# An Interesting Idea- Pujols’ (Theoretical) Effect on the Giants

Albert Pujols. The man is already a legend at the tender age of 29 and seems to be a lock to reach the Hall of Fame. When 80% of your top 10 similarity scores are Hall of Famers, you know you’re special. His 22.6 Wins

Above Replacement over the last 3 years lead all Major Leaguers, and the runner-up, Chase Utley, is still 1.2 wins behind him. The nine-time All-Star, two-time MVP award winner has accomplished a lot in his career and seems poised to become one of the best players to ever play the game.

I thought it’d be fun to do a theoretical analysis of what impact Pujols would have had he played in San Francisco—assuming that he develops the same, of course. Since this is a “theoretical team,” I thought it’d be fun to use a Theoretical Team approach. So instead of using a linear run estimator, I thought I’d just use a dynamic run estimator like Baseruns (BsR). Baseruns is an extremely simple to use metric, expressed as:

A * B / (B+C) + D

Where:

A= H + BB + HBP – 0.5 * IBB

B= (1.4 * TB – 0.6 * H – 3 * HR + 0.1 * (BB + HBP – IBB) + 0.9 * (SB – CS – DP))*1.1

C= AB – H + CS + DP

D= HR

The “A” factor is times on base, “B” is the “advancement rate,” “C” are the outs created, and “D” is the home run total. Because the player’s “B” factor works with the player’s times on base, BsR isn’t suggested for individual hitters—how can an individual hitter create runs through his on-base ability? He’s knocked in by his teammates, of course. That’s more of a reflection of the team than it is on the player. BsR has a tendency to overrate good hitters and underrate bad ones, and so the theoretical team model is ideal. What a Theoretical Team approach does is surround a player with league average hitters instead of the player’s actual team. Brandon Heipp (also known as “Patriot”) gives a beautiful summary and guide to creating a theoretical team model—here’s the formula:

(A + E*PA)*(B + F*PA) / (B + C + (F + G)*PA) + D – (I – H)*PA

Where:

E= 8 * (LgA / PA)

F= 8 * (LgB / PA)

G= 8 * (LgC / PA)

H= 8 * (LgD / PA)

I= 8 * ((LgA/PA) * ((LgB/PA) / (LgB/PA + LgC/PA)) + LgD/PA)

Enough with the technical stuff; let’s start taking a look at the results. I ran Pujols’ numbers from 2004-2008 and park-adjusted it (using a one-year park factor). This is Pujols’ “Neutral BsR,” if he were placed in a league average lineup (as a reference point):

Year Neutral BsR

2004 154

2005 142

2006 149

2007 129

2008 147

I then placed Pujols in the Giants’ lineup for each of those seasons, adjusted for park effects, and subtracted the runs that were created by other Giants’ first basemen during that same time:

Year Pujols Giants 1B Net Gain

2004 155 118 37

2005 147 78 69

2006 143 78 65

2007 127 81 46

2008 148 71 77

Albert adds, on average, around 60 more runs to the Giants’ lineup—a substantial increase in production. Adding those runs to the overall team runs scored shows the subsequent impact it has on the overall team:

Year Pujols Added RS New RS

2004 37 850 887

2005 69 649 718

2006 65 746 811

2007 46 683 729

2008 71 640 711

Remember, offense is only one part of the equation. Defense is just as important. In most cases, I’d use UZR to rate a player’s defense compared to average, but since we’re putting Albert on a theoretical team, that means his pitching staff, opportunities and balls hit into play will differ. So I’m taking a step back and using Revised Zone Rating in tandem with Out Of Zone Plays—this way we can take a look at how many balls hit into his zone he successfully turned into an out compared to the Giants’ first basemen. Say Albert has a RZR of 0.840 on 200 balls hit into his zone (168 plays), as compared to the Giants’ 0.814 in 202 balls hit into their zone. That means he’s (168 – (0.814*200)) = 5 plays above the Giants’ first basemen. We then apply the OOZ rate and error rate of Pujols into the Giants’ defensive innings, and find plays Out Of Zone and Errors above or below average. Converted into runs, this is what we find:

Year Pujols D RA New RA

2004 5 703 698

2005 -8 745 753

2006 18 790 772

2007 39 720 681

2008 22 759 737

“New RA” is the estimated runs allowed with Albert playing first. Because Albert’s runs saved vary from the Giants’ first basemen, it changes the outcome of runs scored against the Giants.

Now that we have adjusted runs scored and runs allowed with Albert as a Giant, we can use a winning percentage estimator to see just how many wins he’d add. My weapon of choice is PythagenPat. After running the numbers through and adjusting based on the Giants’ *actual* wins compared to their expected winning percentages, these are the revised records from 2004-2008:

Year Exp. Wins Exp. Losses Adj. Wins Adj. Losses

2004 97 65 101 61

2005 78 84 80 82

2006 84 77 83 78

2007 85 77 78 84

2008 79 83 80 82

And finally, Albert’s wins added:

Year Added Wins

2004 10

2005 5

2006 7

2007 7

2008 8

AVG Wins 7.4

Beautiful. I expected Albert to add somewhere around these figures, and this supports my guess. There’s always the question as to how much of an impact, if any, Albert would have on the other hitters in the order—but that isn’t something that can really be measured since we’re already using a Theoretical Team to begin with. By adding Albert, the Giants win the West in 2004, take second in the division in 2005, stand pat in 2006, stay in the cellar in 2007, and contend for second in the West in 2008. Of course, there’s always the question as to how the addition of Pujols affects the Giants’ records against their division rivals—but that might be impossible to measure. In any case, they’re looking much better with Prince Albert in the middle of the order.