Does Payroll Matter? (Pt. II)

[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:

Team	No. of seasons as High tier	No. of seasons as Medium tier	No. of seasons as Low tier	Total Number of seasons	Type of spender (1976-2015)
ARI	4	5	9	18	Mid-Low
ATL	18	17	5	40	Mid-High
BAL	8	22	10	40	Mid-Low
BOS	33	7		40	High
CHC	13	22	5	40	Mid-High
CHW	9	18	13	40	Mid-Low
CIN	10	14	16	40	Mid-Low
CLE	8	8	24	40	Mid-Low
COL	3	11	9	23	Mid-Low
DET	12	13	15	40	Mid-Low
HOU	8	20	12	40	Mid-Low
KCR	11	9	20	40	Mid-Low
LAA	24	11	5	40	Mid-High
LAD	28	12		40	High
MIA	2	1	20	23	Low
MIL	6	14	20	40	Mid-Low
MON	4	9	16	29	Mid-Low
MIN	1	8	31	40	Low
NYM	24	10	6	40	Mid-High
NYY	39	1		40	High
OAK	7	9	24	40	Mid-Low
PHI	18	13	9	40	Mid-High
PIT	5	7	28	40	Low
SDP	1	22	17	40	Mid-Low
SEA	9	12	18	39	Mid-Low
SFG	14	21	5	40	Mid-High
STL	9	27	4	40	Mid-High
TBR		2	16	18	Low
TEX	10	16	14	40	Mid-Low
TOR	11	15	13	39	Mid-Low
WAS	2	1	8	11	Low

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.

Team	Payroll Z-score	Actual W%	Expected W%	Gap (%)
STL	0.103	0.528	0.502	4.9%
OAK	–       0.458	0.510	0.486	4.7%
MON	–        0.639	0.496	0.480	3.1%
CIN	–        0.093	0.507	0.497	2.0%
ATL	0.429	0.522	0.512	1.9%
MIN	–        0.841	0.483	0.475	1.8%
CLE	–        0.454	0.494	0.486	1.7%
CHW	–        0.129	0.504	0.496	1.6%
HOU	–        0.168	0.501	0.494	1.3%
BOS	1.071	0.538	0.531	1.2%
SFG	0.192	0.510	0.505	1.0%
LAD	0.888	0.531	0.526	1.0%
TEX	–        0.089	0.499	0.497	0.4%
NYY	2.251	0.567	0.566	0.2%
MIA	–        1.052	0.468	0.468	0.0%
LAA	0.432	0.512	0.512	-0.1%
BAL	0.012	0.499	0.500	-0.2%
MIL	–        0.396	0.486	0.488	-0.3%
TOR	–        0.082	0.495	0.497	-0.4%
PIT	–        0.598	0.480	0.482	-0.4%
ARI	–        0.158	0.492	0.495	-0.6%
SDP	–        0.582	0.477	0.482	-1.0%
PHI	0.495	0.508	0.514	-1.2%
TBR	–        1.004	0.464	0.470	-1.3%
WAS	–        0.429	0.480	0.487	-1.3%
KCR	–        0.261	0.484	0.492	-1.5%
DET	–        0.077	0.489	0.497	-1.6%
SEA	–        0.498	0.467	0.485	-3.7%
NYM	0.504	0.495	0.514	-3.9%
COL	–        0.303	0.467	0.490	-5.1%
CHC	0.218	0.478	0.506	-5.9%

 

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.

Team	1976-1985	1986-1995	1996-2005	2006-2015	Type of team over time
NYY	High	High	High	High	Keep
BOS	Mid-High	High	High	High	Keep
LAD	High	High	High	High	Keep
NYM	Mid-Low	High	High	Mid-High	Keep
PHI	High	Mid-Low	Mid-Low	High	Swinger
LAA	High	Mid-High	Mid-High	High	Keep
ATL	Mid-High	Mid-High	High	Mid-High	Keep
CHC	Mid-High	Mid-High	Mid-High	Mid-High	Keep
SFG	Mid-Low	Mid-High	Mid-High	Mid-High	Keep
STL	Mid-Low	Mid-High	Mid-High	Mid-High	Keep
BAL	Mid-Low	Mid-Low	Mid-High	Mid-Low	Keep
DET	Low	Mid-High	Low	High	Swinger
TOR	Low	High	Mid-Low	Mid-Low	Swinger
TEX	Mid-Low	Low	Mid-High	Mid-Low	Swinger
CIN	Mid-High	Mid-High	Low	Mid-Low	Downward
CHW	Mid-Low	Mid-Low	Mid-Low	Mid-High	Upward
ARI	–	–	Mid-High	Low	Downward
HOU	Mid-High	Mid-Low	Mid-High	Mid-Low	Swinger
KCR	Mid-Low	High	Low	Low	Swinger
COL	–	Mid-Low	Mid-High	Low	Swinger
MIL	Mid-High	Low	Low	Mid-Low	Downward
WAS	–	–	Low	Mid-High	Upwards
CLE	Mid-High	Low	Mid-High	Low	Swinger
OAK	Mid-Low	Mid-High	Low	Low	Swinger
SEA	Low	Low	High	Mid-High	Upwards
SDP	Mid-Low	Mid-Low	Mid-Low	Low	Keep
PIT	Mid-High	Low	Low	Low	Downward
MON	Mid-High	Low	Low	–	Downward
MIN	Low	Mid-High	Low	Mid-High	Swinger
TBR	–	–	Low	Low	Keep
MIA	–	Low	Low	Low	Keep

 

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.