call payroll spread, is simply the standard deviation divided by the mean. This number allows us to quickly assess how spread is the payroll across the league over time. Do you see the trend after ~1985? By 1999, this number had increased continuously for almost 15 years and MLB has had enough. As the power money increased AND the gap widened, MLB commissioned the Blue Ribbon Panel to come up with initiatives to level the field A.K.A. a revenue-sharing program to increase competition. Entertainingly, the correlation of money and winning percentage has decreased steadily but the payroll spread has remained pretty much consistent. I am hesitant to attribute the decline in R-square to the Blue Ribbon Panel or to other factors (read: is this coincidence?). Check out the payroll spread here.

If we go back to the yearly payroll and winning-percentage correlation graphs, you’d notice that I highlighted two periods in red too — from 1982 to 1993 and from 2012 until last season. Those were moments when the correlation of salary power and winning percentage was remarkably low. The first period seems to be closely related to the collusion MLB crisis (check out this link as well). The lowest point was in 1984-1987, when the correlation was only 0.03 and the salary spread was 0.22.

The 2012-onwards period has brought down R-square to a 20-year low (0.06 in 2012-2013). While TV revenue keeps rising, the baseball landscape has changed and new variables are in the mix. There is a redefined revenue-sharing model, we have analytically-inclined organizations, an extended wild-card system and international signings – all these factors have added more complexity to the winning equation, effectively diminishing the relationship between payroll and winning percentage – even with the salary spread still at ~0.40. We are living in interesting times in baseball indeed: If investing money in players doesn’t lead to better on-field results, where do teams need to invest e.g. analytics, managers or front office?

Note: This analysis is also featured in our emerging blog www.theimperfectgame.com

A few days ago, Joe Posnanski wrote about the possibility of Bryce Harper getting the first $500m contract ever. I agree with him on how both amazing and ridiculous it would have sounded 2 or 3 years ago. I also agree it is possible, almost likely, to happen. I might not be a Bryce Harper fan but he is so young that is he is on track to accomplish big things. He is not Mike ‘King’ Trout but he is very good.

Harper’s current contract runs through the end of 2018, which is when I assume he would get the big fat check. The Nationals will try to extend his contract before he is a free agent, just like the Marlins and the Angels did with Giancarlo Stanton and Mike Trout. However, in this post we will assume Harper will not pursue that path, making him a highly-coveted free agent in 2018. I will also exclude the possibility of 9- or 10-year contracts, which would make the mark easily achievable. Let’s run the numbers for Harper’s future:

We have here Harper’s projected value profile. As usual, I am using FanGraphs’ model, which has a player’s aging curve that follows +0.25 WAR/year (Age 18-27), 0 WAR/year (Age 28-30),-0.5 WAR/year (Age 31-37),-0.75 WAR/year (38 and older). It also assumes that open-market WAR sits at $8.4m in 2016 and grows at 5% per year. The starting point is Steamer’s 2016 projection: 6.8 WAR.

Three years from now, in the winter of 2018, he will be negotiating his new contract that includes his theoretical peak 27-30 years at ~7.8 WAR/year. The truth is that a 7-year / $500m+ contract would only be likely if by 2018 he can position himself as a player who consistently accounts for almost 8 wins per year. That is the only reason a team would be eager to invest half a billion dollars in a single player, marketing-related reasons aside.

Now, the question comes down to what he needs to do by 2018 in order to cement that positioning. The model needs him to be a 21.2-win player during the next 3 seasons. While Harper might have taken a significant step up performance-wise, we need to remind ourselves that before 2015 he was “just” a ~4-5 WAR guy. In order to meet the model’s expectations he needs to double those numbers, and remain at that level  for 3 years in a row (i.e.: Between 8-9 WAR for that 3-year period). If he meets those marks, Harper would have accrued 40 WAR during his career by 2018. While that is entirely possible, it is not easy. This is the list of highest cumulative WAR by age-25:

So, two conclusions can be quickly drawn. First, Mike Trout is not human. He is only 24 years old and is already on this list with guys like Cobb, Mantle, Foxx and company. Second, no, it is not an easy task for Harper. I know that you are thinking that he just put up a 9.5 WAR season, why can’t he do it again? Another season like that and he should get to his target easily but, truth be told, those Trout-esque seasons are unlikely to happen. I say this for three main reasons. First, Harper is not an elite defender and has gotten worse every year. For the last 3 seasons (2013-2015), he ranks 37^th in UZR/150 out of 60 qualified OF. In 2015, he compiled -8.5 on Defense (Def) metric, per FanGraphs, which is position-adjusted, in his case for RF. Out of the 69 individual seasons with 8 or higher WAR from players 25 or younger, only 5 players (Hank Aaron, Ted Williams, Stan Musial, Mike Trout (!) and Bryce Harper) had -8 or worse Defense. No, it is not impossible but it is hard.

Second, he is an above-average baserunner, but not an awesome one. Lastly, Harper has not exhibited good health over his career. He has had injuries in 2 out of 4 seasons, which may not seem many but in 2013 and 2014 he only played 67% of Nationals games. Predicting health is tough, especially because there are unforeseeable events. You cannot control a hit by pitch at your wrists or a concussion sliding in second base but your health track record is your best bet on your future injury report. Those three things are vital to get to 21.2 WAR during the next 3 years. Harper needs those factors to come in play in order to get to the 7yr/$500m contract. Harper’s advantage is his age – just like Jason Heyward this offseason.

We have implicitly talked about Mike Trout. He is arguably the best player in baseball right now and was on track to smash the contract record, until he negotiated a 6yr/$144.5m contract extension. That will keep him locked up from ages 24 to 29 at LAA. Now, the question is what type of contract will he command in 2020? Mind you, it is hard enough to try to predict what a Free Agent might get in 2016, but still we took a stab a it.

Here is Trout’s projection. Again, 2016 WAR is courtesy of Steamer. We might think the aging curve slightly benefits Trout because it forecasts a ~10% increase in WAR, and he has not posted those 10 WAR seasons since 2 years ago. Then again, let’s toy with the idea. The $500m contract here seems more feasible for three reasons. First, in MLB, you get paid for what you did and not for what you will do.  By 2020, Trout could have ~85 WAR under his belt –he would be 28 years old. That is just ridiculous and will not happen, right? No one, ever, has done that by age 28 (Ty Cobb is the leader with 78.6 WAR). But what if he does? What if Trout is around the 70 WAR mark with 8 or 9 great seasons on his resume? Second, he needs to do what he has already done e.g. Trout has posted two +10 WAR already. The other two seasons were 8 and 9. This guy runs well and plays above-average defense. Trout does it all and will not stop. Third, unlike Harper, Trout has been very much healthy. During the 2013-2015 period, he played 157, 157 and 159 games, respectively. Again, injuries are hard to predict but we will take what he has shown so far as a given, which is good health. Fourth, fair to say, time value of money. A dollar today is not worth the same as a dollar tomorrow. Therefore, getting a $500m contract in 2020 should be easier than in 2018.

In summary, I think Harper can do it but I would not bet on it. From my perspective this is a long shot. If you ask me today on who is more likely to become baseball’s first 500-million-dollar man, I would put my money on Mike Trout to beat Bryce Harper on this as well.

Note: This analysis is also featured in our emerging blog www.theimperfectgame.com